PHARMACOMETRIC EVALUATION OF IN VITRO AND IN VIVO …

PHARMACOMETRIC EVALUATION OF IN VITRO AND IN VIVO METHODS FOR BIOEQUIVALENCE ASSESSMENT OF ORALLY INHALED DRUG PRODUCTS

By

ABHINAV KURUMADDALI

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2019

To my parents, Kurumaddali Satyanarayana Murthy and Annapurna Rani and my sister, Jaya Madhuri

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ACKNOWLEDGMENTS

I would like to express my deep and sincere gratitude to my research advisor Dr.

Guenther Hochhaus, for giving me the opportunity to pursue doctoral degree under his

excellent mentorship. His guidance and constant motivation have been of immense help

to me in the conduct of this work. I am very grateful to him for supporting my personal

and professional career development. I would like to thank my other PhD committee

members, Drs. Juergen Bulitta, Hartmut Derendorf and Lawrence Winner for taking their

valuable time to provide feedback on my research work. I would like to express my

special appreciation to Dr. Bahru Habtemariam (mentor for my 2016 summer internship

at OCP, CDER, FDA) and Drs. Suresh Kumar Agarwal and Ahmed Salem (mentors for

my 2018 summer internship at Abbvie Inc.) for their excellent guidance during my

summer internships which enhanced my understanding of drug development process.

I would like to thank Dr. Mong-Jen Chen and other members of our clinical study

team for insightful discussions and support in the conduct of clinical trial. I would like to

extend special thanks to to my lab mates, Dr. Sharvari Bhagwat, Dr. Uta Schilling,

Elham Amini, Simon Berger, Jie Shao, Stefanie Drescher and my colleagues Drs.

Abhigyan Ravula and Hardik Chandasana. I would like to thank my interns Christine

Tabulov and Van Truong. I would like to acknowledge the administrative staff and

everybody in the department of Pharmaceutics, department of Biostatistics and

department of Statistics who have contributed to my non-traditional MS/PhD dual

degree program at University of Florida. Finally, I would like to thank my family, friends

and relatives for their constant support, love and motivation.

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TABLE OF CONTENTS page

ACKNOWLEDGMENTS .................................................................................................. 4

LIST OF TABLES ............................................................................................................ 7

LIST OF FIGURES .......................................................................................................... 8

ABSTRACT ................................................................................................................... 10

CHAPTER

1 INTRODUCTION .................................................................................................... 12

Fate of Orally Inhaled Drug Products (OIDPs) ........................................................ 12

Challenges in the Bioequivalence Assessment of OIDPs ....................................... 12

2 CASCADE IMPACTOR EQUIVALENCE TESTING: COMPARISON OF THE

PERFORMANCE OF THE MODIFIED CHI-SQUARE RATIO STATISTIC (MCSRS) WITH THE ORIGINAL CSRS AND EMA’S AVERAGE BIOEQUIVALENCE APPROACH ........................................................................... 15

Background ............................................................................................................. 15

Methods .................................................................................................................. 18 Overall Strategy ................................................................................................ 18

Description of the PQRI Scenarios ................................................................... 19 Evaluation of the PQRI Scenarios by Subject Matter Experts .......................... 20

Application of the Three Statistical Approaches to the PQRI Scenarios ........... 21 Average bioequivalence approach (ABE): ................................................. 21

Chi-Square Ratio Statistic approach (PBE-CSRS): ................................... 23 Modified Chi-Square Ratio Statistic approach (PBE-mCSRS): .................. 26

Comparison of the Outcomes of the 55 PQRI Scenarios from the Three Statistical Approaches to that of the Experts’ Opinion: .................................. 29

Results .................................................................................................................... 32 Discussion .............................................................................................................. 33

Conclusions ............................................................................................................ 41

3 EVALUATION OF THE SENSITIVITY AND ROBUSTNESS OF MODIFIED CHI-

SQUARE RATIO STATISTIC FOR CASCADE IMPACTOR EQUIVALENCE TESTING THROUGH MONTE CARLO SIMULATIONS ......................................... 53

Background ............................................................................................................. 53 Methods .................................................................................................................. 55

Effect of Dataset Generation Method on the Derived mCSRS Test Critical Values and Outcome: .................................................................................... 57

Effect of Number of Bootstrap Iterations on the Outcome Of mCSRS Test:..... 59

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Effect of CI Profile Related Factors on the Power Of mCSRS Test (Power Curves):......................................................................................................... 60

Effect of Dataset Generation Method (Incorporation of ISC) on mCSRS Test Power Curve Calculations ............................................................................. 62

Results .................................................................................................................... 63 Discussion .............................................................................................................. 65

Conclusion .............................................................................................................. 74

4 A SEMI-PHYSIOLOGICAL PHARMACOKINETIC APPROACH FOR

ASSESSING THE BIOEQUIVALENCE OF DRY POWDER INHALER FORMULATIONS OF FLUTICASONE PROPIONATE ........................................... 87

Background ............................................................................................................. 87 Methods .................................................................................................................. 89

Semi-Physiological Modeling of Population Pharmacokinetics (Pop PK) Derived Absorption Profiles of Fluticasone Propionate (FP) Dry Powder Inhaler (DPI) Formulations ............................................................................ 89

Semi-physiological PK model structure and input parameters ................... 91

Validation of the Semi-Physiological Model ............................................... 95 Evaluation of the Sensitivity of Peak Plasma Concentration (Cmax) of FP to

the Regional Lung Deposition Differences of the DPI Formulations .............. 97 Results .................................................................................................................... 98

Discussion .............................................................................................................. 99 Conclusion ............................................................................................................ 106

LIST OF REFERENCES ............................................................................................. 118

BIOGRAPHICAL SKETCH .......................................................................................... 124

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LIST OF TABLES

Table page 2-1 Agreement of ABE, PBE-CSRS and PBE-mCSRS approaches with the

experts’ opinion at ≥50% threshold. .................................................................... 43

2-2 Agreement of ABE, PBE-CSRS and PBE-mCSRS approaches with experts’ opinion at ≥80% threshold. ................................................................................. 43

2-3 Pairwise comparisons of the area under the ROC curves (AUC) for the three statistical approaches. ........................................................................................ 44

2-4 95% CI of specificities for the three statistical approaches at 0.90 and 0.95 sensitivity values. ................................................................................................ 44

2-5 Agreement of ABE approach with experts’ opinion for a range of acceptance limits at ≥50% threshold...................................................................................... 45

2-6 Agreement of PBE-mCSRS approach with experts’ opinion for a range of mCSRS acceptance limits at ≥50% threshold. ................................................... 46

2-7 Pros and Cons of the three statisitcal approaches: ABE, PBE-CSRS and PBE-mCSRS ...................................................................................................... 47

3-1 Results showing the effect of CI profile shape and dataset generation method on the derived critical values and the pass rate outcome of PQRI scenarios no. 20 ................................................................................................................. 76

4-1 Mean population pharmacokinetics model estimates of the three fluticasone propionate (FP) dry powder inhaler (DPI) formulations: A-4.5 µm, B-3.8 µm and C-3.7 µm .................................................................................................... 107

4-2 Semi-physiological PK model parameters obtained from Mimetokis Preludium software ........................................................................................... 108

4-3 Deposition pattern of formulation C-3.7 µm determined using the lung deposition module in the Mimetokis Preludium software .................................. 109

4-4 Estimated parameters of the semi-physiological PK model using the Pop PK derived absorption profiles................................................................................ 109

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LIST OF FIGURES

Figure page 2-1 Representation of Andersen Cascade Impactor (ACI) profiles obtained from

typical test (T) and reference (R) inhalation products of sample size 30 each.... 48

2-2 Scatter plots comparing the results of the three statistical approaches. ............. 49

2-3 Receiver Operating Characteristic (ROC) curves for the three statistical approaches ......................................................................................................... 50

2-4 Pass rate outcomes of the A) Experts’ opinion, B) ABE approach, C) CSRS test alone (without PBE) and D) mCSRS test alone (without PBE) as a function of mean reference variance. ................................................................. 51

2-5 Difference in the pass rate outcomes of CSRS test alone (without PBE) and mCSRS test alone (without PBE) as a function of mean reference variance...... 52

3-1 Population mean depositions (in micrograms) of the typical CI profiles used for simulations in this study................................................................................. 77

3-2 Flowchart of MmCSRS test algorithm (modified from Weber et al, 2014). Default values of algorithm related factors: N = 30; B = 2000; X = ±25% ........... 78

3-3 Plot showing the effect of number of bootstrap iterations on the outcome of MmCSRS test ..................................................................................................... 79

3-4 Power curves showing the effect of population mean differences (0%, 10%, 15%, 20% and 25%) across all deposition sites of T and R CI profiles on the power of MmCSRS test at ±25% acceptance limit as a function of variability of the CI profiles ................................................................................................. 80

3-5 Power curves showing the effect of sample size (N = 15, N = 30 and N = 60) on the power of MmCSRS test at ±25% acceptance limit as a function of variability of the CI profiles.................................................................................. 81

3-6 Power curves showing the effect of population T/R variance ratio (1:1, 1:4 and 4:1) across all deposition sites of T and R CI profiles on the power of MmCSRS test at ±25% acceptance limit as a function of variability of the CI profiles ................................................................................................................ 82

3-7 Power curves showing the effect of high vs low deposition site population mean differences ................................................................................................ 83

3-8 mCSRS test critical value plots derived from different CI profile patterns and dataset generation method ................................................................................. 84

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3-9 Plot showing the effect of normalization of the CI profiles on the variability of each deposition site ............................................................................................ 85

3-10 Plot showing the effect of incorporation of inter-site correlation within the Monte Carlo simulation of datasets on the outcome of MmCSRS test across the 55 PQRI scenarios ....................................................................................... 86

4-1 Semi-physiological PK model structure ............................................................ 110

4-2 Comparison of the fitted semi-physiological absorption profiles (NB + Fick’s law) with that of population PK derived absorption profiles for formulation C-3.7 µm (A) in peripheral lung region (B) in central lung region ......................... 111

4-3 Comparison of the in vivo dissolution profiles in the airway surface liquid, ASL (purple color) with that of absorption profiles (red color) ........................... 112

4-4 Concentration-time profiles of dissolved drug in the airway surface liquid of (A) peripheral lung region (B) central lung region ............................................. 113

4-5 Predicted absorption profiles of formulations A-4.5 µm and B-3.8 µm using the semi-physiological model in comparison to their respective population PK derived absorption profiles................................................................................ 114

4-6 Predicted PK profiles of FP DPI formulations using semi-physiological PK model in comparison to the observed PK data from the clinical study .............. 115

4-7 Semi-physiological PK model predicted relationship between peak plasma concentration (ng/L) and regional lung deposition of FP DPI formulations ....... 116

4-8 Semi-physiological PK model simulations showing the sensitivity of dose normalized Cmax to regional lung deposition differences (or CP ratio differences) ....................................................................................................... 117

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

PHARMACOMETRIC EVALUATION OF IN VITRO AND IN VIVO METHODS FOR BIOEQUIVALENCE ASSESSMENT OF ORALLY INHALED DRUG PRODUCTS

By

Abhinav Kurumaddali

December 2019

Chair: Guenther Hochhaus Major: Pharmaceutical Sciences

Background: Unlike oral drugs, the bioequivalence (BE) assessment of orally

inhaled drug products (OIDPs) is challenging, as drug plasma concentrations are

downstream to the sites of action in the lung. Currently, FDA recommends the

aggregate weight of evidence approach, which involves the in vitro, pharmacokinetic

(PK) and comparative clinical endpoint or pharmacodynamic (PD) BE assessment of

OIDPs, in addition to formulation sameness and device similarity. It should be noted that

there is no approved statistical test for the in vitro BE assessment and the sensitivity of

PD to formulation differences is low often resulting in poor BE outcomes. Objectives:

The two main objectives of this work are: (1) To evaluate the performances of three

statistical approaches for assessing in vitro equivalence of OIDPs. (2) To evaluate the

sensitivity of PK in detecting regional deposition differences of OIDP formulations.

Methods: (1) The three statistical approaches: (A) a stepwise aerodynamic particle size

distribution (APSD) equivalence test integrating population bioequivalence (PBE) testing

of impactor sized mass (ISM) with the CSRS (PBE-CSRS approach), previously

suggested by the USFDA (B) the combination of PBE testing of single actuation

content and ISM with the newly suggested modified CSRS (PBE-mCSRS approach)

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and (C) EMA’s average bioequivalence (ABE approach) were evaluated with a set of 55

scenarios of realistic test (T) and reference (R) cascade impactor (CI) profiles by

comparing the outcomes against experts’ opinion (surrogate for the truth). (2) A semi-

physiological model was developed to understand the link between the biphasic PK

profiles of three DPI formulations assessed in a crossover PK study and their relevant

physiological attributes (dissolution and regional deposition characteristics). Results and

conclusions: (1) The PBE-mCSRS approach showed significantly better overall

agreement with experts’ opinion compared to the other two approaches. (2) The PK was

found to be sensitive to differences in regional lung deposition of the formulations.

Contrary to the ABE approach, the application of PBE-mCSRS approach for assessing

APSD profiles of three DPI formulations supported their PK BE assessment. This work

underlines that PK may be able to provide important supportive information for

pulmonary BE assessment without the conduct of PD studies.

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CHAPTER 1 INTRODUCTION

Fate of Orally Inhaled Drug Products (OIDPs)

Orally inhaled drug products (OIDPs) comprising of inhaled corticosteroids, beta-

2-agonists and anticholinergic drugs are commonly used for the treatment of pulmonary

inflammation conditions such as asthma and chronic obstructive pulmonary disease (1).

When a drug formulation is inhaled, depending upon the device and formulation, about

10-60% of the emitted dose will enter the lung, while the rest of the dose will be

swallowed and potentially absorbed through the gastro-intestinal tract. Drug that is

deposited in the lung will dissolve in the airway surface liquid (ASL) and induces the

pharmacodynamic effects by interacting with the receptors. It is important to recognize

that this portion of the drug will finally be absorbed into systemic circulation and

potentially together with the drug that was absorbed through the gastro-intestinal tract

could lead to systemic side effects (2).

Challenges in the Bioequivalence Assessment of OIDPs

It is thought that for explaining the efficacy of OIDPs at the site of action in lung,

three questions should be answered: what is the dose available to the lung; how long

does the drug molecules stay in the lung; what is the regional deposition? It is important

to consider that the blood is downstream to the site of action in lung and this is the

reason why the FDA believes that the standard pharmacokinetic bioequivalence (PK

BE) studies are not suitable to probe for pulmonary BE (3). They therefore recommend

the so-called weight of evidence approach (4).

Within the weight of evidence approach, FDA recommends performing in vitro

studies which include assessing the equivalence of emitted dose, fine particle dose – an

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in vitro parameter thought to be related to the pulmonary dose and the aerodynamic

particle size distribution (APSD) through cascade impactor (CI) studies. It is worthwhile

mentioning that for testing the equivalence of the shape of CI profiles, the FDA has not

yet recommended any suitable statistical test (5). After passing the in vitro studies, the

FDA recommends conducting PK BE study to ensure equivalence in systemic safety

which should be followed by pharmacodynamics (PD) endpoint studies to ensure

pulmonary equivalence.

The PD endpoint studies are very challenging to pass as several drugs show

poor dose-response relationships for the highly variable endpoints (6–8). Within these

studies, the FEV1 is assessed in a parallel study design making it necessary to include

a very high number of subjects (approximately 1700) eventually leading to low approval

rate of OIDP generics and high cost of asthma therapy.

The goal of the work presented in this dissertation was to understand whether

relevant questions for the assessment of the pulmonary equivalence can be answered

through in vitro and PK studies. The performance of the newly proposed modified chi

square ratio statistic (mCSRS) approach in assessing the in vitro APSD equivalence of

generic and innovator OIDPs was compared with the original CSRS and the EMA’s

average bioequivalence approaches. The sensitivity and robustness of the mCSRS was

evaluated through Monte Carlo simulations. The sensitivity of PK to particle size

distribution differences of OIDP formulations was assessed in a PK BE study through

non-compartmental analysis. Finally, a semi-physiological PK modeling approach was

developed to investigate if PK can detect regional lung deposition differences across

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fluticasone propionate (FP) dry powder inhaler (DPI) formulations, a candidate for

slowly dissolving drugs with negligible oral absorption.

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CHAPTER 2 CASCADE IMPACTOR EQUIVALENCE TESTING: COMPARISON OF THE

PERFORMANCE OF THE MODIFIED CHI-SQUARE RATIO STATISTIC (MCSRS) WITH THE ORIGINAL CSRS AND EMA’S AVERAGE BIOEQUIVALENCE APPROACH

Background

Assessing the bioequivalence of traditional oral dosage forms does not generally

represent a challenge, as established guidelines recommend the assessment of the

systemic drug exposure (AUC and Cmax) between the test (T) and reference (R)

formulations. In contrast, it is quite challenging in the case of locally acting drug

products, such as inhalation drugs, as the active pharmacological ingredient (API) is

directly delivered to the site of action thus blood plasma concentrations are judged by

many stakeholders to be less relevant for bioequivalence decisions (9). It is well

established that the aerodynamic particle size distribution (APSD) of inhaled

formulations plays a crucial role in determining the pulmonary deposited dose and

regional lung deposition pattern (10–13). Hence, the international regulatory agencies

such as the Food and Drug Administration (FDA, United States of America), Health

Canada (HC, Canada), European Medicines Agency (EMA, European Union),

Therapeutic Goods Administration (TGA, Australia) etc. recommend in vitro equivalence

testing using cascade impactors such as the Andersen cascade impactor (ACI) or the

next generation impactor (NGI, see Figure 2-1) as one of the key steps in the approval

of “generic” (or “follow-on”, or “second-entry”) inhalation drug products (9). On a

theoretical level, the cascade impactor profile analysis of test (T) and reference (R)

products should consider the shape of the cascade impactor profile (Figure 2-1) as well

as absolute cumulative dose entering the impactor (impactor sized mass, or ISM). In

addition, the single actuation content is of relevance to ensure that the total dose

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leaving the dosage form is equivalent, as it is also relevant for the orally available drug.

Methods to statistically evaluate equivalence of multivariate vectors with correlated

elements such as T and R cascade impactor profiles are complex, and the statistical

methods used for evaluating the shape of the cascade impactor profiles are not

specified within FDA or Health Canada official guidance (9,14–16).

In June 1999, FDA issued a guidance entitled “Draft Guidance for Industry:

Bioavailability and Bioequivalence Studies for Nasal Aerosols and Nasal Sprays for

Local Action”, recommending the use of a Chi-Square Ratio Statistic (CSRS), a

univariate cumulative assessment metric for evaluating the equivalence in shape of T

and R cascade impactor profiles (based on relative stage depositions) (17,18). In the

same guidance, FDA also proposed the use of Population Bioequivalence (PBE)

criterion for comparing the single actuation content and impactor sized mass of T and R

formulations (17–20). The performance of the combination of PBE applied to ISM and

the CSRS test applied to the full cascade impactor (CI) profile (CSRS approach) was

evaluated by a Product Quality Research Institute Working Group (PQRI WG) focused

on APSD comparisons, using a set of 55 PQRI-developed scenarios of realistic T and R

CI profiles. Since there was no definitive basis established by industry or regulatory

agencies for determining APSD equivalence, the PQRI WG compared the outcomes of

the CSRS approach for the 55 scenarios against an independent assessment of

experts’ opinion. The working group concluded that the CSRS approach could not

discriminate consistently between what experts judged to be equivalent and non-

equivalent cascade impactor profiles (10,18). More specifically, the working group found

that the use of a fixed critical value within the CSRS test (defined in the FDA CSRS

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approach) for making pass/fail decisions and the instability of the CSRS when applied to

a reduced number of deposition sites compromises the discriminatory ability, and

therefore the utility of this approach for making relevant equivalence decisions (10,18).

The European Medicines Agency (EMA) recommends the method of Average

Bioequivalence (ABE) for testing the in vitro bioequivalence of T and R cascade

impactor profiles in its 2009 guidance (16,21). The ABE statistical procedure can be

applied to deposition data of individual impactor stages or justified groups of stages.

Evidence of equivalence is based on confidence intervals of T/R ratios within a window

of ±15% (16,21). It is noteworthy that given the stringent acceptance criteria set in the

EMA guidance and the multiple test comparisons to be performed for T-R profiles (one

test per stage or group), the R product tested against itself generally fails to meet the

bioequivalence criteria(21). Hence, it was of interest to compare the outcome of the

EMA method with those of alternative tests and to determine the effect of less stringent

acceptance criteria on the outcomes of this approach.

To overcome the limitations of the CSRS for relevant decision making identified

in the PQRI WG report, University of Florida (UoF) in collaboration with FDA developed

a modified version of the CSRS (mCSRS) for comparing the T and R cascade impactor

profiles. Unlike CSRS, the mCSRS was shown to be stable even when applied to a

reduced number of cascade impactor stages that are more relevant to lung deposition

(10). Most importantly, the critical value is scaled according to the variability of the

reference product (quantified by a cumulative metric called reference variance scaling,

RVS) following the same idea that was the basis for extending the ABE approach into

the PBE test (12).

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In this chapter, the three statistical approaches, ABE, PBE-CSRS and PBE-

mCSRS were applied to the same sample of CI profiles, namely the 55 PQRI scenarios,

originally used by the PQRI working group. The results of all three statistical

approaches were compared against the experts' opinion (surrogate for the truth) for all

the 55 PQRI scenarios using quadrant (scatter) plots. Each statistical approach was

evaluated for its accuracy/validity (measured by true pass rate and true fail rate which

were defined in terms of agreement with experts’ opinion). The ability of each statistical

approach to discriminate between equivalent and non-equivalent T and R cascade

impactor profiles and its agreement with the experts’ opinion was quantified by means

of receiver operating characteristic (ROC) curves (22–24). To gain more insight into the

applicability of the ABE approach, the effect of relaxing the EMA acceptance criteria on

the outcome was studied by either widening the ±15% acceptance limit or reducing the

confidence level. Finally, the behavior of the three statistical tests in relation to the

variability of the R formulation was assessed.

Methods

Overall Strategy

The predictive performance of the three statistical approaches in evaluating the

equivalence of cascade impactor profiles was tested by analyzing the 55 PQRI

scenarios described below, of T and R cascade impactor profiles and comparing the

results with evaluations of subject matter experts presented in the PQRI WG report.

1. Average Bioequivalence approach (ABE): Assessment of individual stages or groups of stages using the ABE approach, a standard statistical equivalence test, as described by EMA in its guidance (16).

2. Chi-Square Ratio Statistic approach (PBE-CSRS): This method tests first the equivalence of T and R products in impactor sized mass through the population equivalence (PBE) approach followed by evaluating the equivalence in the shape

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of the cascade impactor profiles (based on relative stage depositions) by the chi-square ratio test (18).

3. Modified Chi-Square Ratio Statistic approach (PBE-mCSRS): This method tests first the equivalence of T and R products in single actuation content and impactor sized mass by population equivalence (PBE) approaches followed by evaluating the equivalence in the shape of the cascade impactor profiles (based on relative stage depositions) by the modified chi-square ratio test (12).

Description of the PQRI Scenarios

To compare the above methods, this study used 55 realistic scenarios of 30 T

and 30 R simulated cascade impactor profiles previously published by the Product

Quality Research Institute Working Group (PQRI WG) and results of the evaluation of

these by subject matter experts, who judged these profiles as equivalent or non-

equivalent (18).

The 55 scenarios were developed by the PQRI WG based on statistical variance

component analysis of blinded sets of cascade impactor data from actual products.

This variance component analysis produced for each set of data (e.g., albuterol MDI)

the mean and variance for each CI deposition site, plus a variance-covariance matrix

which characterized the interrelationship among the deposition sites. Using these

values, simulated datasets were produced that closely mimicked all the important

characteristics of the APSD profiles from an actual product. By changing the values for

deposition site means and/or variance (but maintaining the interrelationship among

deposition sites) different scenarios were simulated that ranged from the observed

profiles to profiles with various combinations of differences between T and R in mean

deposition and variability. In brief, the 55 PQRI scenarios were comprised of three main

classes:

• Class I: It includes scenarios # 1 – 44, each scenario representing 30 T and 30 R cascade impactor profiles obtained using an Andersen Cascade Impactor (ACI)

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containing 13 deposition sites (deposition sites 6 through 13 representing impactor sized mass, ISM, sum of amount deposited on ISM deposition sites, the deposition sites with specified upper cut-off size) operated at a flow rate of 28.3 L/min.

• Class II: It includes scenarios # 45 – 51, each scenario representing 30 T and 30 R cascade impactor profiles obtained using an Andersen Cascade Impactor (ACI) containing 11 deposition sites (deposition sites 4 through 11 representing impactor sized mass, ISM) operated at a flow rate of 60 L/min.

• Class III: It includes scenarios # 52 – 55, each scenario representing 30 T and 30 R cascade impactor profiles obtained using the Next Generation Impactor (NGI) containing 10 deposition sites (deposition sites 3 through 10 representing impactor sized mass, ISM) operated at a flow rate of 60 L/min. These profiles were both directly assessed by subject matter experts and analyzed by each of the three statistical approaches.

Evaluation of the PQRI Scenarios by Subject Matter Experts

This study builds upon the previously published PQRI report on the 55 scenarios

of cascade impactor profiles and their visual (not statistical) evaluation by subject matter

experts (who represented experienced product developers, bioequivalence researchers,

and regulatory affairs professionals from industry, academia, pharmacopeia, and FDA)

(18). As described in a previous PQRI publication, for each scenario, fourteen

independent evaluations were received from subject matter experts, who visually

reviewed pairs of CI profiles and adopted a “regulatory perspective” for concluding

equivalence or not based on the assumption that certain changes in CI profiles could be

consistently translated into in vivo pulmonary deposition changes, which in turn might

affect the clinical outcomes (18). Reasons for having to use this subjective way of

assessing the profiles and consequently the statistical test to be evaluated were given in

the same publication together with more information on the subject-matter expertise of

the experts involved.

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For the purpose of comparison, an overall pass was assigned for a given

scenario when the percent of PQRI WG members (experts) that classified T and R

profile of a given scenario as equivalent exceeded the specified threshold value (for

example ≥50% and ≥80%). The experts’ opinion (at ≥50% and ≥80% threshold values)

was defined as a surrogate for ‘the truth’ when evaluating the performance of the three

statistical approaches (ABE, PBE-CSRS and PBE-mCSRS approaches).

Application of the Three Statistical Approaches to the PQRI Scenarios

To evaluate the performance of the statistical approaches, for a given scenario of

the 55 studied, 1,000 sets, each consisting of 30 T and 30 R cascade impactor profiles,

were generated by Monte Carlo simulations as described in the previous publications

(10–12). Briefly, information on the population means and standard deviations of drug

amounts on all deposition sites along with the population inter-site correlations between

all the deposition sites of the cascade impactor profiles was used to generate 1000

random samples of 30 T and 30 R cascade impactor profiles under the assumption of

multivariate normal distribution of the drug amounts on all deposition sites in SAS

software. These 1000 replicates of a given scenario were subjected to the statistical

tests. The three statistical approaches applied to each of the 1000 datasets in all the 55

PQRI scenarios are described below.

Average bioequivalence approach (ABE):

The ABE approach was applied to each of the 1000 datasets within all the 55

PQRI scenarios as recommended in the 2009 EMA guidance using the statistical

software R (version 3.4.4). Briefly, for each dataset of 30 T and 30 R cascade impactor

profiles, all of the deposition sites in a cascade impactor profile were divided into four

groups (21):

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• Group 1: deposition sites with no defined upper cut-off diameter (deposition sites 1 – 4, 1 – 3 and 1 – 2 for PQRI scenarios 1 – 44, 45 – 51 and 52 – 55 respectively),

• Group 2: deposition sites representing coarse mass (deposition sites 5 – 7, 4 – 6 and 3 – 4 for PQRI scenarios 1 – 44, 45 – 51 and 52 – 55 respectively),

• Group 3: deposition sites representing fine particle mass (deposition sites 8 – 10, 7 – 9 and 5 – 7 for PQRI scenarios 1 – 44, 45 – 51 and 52 – 55 respectively), and

• Group 4: deposition sites representing extra-fine particle mass (deposition sites 11 – 13, 10 – 11 and 8 – 10 for PQRI scenarios 1 – 44, 45 – 51 and 52 – 55 respectively).

The T/R ratio 90% confidence intervals (equations shown below) for each group

of deposition sites were constructed by the Geometric Mean Ratio (GMR) method (13,

18). Within each dataset, the T was declared equivalent to R if and only if the lower and

upper bounds of the T/R ratio 90% confidence intervals (LB, UB) for all four stage

groups were maintained within EMA’s ±15% acceptance limits (0.85,1.18). To study the

effect of relaxing the EMA acceptance limits on the outcome of the statistical approach,

the analysis was extended by evaluating whether the 90% confidence intervals were

maintained within the following T/R ratio ranges: 0.80 – 1.25 (±20% acceptance limit),

0.75 – 1.33 (±25% acceptance limit), 0.70 – 1.43 (±30% acceptance limit) and 0.60 –

1.67 (±40% acceptance limit). Further, we calculated 70% and 80% confidence intervals

and evaluated whether these were maintained within the T/R range of 0.85 – 1.18

(±15% acceptance limit). This procedure was applied to all the 1000 replicates of 30 T

and 30 R cascade impactor profiles in each scenario and the T profile within a given

scenario (1000 datasets) was judged as equivalent to the R profile if more than or equal

to 50% or 80% of the 1000 replicates met the ABE approach criteria.

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T/R ratio (100 – α) % CI: 𝑒(𝑀𝑒𝑎𝑛𝐷𝑖𝑓𝑓 ± 𝑀𝐸) (2-1)

𝑀𝑒𝑎𝑛𝐷𝑖𝑓𝑓 = (∑ 𝑇𝑖

𝑛𝑇𝑖=1

𝑛𝑇−

∑ 𝑅𝑗𝑛𝑅𝑗=1

𝑛𝑅)

(2-2)

𝑀𝐸 = 𝑡(1− 𝛼 2)⁄ ,𝑑𝑓 . √𝑠𝑇

2

𝑛𝑇+

𝑠𝑅2

𝑛𝑅

(2-3)

Where Ti represents natural logarithm transformed deposition of the ith (i = 1, …nT

= 30) cascade impactor profile for the T product within each group, Rj represents natural

logarithm transformed deposition of the jth (j = 1, …nR = 30) cascade impactor profile for

the R product within each group; sT represents standard deviation of the natural

logarithm transformed deposition of the ith (i = 1, …nT = 30) cascade impactor profile for

the T product within each group, sR represents standard deviation of the natural

logarithm transformed deposition of the jth (j = 1, …nR = 30) cascade impactor profile for

the R product within each group, α represents type I error, t(1 – α/2) represents quantile of

t-distribution corresponding to (1 – α/2) probability and Wald-Statterthwite’s degrees of

freedom (df).

𝑑𝑓 = (

𝑠𝑅2

𝑛𝑅+

𝑠𝑇2

𝑛𝑇 )

2

1

𝑛𝑅−1(

𝑠𝑅2

𝑛𝑅)

2

+ 1

𝑛𝑇−1(

𝑠𝑇2

𝑛𝑇)

2 (2-4)

Chi-Square Ratio Statistic approach (PBE-CSRS):

Results of a previously published study were used in which the CSRS approach

was applied to the 55 PQRI scenarios as follows in two steps (18):

Step 1: To compare the impactor sized mass (ISM) of T and R products, the

population bioequivalence (PBE) method was applied to each of the 1000 datasets of all

the 55 PQRI scenarios using the reference- or constant-scaled linearized PBE criterion

24

(shown below) approach described in the FDA’s “draft guidance on Budesonide” (which

specified a constant critical value of 7.66) using the statistical software R (version 3.4.4)

(15). First, for each cascade impactor profile, ISM was computed. For each dataset of

30 T and 30 R cascade impactor profiles, 95% upper confidence bound of the

reference- or constant-scaled linearized PBE criterion for ISM (U95) was computed. The

T was declared equivalent to R if and only if the U95 was found to be less than or equal

to zero. If a given data set (consisting of 30 T and 30 R profiles of a given scenario)

lacked equivalence in ISM, the overall test for this data set was defined as failed.

Linearized Criteria:

𝜼𝟏 = (µ𝑻 − µ𝑹)𝟐 + (𝝈𝑻𝟐 − 𝝈𝑹

𝟐 ) − 𝜽𝒑 · 𝝈𝑹𝟐 < 𝟎 𝒇𝒐𝒓 𝝈𝑹 > 𝝈𝑻𝟎

𝜼𝟐 = (µ𝑻 − µ𝑹)𝟐 + (𝝈𝑻𝟐 − 𝝈𝑹

𝟐 ) − 𝜽𝒑 · 𝝈𝑻𝟎𝟐 < 𝟎 𝒇𝒐𝒓 𝝈𝑹 ≤ 𝝈𝑻𝟎

Where,

µ𝑻 − µ𝑹: Mean difference of T (log scale) and R (log scale) products

𝝈𝑻𝟐, 𝝈𝑹

𝟐 : Total variance of T and R products

𝝈𝑻𝟎: Regulatory constant = 0.1

𝜽𝒑: Regulatory constant calculated as following:

𝜽𝒑 = [𝒍𝒏(𝟏.𝟏𝟏)]𝟐+𝟎.𝟎𝟏

𝟎.𝟏𝟐 = 2.089

Step 2: The Chi-Square Ratio Statistic algorithm (as described in the FDA June

1999 draft guidance for industry) was applied in SAS software to all given data sets of a

given scenario if ISM was judged as equivalent (17,18). First, all the cascade impactor

profiles were normalized i.e. all deposition sites were expressed in percent of total mass

deposited (TM; the sum of amount deposited on all deposition sites). From each dataset

of 30 T and 30 R normalized cascade impactor profiles, 500 triplets (two R profiles: Rk

25

and Rm; k ≠ m; k=1,…,30; m = 1,…,30; and one T profile: Tj; j = 1,…,30) were

resampled with replacement and the CSRS of each triplet was calculated using the

computational form shown below.

𝑪𝑺𝑹𝑺𝒋𝒌𝒎 =

∑(𝑻𝒊𝒋 −

𝑹𝒊𝒌 + 𝑹𝒊𝒎

𝟐 )𝟐

𝑻𝒊𝒋 + 𝑹𝒊𝒌 + 𝑹𝒊𝒎

𝟐𝟐

𝒑𝒊=𝟏

∑(𝑹𝒊𝒌 − 𝑹𝒊𝒎)𝟐

𝑹𝒊𝒌 + 𝑹𝒊𝒎

𝟐

𝒑𝒊=𝟏

where p = Number of deposition sites of the cascade impactor profile

Tij = Normalized deposition on the ith deposition site of the jth cascade impactor

profile for the T product

Rik & Rim = Normalized deposition on the ith deposition site of the kth and mth

cascade impactor profile respectively where the kth and mth cascade impactor profiles

represent two different samples of the same R product

Subsequently, the mean of the 500 CSRS’s was calculated and this procedure

was repeated for 300 times to obtain the distribution of the mean of CSRS. The T was

declared equivalent to R if and only if the 95th percentile of the distribution of the mean

of CSRS was found to be less than the fixed critical value of 7.66, as described in the

FDA’s 1999 draft guidance (which specified a constant critical value of 7.66) (9, 10).

Within the chi-square ratio statistic approach, for each of the 1000 datasets, the T was

declared equivalent to R only if it met the bioequivalence criteria of both population

bioequivalence and Chi-Square Ratio Statistic test (i.e. steps 1 – 2). Finally, the T profile

within a given scenario (1000 datasets) was judged as equivalent to the R profile if more

than or equal to 50% or 80% of the 1000 datasets showed equivalence.

26

Modified Chi-Square Ratio Statistic approach (PBE-mCSRS):

The procedure for this statistical approach was described in a previous

publication (12). Briefly, this approach involves the following three steps:

Step 1: This step was identical to the Step 1 under CSRS approach as described

above except that the PBE was applied to the total mass (TM, sum of amount deposited

on all deposition sites, as surrogate for single actuation content). The T product within a

data set of 30 T and 30 R profiles was declared equivalent to R if and only if the 95%

upper confidence bound of the reference- or constant-scaled linearized PBE criterion for

total mass (U95) was found to be less than or equal to zero. If a given data set

(consisting of 30 T and 30 R profiles of a given scenario) lacked equivalence in single

actuation content, the overall test for this data set was defined as failed.

Step 2: PBE for ISM was performed for all given data sets of a given scenario if

single actuation content was judged as equivalent. The statistical procedure was

identical to that in step 1 under mCSRS approach (described above) except that the

PBE was applied to ISM instead of single actuation content. Again, the T was declared

equivalent to R if and only if the 95% upper confidence bound of the reference- or

constant-scaled linearized PBE criterion for ISM (U95) was found to be less than or

equal to zero. If a given data set (consisting of 30 T and 30 R profiles of a given

scenario) lacked equivalence in ISM, the overall test (2 PBEs and 1 mCSRS) for this

test unit was defined as failed.

Step 3: The modified Chi-Square Ratio Statistic algorithm was applied to all

given test units of a given scenario if TM and ISM was judged as equivalent. This

algorithm was applied only to the ISM deposition sites as described in the previous

27

publications using the statistical software R (version 3.4.4) (10–12). This involves two

steps:

Step 3a (Calculation of the test statistic): First, all the ISM cascade impactor

profiles of an individual run were normalized i.e. the percent of ISM mass (obtained by

dividing the absolute deposition on each ISM deposition site by the sum of amount

deposited on all ISM deposition sites) deposited on each deposition site ‘i’ (i = 1,…,p)

was calculated for a given profile. From each dataset of 30 T and 30 R normalized ISM

cascade impactor profiles, 2000 bootstrapped replicates of 30 T and 30 R cascade

impactor profiles were obtained. For each of the 900 pairs of test (Tj; j = 1,…,30) and

reference (Ri; i = 1,…,30) cascade impactor profiles in a bootstrapped replicate, the

mCSRS was calculated using the computational form

𝒎𝑪𝑺𝑹𝑺𝒋𝒌 =

∑(𝑻𝒊𝒋 − �̅�𝒊)

𝟐

�̅�𝒊

𝒑𝒊=𝟏

∑(𝑹𝒊𝒌 − �̅�𝒊)𝟐

�̅�𝒊

𝒑𝒊=𝟏

where p = Number of deposition sites of the normalized ISM cascade impactor

profile

Tij = Normalized deposition on the ith deposition site of the jth cascade impactor

profile for the T product

Rik = Normalized deposition on the ith deposition site of the kth cascade

impactor profile for the R product

�̅�𝑖 = Sample mean of the ith deposition site of all ISM normalized R cascade

impactor profiles in a dataset

28

Subsequently, the median of the 900 mCSRS’s was computed for all the 2000

bootstrapped replicates resulting in a distribution for the median of the mCSRS. From

this distribution, the 90% bias corrected and accelerated (BCA) upper confidence bound

of the median of the mCSRS was computed that served as the test statistic for this

procedure (12).

Step 3b (Calculation of the critical value): As described in a previous

publication, the critical value for this procedure depends on the maximum allowable

difference between T and R (acceptance limit) and the variability of the R product (12).

For each dataset, the variability of the R product was estimated by computing the

reference variance scaling metric (RVS, equation given below) of the normalized ISM

cascade impactor R profiles.

𝑅𝑉𝑆 = √∑ �̅�𝒊 ∗ 𝑪𝑽𝒊

𝟐𝑝𝑖=1

∑ �̅�𝒊𝑝𝑖=1

where RVS = Reference Variance Scaling metric for each dataset of 30 T

and 30 R normalized ISM cascade impactor profiles

CVi = Coefficient of variation (%) of the ith deposition site of the

normalized ISM cascade impactor profiles of the R product

(also called RSD, relative standard deviation, the sample standard

deviation expressed in percent of the average)

p = Total number of ISM deposition sites

29

Subsequently, the critical value for each of the 1000 datasets at ±10%, ±15% ,

±20%, ±25% and ±30% acceptance limits were computed using the equations shown

below derived in a previous publication (12).

C10 = 0.993 + 124*RVS-2

C15 = 0.970 + 294*RVS-2

C20 = 0.949 + 536*RVS-2

C25 = 0.916 + 856*RVS-2

C30 = 0.896 + 1245*RVS-2

where C10, C15, …, C30 = Critical values at ±10%, ±15%, …, ±30% acceptance

limits respectively for each dataset of 30 T and 30 R normalized ISM cascade impactor

profiles

RVS = Reference Variance Scaling metric for each dataset of 30 T and 30 R

normalized ISM cascade impactor profiles

The T was declared equivalent to R if and only if the test statistic (from Step 3a)

was found to be less than the critical value (from Step 3b). Within the mCSRS

approach, for each of the 1000 data sets, the T was declared equivalent to R only if it

met the bioequivalence criteria of both the population bioequivalence test and mCSRS

test at ± 25% acceptance limit (i.e. steps 1 – 3). Finally, the T profile within a given

scenario (1000 datasets) was judged as equivalent to the R profile if more than or equal

to 50% or 80% of the 1000 data sets showed equivalence.

Comparison of the Outcomes of the 55 PQRI Scenarios from the Three Statistical Approaches to that of the Experts’ Opinion:

Results of the statistical tests for a given scenario (% of the 1000 datasets

resulting in equivalence) were plotted against the experts’ opinion (% of subject matter

30

experts classifying R and T profiles of a given scenario as equivalent). Classifying a

scenario as ‘equivalent’ either at the 50% (T and R are judged as equivalent if more

than or equal to 50% of the datasets of a given scenario suggested equivalence) or at

the 80 % threshold level (T and R are judged as equivalent if more than or equal to 80%

of the datasets of a given scenario were suggested to be equivalent) and considering

the experts’ opinion (at ≥50% or ≥80% threshold values) as surrogate for ‘the truth’,

each scenario could fall into one of the four quadrants of the scatter plots (see Figure 2-

2): (1) top-right quadrant PP (Experts’ opinion: pass; Statistical approach: pass), (2) top-

left quadrant FP (Experts’ opinion: fail; Statistical approach: pass), (3) bottom-left

quadrant FF (Experts’ opinion: fail; Statistical approach: fail) and (4) bottom-right

quadrant PF (Experts’ opinion: pass; Statistical approach: fail). Subsequently, the

estimates of percent agreement, false pass rate (complement of true fail rate, also

defined as complement of specificity) and false fail rate (complement of true pass rate,

also defined as complement of sensitivity) were computed for each statistical approach.

Percent agreement with experts’ opinion was defined as the percent of the 55 scenarios

that fall into PP and FF categories at a specified threshold value (≥50% or ≥80%). False

pass rate was defined as the percent of scenarios for which the statistical test

suggested “pass” while the experts classified them as “fail” (i.e. the number of scenarios

falling into the FP quadrant divided by the number of scenarios present in FP and FF

quadrants) at a specified threshold value (≥50% or ≥80%) (22). False fail rate was

defined as the percent of scenarios for which the statistical test suggested “fail” while

the experts classified them as “pass” (i.e. the number of scenarios falling into the PF

31

quadrant divided by the number of scenarios present in PF and PP quadrants) at a

specified threshold value (≥50% or ≥80%) (22).

To get an estimate of the accuracy of each statistical approach (ABE, PBE-

CSRS and PBE-mCSRS) in comparison to the experts’ opinion (at ≥80% threshold

value), receiver operating characteristic (ROC) curves were constructed using the R

statistical software package ‘pROC’ (22). The accuracy of each statistical approach was

estimated from the ROC curves (see Figure 2-3) as the area under the ROC curve

(AUC) and the 95% confidence intervals for the AUC were calculated by DeLong

method (22). Statistical significance testing of the difference among AUC of the ROC

curves was performed at 5% significance level using the R statistical software package

‘pROC’ based on the non-parametric DeLong’s test for comparing correlated ROC

curves and pairwise comparisons were made based on Bonferroni adjusted p-values

(25–27). In addition, to determine the relative performance of the three approaches at

high sensitivity values, point estimates and 95% CI of the specificities at 90% and 95%

sensitivities were computed for each approach using the R statistical software package

‘pROC’. Finally, to understand the behavior of the statistical tests for evaluating the

equivalence in shape of the cascade impactor profiles in relation to R formulation

variability, the linear relationship between the outcomes (pass rate) of CSRS test alone,

mCSRS alone for the 55 PQRI scenarios and mean reference variance (MRV, a

cumulative estimate of the R formulation variability for a given scenario) was assessed

and compared with that of the ABE approach and the experts’ opinion (see Figure 2-4).

MRV for a given scenario was obtained by calculating the arithmetic mean of reference

32

variance scaling (RVS, equation given above) of each of the 1000 replicates of 30 R

cascade impactor profiles.

Results

When the ABE method was applied to compare T and R profiles of the 55

scenarios, only 4 scenarios were judged to be equivalent (threshold level ≥50%). A

larger number of equivalent scenarios was suggested by the PBE-mCSRS method (15

scenarios), by PQRI subject matter experts (31 scenarios) and the PBE-CSRS method

(36 scenarios) with a ≥50% threshold value. Quadrant plots compared the results

obtained with ABE, PBE-CSRS and PBE-mCSRS with those of the subject matter

experts’ opinion (Figure 2-2, classification threshold: ≥50%). The percent agreement

with experts’ opinion, false pass rate and false fail rate for the three statistical

approaches at ≥50% and ≥80% classification threshold are further summarized in

Tables 2-1 and 2-2, respectively.

The ROC curves for the three statistical approaches (Figure 2-3) along with the

corresponding analysis (AUC [95% DeLong’s confidence interval], a cumulative

measure of the accuracy of the statistical approaches) are shown in Figure 2-3 and

Table 2-3, indicating the highest accuracy for the PBE-mCSRS method. To compare the

performance of ROC curves at high sensitivity values, 95% CI of specificities for each

approach at 0.90 and 0.95 sensitivity values are shown in Table 2-4, indicating the best

performance of PBE-mCSRS approach with higher specificity values.

Because of the high failing rate of the ABE when EMA’s criteria were used

(confidence interval 90%; range of bioequivalence limit: 0.85-1.18), outcomes using

different criteria were compared with the experts’ opinions (Table 2-5). Similarly, how

33

differences in the mCSRS acceptance criteria would change the outcome of PBE-

mCSRS test was also evaluated (Table 2-6).

Since the PBE-CSRS and PBE-mCSRS methods, as proposed by Christopher

et al. (17,18) and Weber et al. (12), include PBE assessments for ISM (CSRS and

mCSRS) and single actuation content (mCSRS), it was of interest to evaluate the

discriminatory power of CSRS and mCSRS alone to identify differences in shape only

(not including PBE assessments). Results (% of the 1000 data sets for a given scenario

passing) were plotted against the mean reference variance (Figure 2-4c for CSRS; and

4d for mCSRS). While considering both, shape and amount, results provided by the

expert’s (Figure 2-4a) and the ABE method (Figure 2-4b) are shown for comparison.

Overall, the CSRS method lacked any discriminatory power as T and R profiles are

judged to be equivalent for most scenarios. A higher discriminatory power was observed

for the mCSRS method across a wide range of reference variances. Plotting the

difference between passing rate of CSRS and mCSRS for a given scenario vs the

observed mean reference variance (Figure 2-5) suggested that CSRS and mCSRS

judgements differ especially at higher variance (Figure 2-5). In addition, the pros and

cons of the three statistical approaches are summarized in Table 2-8.

Discussion

In this paper, the outcomes from three statistical approaches were compared to

the evaluations of subject matter experts from the PQRI working group. While expert’s

classification and the ABE method considered the absolute drug amounts on given

stages or groups for the equivalence decision, CSRS and mCSRS express stage

depositions relative to the cumulative deposited amount (%TM and %ISM, respectively)

and therefore only evaluate the shape of the profiles. As outlined in the original

34

publications, it was therefore necessary for CSRS and mCSRS tests to include

additional tests into the assessment which probe for dose related differences (single

actuation content and/or impactor sized mass) (12,18). PBE tests for ISM and single

actuation content (SAC) are therefore included in the decision-making process.

Methods and data handling were identical to the ones originally proposed in

relevant publications or guidance (12,16,18,21). This led to the situation that input data

were not always the same. The ABE method considered all deposition sites from which

subsequently defined stage groups were generated. The PBE-CSRS test considered all

available deposition sites but restricted the PBE method to ISM stages. The PBE-

mCSRS test considered potential differences in the SAC, amount of drug deposited on

ISM stages and the shape of the ISM deposition sites. While generally the SAC is

determined in separate experiments, we derived the SAC as the sum of all deposition

sites (drug deposited in USP throat, pre-separator (if used) and all deposition stages)

(15). The assessment of the single actuation content (SAC) as an integrated component

within the mCSRS approach refers to the total amount of drug released from the

inhalation drug product. This evaluation ensures that the test drug product delivers an

equivalent amount of drug relative to the reference product as determined in a specified

test as outlined in U.S. Pharmacopeia (USP) 25, <601> (28). Unfortunately, SAC was

not generated for the 55 PQRI scenarios and hence the total mass (TM, the sum of drug

on all accessories and deposition sites of cascade impactor) was used as the best

available surrogate for SAC, following the procedure described in a previous publication

(12). The total mass represents the sum of individual cascade impactor deposition sites

plus inlet and pre-separator depositions, resulting in similar but probably somewhat

35

more variable estimates. Hence, the use of TM instead of SAC (when the reference

variability is less than test variability) within the PBE-mCSRS approach will result in a

more conservative evaluation, as equivalence will be more difficult to achieve because

of higher variability. The statistical outcomes of the three methods were compared with

the historical judgement of expert members of the PQRI working group. There are

certain limitations to using experts’ opinion as the truth such as lack of complete

information on the methods (especially the subjectivity employed for assessing the

variability of CI profiles) in evaluating the equivalence of the CI profiles (18). However,

considering that no satisfactory predictive in vitro – in vivo relationship between APSD

differences and clinically acceptable differences in lung dose/regional lung deposition of

T and R formulations has been established and no alternative statistical test has been

validated as a “gold” standard (18), these subjective evaluations were used as the best

available surrogate for truth. This was feasible because of the vast experience of the

subject matter experts. However, re-evaluation of scenarios suggested that some of the

decisions of the experts might have been debatable. For example, in the case of

scenario number 32, within which both T and R profiles had identical mean TM, identical

mean ISM and identical variability (%CV), 50% of the subject matter experts concluded

that T and R profiles are non-equivalent (while as per the PBE-mCSRS approach, 87%

of the simulated T and R datasets met the equivalence criteria). Another example is

scenario number 38, which 87% of the subject matter experts concluded that T and R

profiles are non-equivalent despite less than 10% difference in the mean TM and mean

ISM of T and R profiles, low test and low reference variability (while as per the PBE-

mCSRS approach, 99% of the simulated T and R datasets met the equivalence criteria).

36

One of the challenges in studies like this is to obtain representative data sets

describing “real life” scenarios. We decided to use the 55 scenarios originally suggested

by PQRI as these were generated by the PQRI working group after receiving

information on a total of 14 “real life” pairs of cascade impactor profiles (patterns

observed before and after change) that served as the foundation to further generate a

more complete set of scenarios. Considering this, we believe that the data set remains

a representative sample of T and R cascade impactor profiles of orally inhaled

formulations on market or in development (18). While the log-normal parametric

distribution assumption or non-parametric bootstrapping of actual observations are

plausible options for simulation of new datasets for profile comparison investigations,

we had to stay with the data sets evaluated by the experts. This multivariate normal

distribution assumption used by the PQRI group when generating the original scenarios

was based on a previous report which concluded that within all the 55 PQRI scenarios,

the absolute recovery amounts (i.e. the actual CI data used in this study) follow an

approximately normal distribution on each deposition site of CI profile (29). Further, the

55 scenarios were simulated by the PQRI working group based on their judgement that

a multivariate normal distribution would fairly represent real data with different shapes

and inter-correlation structure between stages. As these were the scenarios the experts

evaluated and in order to be consistent with the previous publications, we stayed with

the multivariate normal distribution assumption in our continued evaluation of the

statistical procedures.

We first compared the outcomes obtained from the three statistical approaches

(including PBE tests, where applicable) with the evaluations from subject matter experts

37

(Figure 2-2). The ABE approach as suggested by EMA applied at its ±15% acceptance

limit showed poor agreement with the experts’ opinion (Tables 2-1, 2-2 and 2-5).

Sandell previously reported that it is unlikely to show profile equivalence even when

reference product is tested against itself (30). We confirmed Sandell’s results, when the

55 scenarios were analyzed using single stage analysis, as none of the 55 scenarios

revealed equivalence (data not shown). When we performed the analysis with groups

(see methods section for details of grouping) rather than with individual stages, the ABE

method suggested equivalence for only 4 of the 55 scenarios (Figure 2-2A). Because of

the very small number of equivalent scenarios, it was difficult to probe for relationships

between variance and passing rate. However, the four scenarios that showed

equivalence, exhibited the smallest variance (Figure 2-4b).

The main reason for the poor agreement with the expert judgments, is that the

ABE approach involves the individual assessment of multiple stages or groups, all of

which must meet the equivalence criteria. For example, scenarios # 35 and # 36 which

had pass rates greater than 95% based on experts’ opinion, mCSRS and CSRS

approaches, resulted in 0% pass rate based on the ABE approach owing to the lack of

equivalence in group 2 (representing coarse mass) and group 4 (representing extra-fine

particle mass). It should be noted that both group 2 and group 4 represents a

significantly small proportion of the total mass deposited in the cascade impactor, prone

to high analytical variability and might not be clinically relevant. Since the EMA’s

approach places equal weight on all the four groups, it led to high false fail rate which is

in agreement with the previously reported literature (11,21). Thus, our data together with

those from Sandell further underline that EMA’s ABE approach and acceptance criteria

38

are too restrictive and unrealistic, even if the grouping approach is applied (30). Less

stringent criteria (Table 2-5) were able to increase the pass rate (T and R profiles in 7,

10, 14 and 27 scenarios were judged to be equivalent at ± 20%, ± 25%, ± 30% and ±

40% difference acceptance limits respectively) and the agreement with the expert

opinion (56.4% agreement at acceptance limit of ± 40% compared to 50.9% at ±15%)

which is only slightly lower than the 67.3% agreement observed for mCSRS approach

(Tables 2-1 and 2-5). While under these conditions (acceptance limit: ±40%), the false

fail rate was reduced from 87.1 % to 45.2%, slightly lower than the 54.8% for the PBE-

mCSRS approach, the false pass rate sky-rocketed to 41.7% (compared to 4.2% for the

PBE-mCSRS approach), a value that is not acceptable considering patient safety

concerns. Overall, EMA’s ABE approach using multiple stage (group) comparisons is

too stringent when the current acceptance criteria are applied (false fail rate too high) or

do not provide enough patient protection if criteria are loosened. We were unable to

identify any acceptable compromise. The solution might be, as suggested by Sandell

and in line with the approach taken by FDA for PBE and by Weber et. al. for mCSRS, to

scale the acceptance criteria for each stage or group according to the variability of the R

products, so the same ±15% limits are not used for all endpoints regardless of their

variability.

The PBE-CSRS approach suggested the largest number of scenarios for which T

and R products were judged to be equivalent (36 scenarios, Figure 2-2B at 50%

threshold level). While this resulted in a high agreement with the subject matter experts’

opinions (72.7% for the 50% threshold and 67.3% for the 80% threshold; Tables 2-1

and 2-2), it also translated into the highest number of false positive decisions (41.7%,

39

for the 50% threshold, 42.1% for the 80% threshold Figure 2-2B, Tables 2-1 and 2-2).

This method is therefore unlikely to ensure patient’ safety in a consistent manner. This

re-analysis of the scenarios using slightly different approaches for assessing the

method performance than originally reported by PQRI is in full support of the original

conclusions (18). As apparent from the Figure 2-4c, most of the 55 PQRI scenarios

showed 100% pass rate independent of the reference variance. Thus, the discriminatory

power of this method is purely driven by the ISM-PBE. The inability of the CSRS

method to identify non-equivalent scenarios is likely to due to the use of a fixed critical

value within the CSRS test, not considering reference variance or the selection of a

critical value that was too relaxed (10,18). As shown by the PQRI WG, change of the

critical value from 7.66 to 2.75 increased the number of scenarios not showing

equivalence, however, this did not improve the agreement with the expert’s judgement

(18).

It was more challenging to demonstrate equivalence of T and R APSD profiles

when the PBE-mCSRS approach, employing reference variance scaling, was applied to

the data. The number of scenarios for which T and R products were judged to be

equivalent was smaller (15 scenarios at ≥50% threshold level) than predicted by the

PBE-CSRS method (36 scenarios) or proposed by subject matter experts (31

scenarios). Despite the lower number of equivalent scenarios, the PBE-mCSRS method

showed the highest or second highest agreement with the expert opinion at ≥80% and

≥50% threshold criteria, respectively. More importantly, the PBE-mCSRS approach,

with only a very few false pass decisions (4.2%, Table 2-1; 5.3%, Table 2-2) struck a

good balance between patient’s risk and manufacturer’s risk (Tables 2-1 and 2-2). It

40

should be noted that always for the purpose of comparison with experts’ opinion, within

PBE-mCSRS approach, the mCSRS critical values at ±25% acceptance limit were

employed since good agreement with the experts’ opinion with a reasonably false pass

rate was observed at this acceptance limit (Table 2-6) which is in accordance with the

previously reported literature (12).

To further investigate the overall accuracy of the three statistical approaches, we

compared the corresponding ROC curves using the expert’s opinion as the surrogate

for truth and found that the mCSRS approach has significantly higher accuracy

(Bonferroni-adjusted p-value < 0.05) compared to the other two approaches (see Figure

2-3 and Table 2-3). ROC analysis indicated that the integration of population

bioequivalence methods with the mCSRS test (mCSRS approach) improved the overall

accuracy from 84% (with mCSRS test alone, data not shown) to 95% (with the

combined mCSRS approach). Thus, the stepwise mCSRS approach which ensures

equivalence both in terms of absolute deposition and the shape of the CI profile is

valuable for making correct decisions. Moreover, unlike the ABE approach, the mCSRS

test (by the design of the test statistic) puts more weight on the high deposition sites

that are less variable and clinically more relevant and less weight on the low deposition

sites leading to its superior performance (11).

A critical difference between CSRS and mCSRS is that the former normalizes

stages to the total mass and assesses the complete profile (including non-sizing

components and accessories) while the latter normalize stages to impactor sized mass

and assesses only the sized profile. Considering that experts based their judgement on

the full profile, it is somewhat surprising that the mCSRS performs better in matching

41

experts’ opinion. Had the experts based their evaluation on the sized part of the profile

only, the difference between the approaches would most likely have been even more

impressive.

Considering the results obtained for the CSRS test, it was also of interest to

assess the behavior of the CSRS and mCSRS tests alone (when PBE tests assessing

ISM and SAC were excluded). As shown in Figure 2-4, the mCSRS test alone exhibited

higher discriminatory ability compared to the CSRS test alone, especially for scenarios

with higher reference variability (MRV > 30). This superior performance of the mCSRS

test alone might be attributed to the use of critical values that are scaled to the

variability of the reference formulation as the critical value of mCSRS test decreases

with increasing R formulation variability, while the critical value of CSRS remains

unaltered (11,12). With reference and test variance generally being similar in the data

set of the 55 scenarios (the cumulative T/R variability ratio for the 55 PQRI scenarios

was within the narrow range of 0.82 – 1.29, data not shown), the higher incidences of

failed equivalency tests at higher variance makes sense, as it is more likely to fail the

mCSRS test if variabilities of test and reference samples are high. In this study, since

the cumulative T/R variability ratio for the 55 PQRI scenarios was narrow, the

relationship between the pass rate outcomes and T/R variance ratio could not be

evaluated. A separate simulation study evaluating the effect of changing T/R variance

ratios on the outcome might be of interest.

Conclusions

In this chapter, we compared the performance of three statistical approaches for

testing the equivalence in aerodynamic particle size distribution of orally inhaled drug

products. We found that the ABE approach (average bioequivalence as proposed by

42

EMA) is conservative in conferring a pass with high false fail rate, mainly due to equal

weight and limit allocated to all multiple group of stages involved in T and R equivalence

testing. We also observed that relaxing the EMA acceptance criteria increased false

pass decisions rather than improving the performance of the approach. On the other

hand, the CSRS approach is more tolerant to differences between T and R products as

indicated by the high false pass rate, mainly due to the use of fixed critical value within

CSRS test and the lack of considering the reference variability. As we hypothesized, the

mCSRS approach was on one hand conservative by providing less false pass

decisions, but still able to differentiate between equivalent and non-equivalent scenarios

(contrary to the EMA approach) across the 55 scenarios with balanced number of false

pass and intermediate false-fail rates, most likely due to the scaling of critical value as

per the variability of the reference product and other desirable properties of mCSRS test

as described above.

43

Table 2-1. Agreement of ABE, PBE-CSRS and PBE-mCSRS approaches with the experts’ opinion at ≥50% threshold. Statistical

Approach

Number of 55 PQRI

scenarios that met the

equivalence criteria

Agreement with experts’

opinion

False Pass Rate False Fail Rate

ABE 4 28/55 = 50.9% 0/24 = 0% 27/31 = 87.1%

PBE-CSRS 36 40/55 = 72.7% 10/24 = 41.7% 5/31 = 16.1%

PBE-mCSRS 15 37/55 = 67.3% 1/24 = 4.2% 17/31 = 54.8%

≥50% threshold: A scenario was judged as equivalent if for a given scenario greater than or equal to 50% of the experts or greater than or equal to 50% of the 1000 data sets indicated equivalence between T and R profiles.

Table 2-2. Agreement of ABE, PBE-CSRS and PBE-mCSRS approaches with experts’ opinion at ≥80% threshold. Statistical

Approach

Number of 55

PQRI scenarios

that met the

equivalence

criteria

Agreement with

experts’ opinion


ABE 4 42/55 = 76.4% 0/38 = 0% 13/17 = 76.5%

PBE-CSRS 31 37/55 = 67.3% 16/38 = 42.1% 2/17 = 11.8%

PBE-mCSRS 10 44/55 = 80% 2/38 = 5.3% 9/17 = 52.9%


44

Table 2-3. Pairwise comparisons of the area under the ROC curves (AUC) for the three statistical approaches. Comparison DeLong’s ‘Z’

test statistic

p-value Bonferroni-adjusted

p-value

PBE-mCSRS vs PBE-CSRS 2.84 0.0045 0.0135*

PBE-mCSRS vs ABE 3.86 0.0001 0.0003*

PBE-CSRS vs ABE 1.44 0.1487 0.4461

* Statistically different AUC’s at 5% significance level

Table 2-4. 95% CI of specificities for the three statistical approaches at 0.90 and 0.95 sensitivity values. Statistical approach Sensitivity Specificity (95% CI)

ABE 0.90 0.15 (0.11, 0.25)

PBE-CSRS 0.90 0.55 (0.32, 0.76)

PBE-mCSRS 0.90 0.89 (0.74, 0.97)

ABE 0.95 0.08 (0.05, 0.13)

PBE-CSRS 0.95 0.45 (0.26, 0.68)

PBE-mCSRS 0.95 0.84 (0.68, 0.97)

45

Table 2-5. Agreement of ABE approach with experts’ opinion for a range of acceptance limits at ≥50% threshold. Acceptance

limit

Confidence

level

Number of 55 PQRI



Agreement with

experts’ opinion


EMA: ±15% EMA: 90% 4 28/55 = 50.9% 0/24 = 0% 27/31 = 87.1%

±15% 80% 4 28/55 = 50.9% 0/24 = 0% 27/31 = 87.1%

±15% 70% 4 28/55 = 50.9% 0/24 = 0% 27/31 = 87.1%

±20% 90% 7 27/55 = 49.1% 2/24 = 8.3% 26/31 = 83.9%

±25% 90% 10 28/55 = 50.9% 3/24 = 12.5% 24/31 = 77.4%

±30% 90% 14 30/55 = 54.6% 4/24 = 16.8% 21/31 = 67.7%

±40% 90% 27 31/55 = 56.4% 10/24 = 41.7% 14/31 = 45.2%


46

Table 2-6. Agreement of PBE-mCSRS approach with experts’ opinion for a range of mCSRS acceptance limits at ≥50% threshold.

mCSRS Acceptance

limit

Number of 55 PQRI



Agreement with

experts’ opinion

False Pass

Rate

False Fail Rate

±10% 3 27/55 = 49.1% 0/24 = 0% 28/31 = 90.3%

±15% 8 32/55 = 58.2% 0/24 = 0% 23/31 = 74.2%

±20% 12 34/55 = 61.8% 1/24 = 4.2% 20/31 = 64.5%

±25%

(previously used, (12))

15 37/55 = 67.3% 1/24 = 4.2% 17/31 = 54.8%

±30% 22 38/55 = 69.1% 4/24 = 16.7% 13/31 = 41.9%


47

Table 2-7. Pros and Cons of the three statisitcal approaches: ABE, PBE-CSRS and PBE-mCSRS

Method Pros Cons

1) ABE approach (EMA)

• simple algorithm

• computationally less intensive

• stringent acceptance criteria

• high false fail rate

2) PBE-CSRS approach

• considers fine particle mass (PBE test)

• considers shape of the CI profile (CSRS test).

• high false pass rate

• affected by # of deposition sites

• no reference scaling

• complex algorithm 3) PBE-mCSRS

approach • considers fine particle mass

(PBE test)

• considers shape of the CI profile (mCSRS test).

• reasonably low false pass rate

• not affected by number of deposition sites

• integrates reference scaling

• complex algorithm

• involves bootstrapping

48

Figure 2-1. Representation of Andersen Cascade Impactor (ACI) profiles obtained from typical test (T) and reference (R) inhalation products of sample size 30 each.

49

Figure 2-2. Scatter plots comparing the results of the three statistical approaches: A) Average bioequivalence approach (ABE), B) Chi Square Ratio Statistic approach (PBE-CSRS) and C) Modified Chi Square Ratio Statistic approach (PBE-mCSRS); x-axis: Percent of experts that declared T equivalent to R for each scenario; y-axis: Percent of 1000 simulated datasets that met the T and R equivalence criteria as per the particular statistical approach for each scenario; Four quadrants: (1) Higher right quadrant PP (Experts’ opinion: pass; Statistical approach: pass), (2) higher left quadrant FP (Experts’ opinion: fail; Statistical approach: pass), (3) lower-left quadrant FF (Experts’ opinion: fail; Statistical approach: fail), (4) lower-right quadrant PF (Experts’ opinion: pass; Statistical approach: fail). Quadrants are based on a passing criterion of ≥50% (A scenario was judged as equivalent if greater than or equal to 50% of the 1000 data sets or greater than or equal to 50% of the experts judged a given scenario equivalent). Expert opinions have previously been reported (17,18).

50

Figure 2-3. Receiver Operating Characteristic (ROC) curves for the three statistical approaches A) Average bioequivalence approach (ABE, in red), B) Chi Square Ratio Statistic approach (PBE-CSRS, in blue) and C) Modified Chi Square Ratio Statistic approach (PBE-mCSRS, in green) against the experts’ opinion (Threshold value for experts’ opinion is set to be 80% i.e. if greater than or equal to 80% of the experts declared equivalency, the particular scenario was considered truly equivalent and vice-versa) obtained from the R package ‘pROC’; Please note that the direction of the x-axis is reversed. Thus, the x-axis represents false pass rate (the complement of true fail rate). Area Under the ROC Curves calculated by DeLong’s method, AUC [95% confidence interval] – ABE approach: 0.669 [0.534, 0.803]; PBE-CSRS approach: 0.793 [0.675, 0.912]; PBE-mCSRS approach: 0.950 [0.898, 1.000].

51

Figure 2-4. Pass rate outcomes of the A) Experts’ opinion, B) ABE approach, C) CSRS test alone (without PBE) and D) mCSRS test alone (without PBE) as a function of mean reference variance.

52

Figure 2-5. Difference in the pass rate outcomes of CSRS test alone (without PBE) and mCSRS test alone (without PBE) as a function of mean reference variance.

53

CHAPTER 3

EVALUATION OF THE SENSITIVITY AND ROBUSTNESS OF MODIFIED CHI-SQUARE RATIO STATISTIC FOR CASCADE IMPACTOR EQUIVALENCE TESTING

THROUGH MONTE CARLO SIMULATIONS

Background

Cascade impactor (CI) studies are central within the regulatory approval process

of orally inhaled drug products (OIDPs) as these tests, either performed with the

Anderson cascade or Next Generation impactors, provide information on the

aerodynamic particle size distribution (APSD), as an in vitro marker of pulmonary

deposition. However, a statistical evaluation of the derived cascade impactor profiles is

a challenge (9). While population bioequivalence (FDA) or average bioequivalence

(EMA) are employed for equivalence testing of the absolute amount of drug entering the

cascade impactor deposition sites, no formal statistical procedure for evaluating the

shape of CI profiles is specified in the FDA regulatory guidance (5,19,21). The modified

chi-square ratio statistic (mCSRS), a univariate cumulative assessment metric, was

proposed for analyzing the shape of normalized (percent of amount deposited) test (T)

and reference (R) CI profiles (10).

Unlike the original chi-square ratio statistic (CSRS) previously proposed by FDA

in the “Draft Guidance for Industry: Bioavailability and Bioequivalence Studies for Nasal

Aerosols and Nasal Sprays for Local Action”, the mCSRS was found to be stable

irrespective of the number of deposition sites in the CI profile (10,18). It was shown that

under the assumption of identical T and R CI profiles (with only a few low deposition

sites), mCSRS shows a favorable distributional behavior and follows an approximate F

distribution, with both numerator and denominator degrees of freedom equal to number

of deposition sites (p) - 1. Moreover, when the T and R CI profiles are identical, it was

54

shown that the median of mCSRS (MmCSRS) is always equal to one irrespective of the

shape of T and R CI profiles, indicating that MmCSRS is a robust metric (10).

It was reported that MmCSRS is sensitive to both single site and multiple site

mean deposition differences and selectively more sensitive to high deposition sites (11).

A linear relationship was found between MmCSRS and the inverse square of reference

product variability which eventually led to the development of critical values for the

mCSRS test, the last step in the previously proposed stepwise APSD test (12). For

deriving the mCSRS test critical values, rank ordered (by decreasing magnitude of their

normalized deposition) M8 CI profile (shown in Figure 3-1a), the profile that resembles

the general shape of real CI profiles across different inhalation products was chosen as

the reference profile. The critical values for mCSRS test are dependent on the allowable

mean difference (or acceptance limit) between T and R CI profiles as well as scaled by

the variability of the reference product. As reported in a previous publication, reference

variance scaling of the critical values resulted in the better performance of mCSRS test

as compared to the original CSRS test and EMA’s average bioequivalence test (5). In

this paper, the influence of dataset generation method (from different typical CI profile

patterns shown in Figure 3-1) with and without inter-site correlation (ISC) on the

derivation of critical values and subsequently its effect on the outcome of mCSRS test

was assessed. The influence of number of bootstrap iterations used within the algorithm

on the consistency of the pass rate outcome was assessed within the range of 10 to

10000 iterations (default value = 2000). While the previous publications in literature

suggested the sensitivity and robustness of the MmCSRS, this paper formally evaluated

the effect of differences in T and R mean stage deposition, T/R variance ratios,

55

differences between T and R profiles in high or low deposition sites and sample size on

the probability of showing equivalence between T and R CI profiles (that is passing the

mCSRS test) through Monte Carlo simulations.

Methods

The flowchart of the mCSRS test algorithm is shown in Figure 3-2 and the

computational form of mCSRS is given below:

𝒎𝑪𝑺𝑹𝑺𝒋𝒌 =

∑(𝑻𝒊𝒋 − �̅�𝒊)

𝟐

�̅�𝒊

𝒑𝒊=𝟏

∑(𝑹𝒊𝒌 − �̅�𝒊)𝟐

�̅�𝒊

𝒑𝒊=𝟏

where p = Number of deposition sites of the normalized ISM (impactor sized

mass, the deposition sites with specified upper cut-off size) CI profile

Tij = Normalized deposition on the ith deposition site of the jth CI profile for the T

product

Rik = Normalized deposition on the ith deposition site of the kth CI profile for the

R product

�̅�𝑖 = Sample mean of the ith deposition site of all ISM normalized R CI profiles in

a dataset

Briefly, from a given dataset of ‘N’ reference (R) + ‘N’ test (T) normalized ISM

(impactor staged mass, sum of absolute mass deposited on deposition sites with upper

diameter cut-off) CI profiles (default value of N = 30), ‘B’ (default value of B = 2000)

bootstrap samples were obtained. For each of the bootstrapped sample, the median of

‘N2’ mCSRS (MmCSRS i.e. the median of 900 mCSRS when N = 30) was obtained

56

followed by the computation of the upper bound of 90% BCA (bias corrected and

accelerated) confidence interval (U90) for a given dataset. If U90 was found to be less

than a particular critical value (previously published critical values C10, …,C30 are

shown below) , then the T product was declared equivalent to the R product at and

beyond that specified acceptance limit. For this test, as described in a previous

publication, a non-parametric bootstrapping procedure was employed for the purpose of

constructing 90% confidence interval for the MmCSRS as there is no closed form

solution for the distribution of median of the mCSRS (12). For all the simulations in this

study, both T and R products had identical total amount of drug deposition. Hence, the

first two steps of the previously published stepwise APSD test (population

bioequivalence of single actuation content and ISM) were not applied to any of the

datasets (more details on this assumption are given in the discussion section).

C10 = 0.993 + 124*RVS-2

C15 = 0.970 + 294*RVS-2

C20 = 0.949 + 536*RVS-2

C25 = 0.916 + 856*RVS-2

C30 = 0.896 + 1245*RVS-2

where C10, C15, …, C30 = Critical values at ±10%, ±15%, …, ±30% acceptance

limits (allowable mean difference on all deposition sites) respectively for each dataset of

30 T and 30 R normalized ISM cascade impactor profiles

𝑅𝑉𝑆 = √∑ �̅�𝒊 ∗ 𝑪𝑽𝒊

𝟐𝑝𝑖=1

∑ �̅�𝒊𝑝𝑖=1

57

where RVS = Reference Variance Scaling metric for each dataset of 30 T and 30

R normalized ISM cascade impactor profiles

CVi = Coefficient of variation (%) of the ith deposition site of the normalized ISM

cascade impactor profiles of the R product (also called RSD, relative standard deviation,

the sample standard deviation expressed in percent of the average)

p = Total number of ISM deposition sites

�̅�𝑖 = Sample mean of the ith deposition site of all ISM normalized R cascade

impactor profiles in a dataset

Effect of Dataset Generation Method on the Derived mCSRS Test Critical Values and Outcome:

In a previous publication, rank-ordered (by decreasing magnitude of amount

deposited on ISM deposition sites) M8 CI profile (see Figure 3-1a) was used as the

reference CI profile (see discussion section for justification) for deriving critical values

through iterative procedure. To investigate if the derived mCSRS test critical values and

the mCSRS test outcome is influenced by the dataset generation method (i.e. by the

shape of the reference CI profile and the incorporation of ISC, the outcomes from

different sets of critical values derived from different type of datasets (M8 rank-ordered

without ISC, M8 rank-ordered with ISC, M8 non-rank ordered with ISC and M1 rank-

ordered without ISC, see Figure 3-1) were compared with that of previously published

critical values. This evaluation was conducted in two steps:

Dataset generation procedure: As shown in Figure 3-1, the typical CI profiles

used as reference CI profiles for dataset generation contain eight deposition sites (four

pairs, where the two deposition sites in a pair had identical deposition except for CI

profile 1(e)). The total amount of deposited drug on all eight sites was equal to 100 µg

58

for both T and R CI profiles (see Figure 3-1f). The T CI profile was simulated with a

specific mean population difference (0%, 10%, 15%, 20% and 25%) from R CI profile on

all deposition sites. To ensure mass balance (100 µg) between T and R, a reduction in

mean mass deposition on one deposition site of a given pair by Y% was counteracted

with an increase in mean deposition on the other member of the pair by the same

degree (Y%). Thus, in the T CI profile population mean vector, four sites had higher and

four sites had lower deposition compared to the corresponding R CI profile (see Figure

3-1f). For a given population mean difference (0%, 10%, 15%, 20% and 25%) between

T and R CI profiles, datasets were generated across a wide range of variability (5%,

10%, 15%, 20%, 25%, 30%, 35%, 40% and 45% CV, both T and R had identical %CV

on each deposition site), yielding a total of 45 (5 X 9 = 45) scenarios. In each of the 45

scenarios, a thousand datasets of 30 T and 30 R CI profiles were generated by Monte

Carlo simulations using the population mean vector and population variance-covariance

matrix without inter-site correlation by assuming multivariate normal distribution in R

software (v3.4.2) as described in a previous publication (11).

Derivation of critical values and determination of mCSRS test outcome: For

each scenario, the mean of MmCSRS’s and the mean of reference product variability

(MRV) obtained from the thousand 30 T and 30 R datasets was computed.

Subsequently, for all scenarios with a given acceptance limit, their mean MmCSRS was

regressed against the inverse square of its MRV to obtain intercept and slope estimates

of critical value equations at 10%, 15%, 20%, 25% and 30% acceptance limits. This

procedure was applied to all the four types of datasets generated from the typical CI

profile patterns described above, yielding four different sets of critical values. Finally, the

59

mCSRS test was applied to one realistic PQRI scenario (where T was equal to R) that

was comprised of thousand datasets of 30 T and 30 R CI profiles. The proportion of the

thousand datasets that met the equivalence criteria at ±25% acceptance limit based on

the four different sets of critical values derived was compared against the pass rate

obtained using the previously reported critical values generated by iterative procedure

(12).

Effect of Number of Bootstrap Iterations on the Outcome Of mCSRS Test:

For this evaluation, one of the previously studied realistic PQRI (Product Quality

Research Institute) scenario was selected (see discussion section for justification). In

this scenario, the population mean vector and population variance-covariance matrix for

T and R CI profiles were identical i.e. T was equal to R (18). A thousand input datasets

of 30 T and 30 R CI profiles were generated by Monte Carlo simulations by assuming

multivariate normal distribution in SAS software as described in a previous publication

(18). For one of the simulated input dataset of 30 T and 30 R CI profiles, the upper

bound of 90% BCA confidence interval for MmCSRS (U90) was computed (using the

procedure outlined in Figure 3-2) by changing the number of bootstrap iterations within

the mCSRS algorithm ranging from 10 to 10,000 with an interval of 10 and the precision

of the U90 estimate in the bootstrap iteration intervals of 300-700, 1800-2200 and 7800-

8200 was calculated. Subsequently, the mCSRS test was applied to all the thousand

simulated datasets of 30 T and 30 R CI profiles within the selected PQRI scenario. The

proportion of the thousand datasets that met the equivalence criteria at ±25%

acceptance limit over the range of number of bootstrap iterations (10 to 10000) was

recorded.

60

Effect of CI Profile Related Factors on the Power Of mCSRS Test (Power Curves):

Effect of test (T) and reference (R) multiple site mean differences on the

power of mCSRS test: For this study, the rank ordered M8 CI profile (see Figure 3-1a)

was chosen as the model reference (R) profile (see discussion section for justification).

A total of 45 scenarios of datasets were generated as described under methods section

(I)(a). Within each scenario, the proportion of the thousand datasets that met the

equivalence criteria as per the mCSRS algorithm (see Figure 3-2) at ±25% acceptance

limit was computed.

Effect of T/R variance ratio on the power of mCSRS test: To study the effect

of the T/R variance ratio, the M8 cascade impactor (CI) profile (Figure 3-1a) was chosen

as the model reference CI profile (see discussion section for justification). The effect of

differences in the T/R population variance ratio (1:4, 1:1 and 4:1) on each deposition

site for a range of reference variabilities (5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%

and 45% CV, both T and R had identical population mean amounts on each deposition

site) was evaluated in a total of 27 (3 X 9 = 27) scenarios. In each of the 27 scenarios, a

thousand sets of 30 T and 30 R CI profiles were generated by Monte Carlo simulations

using the population mean vector and population variance-covariance matrix without

inter-site correlation by assuming multivariate normal distribution in R software (v3.4.2)

as described in a previous publication (11). Within each scenario, the proportion of the

thousand datasets that met the equivalence criteria as per the mCSRS algorithm (see

Figure 3-2) at ±25% acceptance limit was computed.

Effect of sample size on the power of mCSRS test: To study the effect of

sample size, the M8 cascade impactor (CI) profile (Figure 3-1a) was chosen as the

model reference CI profile (see discussion section for justification). The effect of number

61

of cascade impactor (CI) profiles in a given dataset (15, 30 and 60 T and R CI profiles)

was evaluated. Simulations were performed for a range of variabilities (5%, 10%, 15%,

20%, 25%, 30%, 35%, 40% and 45% CV). Both T and R had identical population mean

amounts and population %CV on each deposition site). A total of 27 (3 X 9 = 27)

scenarios were evaluated. In each of the 27 scenarios, a thousand sets of specified

number (15 or 30 or 60) of T and R CI profiles were generated by Monte Carlo

simulations using the population mean vector and population variance-covariance

matrix without inter-site correlation by assuming multivariate normal distribution in R

software (v3.4.2) as described in a previous publication (11). Within each scenario, the

proportion of the thousand datasets that met the equivalence criteria as per the mCSRS

algorithm (see Figure 3-2) at ±25% acceptance limit was computed.

Sensitivity of the outcome of mCSRS test towards T and R mean

differences on high and low deposition sites: The M6 CI profile (see Figure 3-1d)

was chosen as the model reference CI profile (see discussion section for justification).

This reference CI profile consisted of eight deposition sites. Two deposition sites formed

one pair. Deposition sites of a given pair contained identical amounts of drug. Two of

these four pairs represented stages of high drug deposition (population mean deposition

= 22.5 mcg), while the other two pairs represented stages of low drug deposition

(population mean deposition = 2.5 mcg). The total amount of deposition on all eight

sites summed up to 100 µg for both T and R CI profiles. These simulations evaluated

the sensitivity to identify differences in the T and R mean depositions on high and low

deposition sites. The effect of T and R population mean differences (no difference in

mean deposition on all deposition sites, or 20% on low deposition sites only, or 20% on

62

high deposition sites only or 20% on all deposition sites) was simulated for a range of

variabilities (5%, 10%, 15%, 20%, 25%, 30%, 35%, 40% and 45% CV, both T and R

had identical %CV on each deposition site). Thus, a total of 36 (4 X 9 = 36) scenarios

were assessed. These 36 dataset scenarios were generated by following the procedure

that is similar to the one described under methods section (I) (a) with the only exception

that this evaluation was based on M6 model reference CI profile. Within each scenario,

the proportion of the thousand datasets that met the equivalence criteria as per the

mCSRS algorithm (see Figure 3-2) ±25% acceptance limit was computed.

Effect of Dataset Generation Method (Incorporation of ISC) on mCSRS Test Power Curve Calculations

To investigate the effect of incorporating inter-site correlation within Monte Carlo

simulations of input CI profile datasets on the power curve calculations described

above, all the previously studied realistic 55 PQRI scenarios (18) were selected (see

discussion section for justification). Within each scenario, a thousand datasets of 30 T

and 30 R CI profiles were generated by Monte Carlo simulations using the population

mean vector and population variance-covariance matrix with inter-site correlation by

assuming multivariate normal distribution in SAS software as described in a previous

publication (18). The mCSRS test (as per the procedure outlined in Figure 3-2) was

applied to all the 55 scenarios and the proportion of the thousand datasets that met the

equivalence criteria at ±25% acceptance limit in each scenario was recorded. These

results were compared to the ones obtained from their corresponding 55 PQRI datasets

generated without inter-site correlation.

63

Results

The derived mCSRS test critical values were influenced by the dataset

generation method and the observed variability of the reference drug product. When the

mean variance of the reference drug product is high (Mean Reference Variance,

MRV=32.4), the critical values generated from M8 rank-ordered datasets through

iterative procedure (M8 ITP, previously published) resulted in the most conservative

critical value and pass rate outcome at ±25% acceptance limit. At high variability, M8

without ISC and M1 without ISC critical values yielded similar pass rate outcomes since

the lower slope estimate of M1 without ISC critical value line (see Figure 3-8, Table 3-1)

was counteracted by its higher intercept value. On the other hand, at low variability

(MRV=6.81), M1 without ISC critical values resulted in the most conservative pass rate

outcome (17% lower pass rate compared to the M8 without ISC critical values, see

Table 3-1). Both at high and low variability, datasets with ISC yielded higher critical

values and higher pass rate compared to their counterparts without ISC (see Table 3-1,

Figure 3-8).

As the number of bootstrap iterations within the mCSRS algorithm increased

from 10 to 10,000, the precision of the test statistic (U90: upper bound of the 90% BCA

confidence interval of the MmCSRS) increased as measured by the relative standard

deviations (%RSD) in the following bootstrap iteration intervals: iterations 300 to 700 –

2.00% RSD; iterations 1800 to 2200 – 0.96% RSD; iterations 7800 to 8200 – 0.69%

RSD (Figure 3-3a). However, we found that the pass rate outcome remained fairly

constant around 75±1% irrespective of the bootstrap iterations except for the first few

hundred iterations (Figure 3-3b), indicating that the proposed method with 2000 default

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bootstrap iterations strike a reasonable balance between computational time and

accuracy of the outcome.

The sensitivity and robustness of mCSRS was evaluated through the

construction of power curves across a wide range of variability (5-45% CV) (Figures 3-4

to 3-7). The mCSRS test was found to be sensitive and robust to the mean differences

between T and R CI profiles. As shown in Figure 3-4, at ±25% acceptance limit and at

lower variability (5% CV), when T was equal to R (no difference in population mean

deposition and variability of the T and R CI profiles), the probability of showing

equivalence was equal to 100%. When the mean difference between T and R CI

profiles was increased to ±25% by keeping the variability constant (5% CV), the

probability of showing equivalence decreased to <10%. Further, when the variability of T

and R CI profiles was increased to 25% CV (and beyond) by keeping the mean

deposition difference between T and R CI profiles constant (i.e. T was equal to R), the

probability of showing equivalence decreased consistently, indicating that the method

was conservative in conferring a pass at higher variability (Figure 3-4). When the

sample size (number of T and R CI profiles) was increased to N=60 from N=30, the

probability of showing equivalence increased, indicating that a larger sample was

required at higher variability for better decision-making (Figure 3-5). When there was no

mean deposition difference between T and R CI profiles and the variance of T CI profile

was only one-fourth as that of R CI profile, the probability of showing equivalence

stayed at 100% even at higher variability (R CI profile: 45% CV; T CI profile: 22.5% CV,

Figure 3-6). On the other hand, when the T CI profile was four times as variable as that

of R CI profile, the probability of showing equivalence decreased drastically showing

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less than 5% pass rate at 20% CV (for R CI profile, Figure 3-6). This indicates that the

method penalized higher T variability, while rewarding the T products that were less

variable. In addition to being sensitive to T product variability, the mCSRS test was also

found to be selectively more sensitive to high mean deposition sites. As shown in Figure

3-7, in comparison to the power curve for T equal to R (identical variability and no mean

deposition difference between T and R CI profiles, shown in green), the power curve for

20% mean deposition difference between T and R CI profiles (shown in red) was

consistently much lower at all levels of variability (5 to 45% CV). While applying 20%

mean deposition difference only on the low deposition sites shifted the power curve

marginally (shown in the light blue color), 20% mean deposition difference applied only

on the high deposition sites shifted the power curve drastically (shown in yellow)

bringing it very close to the power curve with 20% mean deposition difference on all

deposition sites i.e. red power curve (Figure 3-7). This confirmed that the method gives

less weightage to low deposition sites that are prone to higher analytical variability and

are less clinically relevant. The input datasets for constructing the power curves

described above were generated without the incorporation of ISC. In the input dataset

validation study, we observed that the datasets generated with the incorporation of real

data ISC showed consistently higher MmCSRS (or lower pass rate) compared to their

counterparts generated without ISC across the 55 PQRI scenarios tested (see Figure 3-

10).

Discussion

In this paper, the influence of various algorithm and CI profile related factors on

the performance of mCSRS test was studied through Monte Carlo simulations. Within

all these simulations, we assumed that both T and R products had identical total amount

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of drug deposition (i.e. the sum of mean population amount on all deposition sites of CI

profile is identical for T and R). This assumption was based on a pre-condition that must

be met in previously proposed stepwise APSD tests before truly testing for equivalence

in the shape of CI profiles. In fact, the stepwise APSD test procedure precludes the

assessment of CI profiles through the mCSRS statistical test if T and R fails to meet the

population bioequivalence criteria for single actuation content and ISM mass (sum of

amount deposited on all ISM sites) (12). The rank ordered M8 CI profile (see Figure 3-

1a) was selected as the model reference profile for evaluating T and R mean deposition

differences, T/R variance ratio, T and R sample size since it resembles the general

shape of real ISM profiles across different inhalation products as described in a

previous publication (11). However, for clearly distinguishing the sensitivity of mCSRS

when high or low deposition sites differ, the M6 CI profile with four high and four low

deposition sites was used (see Figure 3-1d). A high to low mean deposition ratio of 9:1

was selected while the sum of mean amount deposited on all deposition sites was fixed

to 100 µg for both T and R CI profiles. Had there been fewer high or fewer low

deposition sites and if the high to low mean deposition ratio was different in the selected

model CI profile, the magnitude of probability of showing equivalence between T and R

would be different, but the trend observed in these simulations should always be valid.

While the log-normal parametric distribution assumption or non-parametric

bootstrapping of actual observations are plausible options for generating new datasets

through Monte Carlo simulations, we stayed with the multivariate normal distribution

assumption used by the PQRI group in its previous investigations (18). This assumption

was based on a previous report which concluded that within all the 55 realistic PQRI

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scenarios, the absolute recovery amounts (i.e. the actual CI data used in this study)

follow an approximately normal distribution on each deposition site of CI profile (29).

For the derivation of mCSRS critical values, T and R CI profiles should be

generated systematically (see methods section for details). To investigate if the derived

mCSRS test critical values and the test outcome are sensitive to the dataset generation

method (see methods section for details), the outcomes from different sets of critical

values derived were compared. Linear regression analysis of mean MmCSRS against

Inverse Square of mean reference variability resulted in 14% higher slope and 8% lower

intercept estimates for M8 without ISC compared to M1 without ISC CI profile type

datasets (see Table 3-1). Lower slope for M1 CI profile is expected since the normalized

squared difference (NSD) for M1 profile (NSD = 78.1) is lower than M8 profile (NSD =

167.8) and a positive correlation between estimated slope and NSD was previously

reported (11). The lower slope for M1 profile was balanced by its higher intercept value

(this is again expected since a negative correlation between estimated intercept and

NSD was previously reported (11)) which led to no difference in the pass rate when

critical values derived from rank-ordered M8 or M1 CI profiles (without ISC) were

employed for decision-making at high variability (see Table 3-1). On the other hand,

when the variability is low, M1 critical values were 12% lower compared to their M8

counterparts since the effect of slope was magnified (given that MmCSRS is inversely

related to the squared reference product variability) which counteracted the contribution

of intercept.

The slope estimates for datasets generated with ISC were higher compared to

their counterparts generated without ISC (see Table 3-1). This trend agrees with the

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previously published findings (11) which led to higher pass rate when critical values

derived from datasets with ISC were employed for decision-making. This observed

trend might be explained by the fact that for datasets generated with ISC, after

normalization of ISM CI profiles (first step in the mCSRS statistical test algorithm), the

observed CV% deviated away from the target CV% of the originally generated non-

normalized CI profiles (see Figure 3-9a). While generating the datasets to derive critical

values, since a constant CV% was applied across all the deposition sites (irrespective of

the mean deposition), the lower deposition sites showed higher relative variability when

normalized to the mean and vice-versa (see Figure 3-9a). When ISC was employed

during the generation of datasets (Figure 3-9a), reflecting what is observed in real data

(and consistent with understanding of fundamental particle physics principles) the

difference is more pronounced than when this pattern is more obscured by the “noise”

of independence (no ISC) between deposition sites (Figure 3-9b). Thus, when datasets

generated without ISC were employed, the observed CV% after normalization agreed

closely with the target CV% of the initially generated non-normalized CI profiles (see

Figure 3-9b) which led to optimal and conservative critical value estimates. On the other

hand, the critical values derived from datasets with ISC were higher (as compared to

the ones derived from datasets without ISC) representing a case of non-optimal scaling

of critical values. In the presence of ISC, rank-ordering led to 17% higher critical value

at high variability (MRV=32.4) and 1.5% lower critical value at low variability

(MRV=6.81) compared to the previously published critical values probably owing to the

partial distortion of real data pattern characteristics during dataset generation (see

Table 3-1, Figure 3-8). In summary, this study clearly identified that dataset generation

69

(a pre-requisite for deriving critical values) method with or without incorporation of ISC

could potentially influence the derived critical values and subsequently the probability of

showing equivalence between T and R CI profiles. Since the M8 ITP and M1 without

ISC critical value lines cross each other at mean reference variability, MRV = 27 (see

Figure 3-8), the most conservative results can be obtained by employing critical values

generated from M1 rank-ordered datasets without ICS at low reference variability

(MRV<27) and using critical values generated from M8 rank-ordered datasets through

iterative procedure at high reference variance (MRV≥27). At the same time, it is

important to notice that M1 profile is hardly seen in practice and using M1 critical values

could lead to unnecessary stringency of the method. Nonetheless, further analysis

across different products available on the market is required to confirm the influence of

rank-ordering on the critical values derived from datasets with ISC and to reach a

consensus on the most appropriate method of dataset generation for deriving mCSRS

test critical values. For constructing the power curves, always the previously published

(12) ±25% acceptance limit critical values generated by iterative procedure (based on

rank-ordered M8 CI profile) were employed for making T and R equivalence decisions.

It is because employing these previously published critical values at ±25% acceptance

limit led to the best overall agreement (95% accuracy) when compared against PQRI

experts’ opinion (surrogate for the truth) as described in the literature (5,12).

As per the mCSRS test procedure previously published in the literature, 2000

bootstrap iterations were used by default for generating the test statistic (U90) while

constructing the power curves shown in Figures 3-4 to 3-7. A realistic PQRI scenario

with T equal to R was selected to evaluate the influence of number of bootstrap

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iterations on the outcome of mCSRS test. The selection of a scenario wherein T=R

enabled to directly assess the precision of the power of mCSRS test over a range of

bootstrap iterations (10-10,000). When the number of bootstrap iterations were

increased from 2000 to 10000, the precision of U90 increased which did not translate

into increased precision of pass rate outcome (Figure 3-3). The increased precision of

U90 was due to decreased standard error of MmCSRS at larger number of bootstrap

iterations (31,32). However, for a multivariate vector with eight deposition sites (like the

CI profiles studied in this paper), as per the formula developed by Booth and Sarkar, at

least 1500 resamples (approximately) would be required to achieve simultaneous

accuracy of less than 10% relative error in bootstrap variance (or Monte Carlo error)

with 95% probability (33). Thus, with 2000 bootstrap iterations (as proposed in the

original algorithm), the conclusion of the analysis should not be significantly influenced

by the seed of a random number generator, indicating that the selection of 2000

bootstrap iterations strike a reasonable balance between computational speed and

accuracy of the outcome. When the mCSRS test was applied in the following simulation

work, we employed 2000 bootstrap iterations and previously published critical values

generated through iterative procedure at ±25% acceptance limit due to the reasons

discussed above.

The power calculations for mCSRS test were performed by applying the above

validated conditions. The mCSRS test was found to be sensitive to all the CI profile

related factors evaluated in this paper. At lower variability (5% CV) and ±25%

acceptance limit, the probability of showing equivalence stayed at 100% when the true

mean deposition difference between T and R CI profiles was less than or equal to

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±15%. The probability decreased to 93% and <10% when the true difference was

increased to ±20% and ±25% respectively. On the other hand, the probability of

showing equivalence was always <10% when the true difference is ±25% irrespective of

the variability of the T and R CI profiles (Figure 3-4). This is a desirable and expected

property of the mCSRS statistical test which can be explained by the interplay between

the test statistic and the critical value that is scaled by the variability of the reference

product variability. It is apparent from the computational form of mCSRS that at a

constant variability and constant denominator, increase in T to R mean deposition

difference leads to larger MmCSRS values. It was also previously reported that a

perfect linear relationship was found between MmCSRS and normalized squared

difference reference scaled (NSDRS), which confirms that a higher mean deposition

difference (at constant variability) between T and R CI profiles translates to larger

MmCSRS and eventually to larger test statistic (U90) values (11). It was previously

established that the MmCSRS and critical values are inversely related to the variability

of the reference product (11). From the mCSRS test algorithm (Figure 3-2), it is easy to

see that the smaller the observed test statistic (U90) in comparison to the critical value,

the higher will be the probability of showing equivalence between T and R CI profiles. At

lower variability (5% CV), the observed mean U90 up to ±20% true mean difference

(data not shown) was found to be less than the ±25% acceptance limit critical value

(mean C25 = 48.77) which led to higher probability of showing equivalence between T

and R CI profiles (see Figure 3-4). In contrast, the observed mean U90 at ±25% true

mean difference (data not shown) was always found to be greater than its

corresponding ±25% acceptance limit critical value at all the levels of variability studied

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(5%, 10%, 15%, 20%, 25%, 30%, 40%, 45% CV) which led to <10% probability of

showing equivalence between T and R CI profiles (see Figure 3-4).

The probability of showing equivalence decreased more rapidly (as a function of

variability of the R product) when the T : R variance ratio was 4:1 as compared to T : R

variance ratio of 1:1 and 1:4 (Figure 3-6). This is an expected behavior of mCSRS

statistical test which can be explained by the design of the computational form of

mCSRS. For a constant denominator and a constant mean difference between T and R

CI profiles, MmCSRS increases with increasing variability of the T product and vice

versa (11). Thus, when the T : R variance ratio was 4:1, the test statistic (U90) exceeded

its corresponding ±25% acceptance limit critical value at much lower R product

variability as compared to the T : R variance ratio of 1:1 or 1:4. Similarly, when T is

equal to R (identical population mean vector and identical variance-covariance matrix),

the probability of showing equivalence decreased more rapidly (as a function of

variability of the R or T product) when the sample size was 15 as compared to the

sample size of 30 and 60 (Figure 3-5). This is a desirable feature of the mCSRS

statistical test which can be explained by asymptotic theory or law of large numbers

(34,35). As the sample size increased, the point estimate of MmCSRS tended more

towards its true value (which is equal to 1 when T = R) and as the sample size

decreased, the point estimate of MmCSRS slightly increased and deviated away from

its true value. More importantly, the width of the 90% BCA confidence interval increased

with decrease in sample size leading to larger observed U90 (11). Thus, at a lower

sample size, the test statistic (U90) exceeded its corresponding ±25% acceptance limit

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critical value at much lower variability, indicating that a larger sample size was required

for better decision-making at higher variability.

The probability of showing equivalence was found to be selectively more

sensitive to mean deposition differences on high deposition sites as compared to low

deposition sites (Figure 3-7). This is another desirable property of mCSRS statistical

test which can be explained by the design of the computational form of mCSRS, where

both numerator and denominator represent modified forms of normalized squared

distance between two CI profiles (11). The squaring of distance between T and R CI

profiles translated into providing more weightage for high deposition sites. For example,

at 5% CV when 20% mean deposition difference was applied only on the high

deposition sites MmCSRS increased to 23.79 as compared to 3.76 when the same

mean deposition difference was applied only on low deposition sites (MmCSRS = 27.55

when 20% mean deposition difference was applied on all deposition sites). Thus, for a

pair of T and R CI profiles with X% percent mean deposition difference on low

deposition sites, the test statistic will be smaller which might lead to higher probability of

showing equivalence compared to the case with the same X% mean deposition

difference on high deposition sites. This property of mCSRS statistical test giving low

weightage to the low deposition sites that might not be clinically very relevant (given that

they represent only small portion of the total therapeutic dose) and are prone to

unwanted higher analytical variability is highly desirable (11).

To provide for simplistic and systematic evaluation of various factors on the

power of mCSRS statistical test, the simulated datasets used for constructing power

curves described above were generated under the assumption that the CI profile

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deposition sites are independent of each other (i.e. no ISC). The effect of ISC was

tested using the realistic 55 PQRI scenarios since they altogether form a representative

sample of T and R CI profiles of orally inhaled formulations on market or in development

and the sample size of 55 is large enough to capture any trend in the outcomes. It was

observed that for the 55 PQRI scenarios studied, the datasets generated with the

incorporation of real data ISC resulted in consistently lower probability of showing

equivalence between T and R compared to their counterparts generated without ISC

(Figure 3-10). It implies that datasets generated with the incorporation of ISC, are more

likely to be declared non-equivalent. However, the trend of shift in power curves

observed in Figures 3-4 to 3-7 would still be valid even if these evaluations were

conducted on real datasets with ISC. Moreover, the incorporation of ISC within

simulated input datasets for analysis is not of practical importance because data is

generated experimentally for routine bioequivalence analysis of T and R CI profiles.

Since the value of mCSRS, by the design of its computational form, is independent of

ordering of the deposition sites (in the absence of ISC), it was sufficient to conduct the

evaluation of the power of mCSRS test only on rank-ordered (by decreasing magnitude

of their ISM normalized deposition) CI profiles.

Conclusion

In this paper, we analyzed the performance of mCSRS test by studying the effect

of various CI profile and algorithm related factors on T and R CI profile equivalence

decisions. We have shown that the dataset generation method could potentially

influence the derived critical values and the equivalence outcome of mCSRS test. The

default number of bootstrap iterations (as proposed in the mCSRS test algorithm) are

sufficient for achieving a precise pass rate outcome. The probability of showing

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equivalence between T and R CI profiles (or passing the mCSRS test) increased with

decrease in mean deposition differences, decrease in T product variability and increase

in sample size. The simulations also clearly elucidated that the mCSRS outcome is less

sensitive to low deposition sites that are often prone to high analytical variability and

show less clinical relevance (due to small fraction of drug dose deposited on low

deposition sites). In conclusion, except for the complex nature of the mCSRS test

algorithm, it exhibited all the desirable properties of a sensitive and robust statistical test

for testing the in vitro bioequivalence of generic inhalation drug products.

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Table 3-1.Results showing the effect of CI profile shape and dataset generation method on the derived critical values and

the pass rate outcome of PQRI scenarios no. 20 (high mean reference variability = 32.4)a and 37 (low mean reference variability = 6.81)b at ±25% acceptance limit

CI profile type

CI profile pattern

Dataset generation method

Intercept Slope Mean observed critical value for PQRI scenario no. 20a

Pass rate for PQRI scenario no. 20a

Mean observed critical value for PQRI scenario no. 37b

Pass rate for PQRI scenario no. 37b

M8 Rank ordered

Iterative procedure (previously published)

0.916 856 1.75 75.2% 19.72 33.9%

M8 Rank ordered

Without inter-site correlation

1.03 820 1.83 80.3% 19.05 25.0%

M8 Rank ordered

With inter-site correlation

1.25 827 2.06 91.0% 19.42 29.8%

M8 Not rank ordered

With inter-site correlation

1.05 925 1.96 86.9% 21.37 52.8%

M1 Rank ordered

Without inter-site correlation

1.12 719 1.82 80.3% 16.91 8.20%

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Figure 3-1. Population mean depositions (in micrograms) of the typical CI profiles used for simulations in this study: A) Rank-ordered M8 profile B) Non-rank-ordered M8 profile C) Rank-ordered M1 profile D) Rank-ordered M6 profile E) PQRI scenario no. 20 profile F) Illustration of the generation of T product population mean vector with ±Y% mean difference on all deposition sites from its corresponding R product M8 profile (modified from (11)). Rank-ordered implies that the deposition sites are ordered by decreasing magnitude of mean amount deposition

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Figure 3-2. Flowchart of MmCSRS test algorithm (modified from Weber et al, 2014). Default values of algorithm related factors: N = 30; B = 2000; X = ±25%

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Figure 3-3. Plot showing the effect of number of bootstrap iterations on the outcome of MmCSRS test. A) Variation in the test statistic (U90) as a function of number of bootstrap iterations B) Variation in the pass rate outcome of MmCSRS test as a function of number of bootstrap iterations

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Figure 3-4. Power curves showing the effect of population mean differences (0%, 10%, 15%, 20% and 25%) across all deposition sites of T and R CI profiles on the power of MmCSRS test at ±25% acceptance limit as a function of variability of the CI profiles

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Figure 3-5. Power curves showing the effect of sample size (N = 15, N = 30 and N = 60) on the power of MmCSRS test at ±25% acceptance limit as a function of variability of the CI profiles

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Figure 3-6. Power curves showing the effect of population T/R variance ratio (1:1, 1:4 and 4:1) across all deposition sites of T and R CI profiles on the power of MmCSRS test at ±25% acceptance limit as a function of variability of the CI profiles

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Figure 3-7. Power curves showing the effect of high vs low deposition site population mean differences (All 20%: ±20% population mean difference across all deposition sites of T and R CI profiles; All 0%: no population mean difference across all deposition sites of T and R CI profiles; High 20%: ±20% population mean difference across only high deposition sites of T and R CI profiles; Low 20%: ±20% population mean difference across only low deposition sites of T and R CI profiles) on the power of MmCSRS test at ±25% acceptance limit as a function of variability of the CI profiles

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Figure 3-8. mCSRS test critical value plots derived from different CI profile patterns and dataset generation method. M8: M8 CI profile, M1: M1 CI profile, ISC: Inter-site correlation, RO: Rank-ordered, NRO: Non-rank ordered, ITP: Iterative procedure, w/o: without, w: with. On x-axis, variability of the R CI profiles is displayed as the squared inverse of the co-efficient of variation (%CV)

85

Figure 3-9. Plot showing the effect of normalization of the CI profiles on the variability of each deposition site A) For datasets with inter-site correlation B) For datasets without inter-site correlation (‘X’ represents %CV before normalization and ‘N’ represents %CV after normalization of the CI profiles)

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Figure 3-10. Plot showing the effect of incorporation of inter-site correlation within the Monte Carlo simulation of datasets on the outcome of MmCSRS test across the 55 PQRI scenarios

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CHAPTER 4 A SEMI-PHYSIOLOGICAL PHARMACOKINETIC APPROACH FOR ASSESSING THE

BIOEQUIVALENCE OF DRY POWDER INHALER FORMULATIONS OF FLUTICASONE PROPIONATE

Background

Unlike oral drugs, the bioequivalence (BE) assessment of orally inhaled drug

products (OIDPs) is challenging, as drug plasma concentrations are downstream to the

sites of action in the lung (36). Currently, FDA recommends the aggregate weight of

evidence approach, which involves the in vitro, pharmacokinetic (PK) and comparative

clinical endpoint or pharmacodynamic (PD) BE assessment of OIDPs, in addition to

formulation sameness and device similarity (37–40). It is important to note that the

process of establishing PD BE is often hampered by poor dose response relationship of

highly variable endpoints (e.g. FEV1: Forced Expiratory Volume in one second) for

several OIDPs (6–8). It is believed that for explaining the comparative pulmonary

efficacy of OIDPs, three questions need to be addressed: (1) Is the available pulmonary

dose equivalent? (2) Is the mean pulmonary residence time equivalent? (3) Is the

regional lung deposition equivalent? Most subject matter experts agree that PK can

capture the former two aspects in the absence of oral absorption (36).

Given the pulmonary anatomy and physiology, we hypothesized that PK should

be able to capture regional deposition differences between fluticasone propionate (FP)

dry powder inhaler (DPI) formulations (41). The defensive mechanism of muco-ciliary

clearance (MCC) is primarily expressed in central lung regions. For slowly dissolving

drugs such as fluticasone propionate, if a formulation is preferentially deposited more in

the central lung region, more drug would be removed by MCC leading to lower AUC

(area under the plasma concentration-time profile) compared to a formulation that is

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preferentially deposited more in the peripheral lung region (3,42,43). The absorption

process in the peripheral lung region is faster (compared to central lung region) due to

thinner membranes. If a formulation is preferentially deposited more in the peripheral

lung region, it should show higher Cmax (peak plasma concentration) compared to the

one that deposits more centrally. Thus hypothetically, two formulations, that deposits

same lung dose but to different regions of the lung, should have different AUC and

Cmax (3).

To test our hypothesis whether PK can detect differences in regional lung

deposition, three carrier-based dry powder inhaler (DPI) formulations (A-4.5 µm, B-3.8

µm and C-3.7 µm) of fluticasone propionate (FP, a slowly dissolving candidate drug with

negligible oral bioavailability) were manufactured with the intent of achieving different

regional lung depositions, but similar lung doses. These formulations were thoroughly

characterized by multiple in vitro approaches, followed by a crossover PK study in 24

healthy volunteers (Hochhaus and Chen et al, unpublished).

The average of in vitro ex-throat dose determined from various anatomical

throats, a surrogate measure for deposited lung dose, was found to be different for the

three FP DPI formulations (Hochhaus and Chen et al., unpublished). Hence, a dose

normalization factor (A-4.5 µm : B-3.8 µm : C-3.7 µm = 1.00 : 1.30 : 1:20) was applied to

the PK data to account for lung dose differences between the formulations. It was

established from transwell dissolution experiments that formulation A-4.5 µm dissolves

slowly (mean dissolution time, MDT = 15.4 h) compared to the other two formulations B-

3.8 µm (MDT = 13.3 h) and C-3.7 µm (MDT = 10.3 h) (Amini and Kurumaddali et al.,

unpublished). The dose-adjusted Cmax of formulation A-4.5 µm was found to be

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significantly lower than that of formulations B-3.8 µm and C-3.7 µm. However, it was not

clear if this observed difference in the dose adjusted Cmax was due to differences in

dissolution rate or regional deposition (central to peripheral lung deposition ratio, CP

ratio).

To understand the regional deposition differences across the three FP DPI

formulations, a population pharmacokinetic (pop PK) model with two parallel first order

absorption processes (i.e., one slow, presumably from central lung regions, and one

fast, presumably peripheral lung regions) and three body compartments was

established previously (Drescher et al, unpublished). In this paper, a semi-physiological

PK model was developed (integrating the in vitro/physicochemical properties and

physiological lung parameters) to describe the lung absorption processes

mechanistically and link the pop PK regional deposition/absorption estimates to regional

lung physiology/anatomy. This semi-physiological model together with the in vitro

dissolution experiments was eventually used to evaluate the sensitivity of the PK

(especially peak plasma concentration) to central and peripheral regional lung

deposition differences between the formulations. In other words, we investigated if the

observed dose adjusted Cmax differences between formulations can be attributed to

dissolution rate differences alone or if it is a composite effect of both dissolution rate

and regional deposition differences across the formulations.

Methods

Semi-Physiological Modeling of Population Pharmacokinetics (Pop PK) Derived Absorption Profiles of Fluticasone Propionate (FP) Dry Powder Inhaler (DPI) Formulations

The central and peripheral lung dose, absorption rate constants of three FP DPI

formulations (A-4.5 µm, B-3.8 µm and C-3.7 µm) were estimated previously by

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population pharmacokinetic (pop PK) analysis. Briefly, three FP DPI formulations

prepared using the same batch of active pharmaceutical ingredient (FP) but different

amount and particle size distribution of lactose fines were administered in a single-

center, single-dose, double-blinded, four-way crossover pharmacokinetic clinical study

with 24 healthy subjects. A pop PK model with two parallel first order absorption

processes (i.e., one slow, presumably from central lung regions, and one fast,

presumably peripheral lung regions) and three body compartments developed in S-

ADAPT software (v 1.57) described the observed PK profiles of the three FP DPI

formulations well (Drescher et al, unpublished, will be published elsewhere). The mean

pop PK estimates for the three formulations along with the systemic compartment model

parameters for fluticasone propionate (FP) are shown in Table 4-1. To describe the

pulmonary absorption processes mechanistically and link it to the pulmonary anatomy

and physiology, the semi-physiological model structure shown in Figure 4-1 was

employed. The mechanistic pulmonary absorption profiles both in central and peripheral

lung regions were generated by considering four pulmonary events in sequence:

pulmonary deposition pattern of lung dose in the airway lumen, dissolution of solid lung

dose in the airway surface liquid (ASL), permeation of the dissolved drug through the

pulmonary tissue and perfusion into the systemic circulation. This semi-physiological

model describing the four pulmonary events was developed with the help of pop PK

derived central and peripheral lung absorption profiles of formulation C-3.7 µm.

Subsequently, the semi-physiological model was validated against the population PK

absorption profiles and observed PK data of the other two formulations (A-4.5 µm and

B-3.8 µm).

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Semi-physiological PK model structure and input parameters

Determination of pulmonary deposition pattern of lung dose: For

mechanistic modeling of dissolution process in the lung, the pulmonary deposition

pattern of lung dose i.e. the in vivo particle size distribution of the deposited lung dose in

different regions of the lung (central and peripheral regions) is a required input

parameter. First, the in vitro aerodynamic particle size distribution of a given formulation

was determined by Catalent using the next generation impactor (NGI) at 60 L/min as

described previously (Hochhaus and Chen et al., unpublished). Subsequently, using the

NGI profile as an input, the regional lung deposition pattern of the formulation was

determined using the lung deposition module in Mimetikos Preludium software, a

program that calculates aerosol deposition in the human respiratory tract using

algebraic equations for particle impaction, sedimentation and diffusion. The lung

deposition pattern was determined for a healthy human male adult with average PIFR of

132.9 L/min and tidal volume of 1680 ml. In each region of the lung, the fraction of dose

that corresponds to the bin (total 8 bins per each lung region) of a particular

aerodynamic diameter was determined. While the central lung deposition pattern was

obtained as the sum of fractions deposited in tracheobronchial (BB) and bronchiolar

(bb) regions of the lung (generations 1-15 of Weibull lung model), the peripheral lung

deposition pattern was obtained from the alveolar region (generations 16-23 of Weibull

lung model). For each bin of a given aerodynamic diameter and region of the lung, the

amount of deposited dose was obtained by multiplying the pre-determined fraction (from

Mimetikos Preludium) with the total lung dose deposited in that particular lung region

(central or peripheral region dose as estimated from pop PK).

Xc0i = Frci * Xc0

92

Xp0i = Frpi * Xp0

Where

i = bin number (1 to 8); each bin is characterized by its aerodynamic diameter

Xc0i = dose deposited in bin ‘i’ of central lung region

Frci = fraction of central lung regional dose deposited in bin ‘i’

Xc0 = dose absorbed from the central lung region as estimated by pop PK

Xp0i = dose deposited in bin ‘i’ of peripheral lung region

Frpi = fraction of peripheral lung regional dose deposited in bin ‘i’

Xp0 = dose absorbed from the peripheral lung region as estimated by pop PK

Modeling of dissolution, permeation and perfusion processes in the

peripheral lung region (fast absorption process): The peripheral lung deposition

pattern as determined in the above step was used as input parameter for mechanistic

modeling of dissolution process. In each bin ‘i’ (i = 1 to 8) of peripheral lung region, the

dissolution of deposited dose in the airway surface liquid (ASL) was described by the

Nernst-Brunner process shown below. The total dissolved drug amount in the peripheral

lung region at any given time was obtained by summing up the dissolved amount of

drug in all the eight bins.

𝑑𝑋𝑝𝑖

𝑑𝑡=

−3 ∗ 𝐷 ∗ 𝑋𝑝0𝑖(23

) ∗ 𝑋𝑝𝑖(13

) ∗ (𝐶𝑠 − 𝑋𝑝𝑑 ∗ 𝑓𝑢𝑙

𝑉𝑝𝑙 )

𝑟0𝑖2 ∗ 𝜌

𝑟0𝑖2 = 𝑑𝑔𝑒𝑜𝑖

2

𝑑𝑔𝑒𝑜𝑖 = 𝑑𝑎𝑒𝑟𝑜𝑖 ∗ √𝑠

𝜌

93

Where Xpi = amount of undissolved drug in each bin ‘i’ of the peripheral lung

region at any time = t

Xp0i = dose deposited in bin ‘i’ of peripheral lung region

Xpd = amount of dissolved drug in the ASL in the peripheral lung region at time ‘t’

r0i = radius of the particles in bin ‘i’ at time t = 0

dgeoi = geometric diameter of the particles in bin ‘i’ at time t = 0

daeroi = aerodynamic diameter of the particles in bin ‘i’ at time t = 0

Both ‘daeroi’ and ‘Xp0i’ were obtained from the peripheral lung deposition pattern

as described above. Both drug-related and lung physiological model parameters

obtained from the literature are shown in Table 4-2. The fraction of unbound drug in the

ASL (ful) was assumed to be equal to one. Due to lack of availability of data on human

lung permeability, the permeability of ex vivo rat lung was taken as the peripheral lung

permeability. The only unknown parameter, saturation solubility of fluticasone

propionate in the ASL (Cs) was estimated with the help of pop PK derived absorption

profile (for formulation C-3.7 µm) using ‘deSolve’ (for solving differential equations) and

‘minpack.lm’ (for fitting by the Levenberg-Marquardt routine) packages in R software (v

3.5.2).

The permeation of the dissolved drug from the ASL into the lung tissue was

modeled by Fick’s law. The perfusion rate per unit volume of tissue was obtained from

the literature. The model parameters are shown in Table 4-2 and the system of

differential equations describing absorption process from the peripheral lung region are

given below:

Step 1: Drug lost from the ASL by dissolution

94

𝑑𝑋𝑝𝑖

𝑑𝑡=

−3∗𝐷∗𝑋𝑝0𝑖(

23)

∗𝑋𝑝𝑖(

13)

∗(𝐶𝑠− 𝑋𝑝𝑑∗𝑓𝑢𝑙

𝑉𝑝𝑙)

𝑟0𝑖2∗ 𝜌

Step 2: Drug gained by dissolution from ASL; Drug lost by permeation to the lung

tissue

𝑑𝑋𝑝𝑑

𝑑𝑡= − ∑

𝑑𝑋𝑝𝑖

𝑑𝑡

𝑖=8

𝑖=1

− 𝑃𝑝 ∗ 𝐴𝑝 ∗ (𝑋𝑝𝑑 ∗ 𝑓𝑢𝑙

𝑉𝑝𝑙−

𝑋𝑝𝑡

𝑉𝑝𝑡 ∗ 𝐾𝑝𝑢)

Step 3: Drug gained by lung tissue through permeation from the ASL; Drug lost

by perfusion to the systemic circulation

𝑑𝑋𝑝𝑡

𝑑𝑡= 𝑃𝑝 ∗ 𝐴𝑝 ∗ (

𝑋𝑝𝑑 ∗ 𝑓𝑢𝑙

𝑉𝑝𝑙−

𝑋𝑝𝑡

𝑉𝑝𝑡 ∗ 𝐾𝑝𝑢) − 𝑄𝑝 ∗ 𝑉𝑝𝑡 ∗ (

𝑅𝑏𝑝

𝑓𝑢𝑝)

∗ (𝑋𝑝𝑡

𝑉𝑝𝑡 ∗ 𝐾𝑝𝑢−

𝑋𝑝𝑠 ∗ 𝑓𝑢𝑝

𝑉𝑝𝑠 ∗ 𝑅𝑏𝑝)

Step 4: Drug gained by systemic circulation through perfusion from the lung

tissue

𝑑𝑋𝑝𝑠

𝑑𝑡= 𝑄𝑝 ∗ 𝑉𝑝𝑡 ∗ (

𝑅𝑏𝑝

𝑓𝑢𝑝) ∗ (

𝑋𝑝𝑡

𝑉𝑝𝑡 ∗ 𝐾𝑝𝑢−

𝑋𝑝𝑠 ∗ 𝑓𝑢𝑝

𝑉𝑝𝑠 ∗ 𝑅𝑏𝑝)

Where

Xpt = amount of dissolved drug in the peripheral lung region tissue at time ‘t’

Xps = amount of dissolved drug in the systemic circulation absorbed from the

peripheral lung region at time ‘t’

Modeling of dissolution, permeation and perfusion processes in the central

lung region (slow absorption process): The system of differential equations used for

modeling central lung region absorption profiles are similar to that of peripheral lung

95

region with the exception that the parameters represent the central lung physiology (see

Table 4-2) and the model describes the amounts in the central lung region. The

saturation solubility (Cs) in the central lung region was assumed to be identical to the

Cs estimated in the peripheral lung region. The only unknown parameter, permeability

of the drug from the ASL to the lung tissue in central lung region was estimated with the

help of population PK derived absorption profile (for formulation C-3.7 µm) using

‘deSolve’ (for solving differential equations) and ‘minpack.lm’ (for fitting by the

Levenberg-Marquardt routine) packages in R software (v 3.5.2).

Validation of the Semi-Physiological Model

The semi-physiological model developed in step (a) developed based on

formulation C-3.7 µm PK data was validated by simulating the absorption profiles for the

other two formulations (A-4.5 µm and B-3.8 µm). The following input parameters were

used to generate absorption profiles of formulations A-4.5 µm and B-3.8 µm for

validation:

The ‘Cs’ and ‘Pc’ estimates obtained in step (a)

The central and peripheral lung doses obtained from pop PK (see Table 4-1),

Other physiological and drug related parameters shown in Table 4-2 and

The relative dissolution rates of formulations (with respect to formulation C-3.7

µm as reference) obtained from transwell dissolution experiments were used as input

parameters.

The Transwell® dissolution experiments were conducted using the previously

published procedure (44–46). Briefly, the respirable fraction of each formulation was

collected as the dose passing through a mouth-throat model onto a 24 mm glass

microfiber filter paper (pore size of 0.45 µm, Whatman GF/C™). The collected dose

96

along with the filter paper was immediately transferred to the donor compartment (drug

facing down and sandwiched between filter paper and membrane) of the Transwell®

system (a six well 24mm Transwell® plate with 0.4 µm pore polyester membrane

inserts). The transferred samples were processed as described previously using 0.5%

Tween 80 in water as dissolution medium (with 1.5 mL in the receptor and 0.58 mL in

the donor compartment) and frequent serial sampling/replenishment of 0.5 mL over 24

h. Drug content was assayed by reversed phase HPLC. The cumulative amount of drug

entering the receptor compartment over the 24 h was plotted to obtain the in vitro

dissolution profiles. The procedure for obtaining relative dissolution rates of the

formulations will be published elsewhere (Amini and Kurumaddali et al., unpublished).

Briefly, the observed in vitro transwell dissolution profiles (percent transferred vs time)

of the three formulations were modeled by a system of differential equations which

described dissolution in the donor compartment through Nernst-Brunner equation

followed by permeation into the receptor compartment through Fick’s law. A formulation

specific fitting factor was introduced in the Nernst-Brunner part of the differential

equations, which was estimated by fitting to the observed Transwell® dissolution profiles

using ‘deSolve’ and ‘minpack.lm’ (Levenberg-Marquardt algorithm) packages in R

software (v 3.5.2). The ratio of these estimated formulation specific fitting factors

(defined as correction factor) represents the relative dissolution rate (or relative surface

area of the deposited particles) of the formulations. The relative dissolution rate of

formulations A-4.5 µm and B-3.8 µm was incorporated into the validation model

structure as a correction factor (Cf) in the Nernst-Brunner part of the system of

differential equations (for both central and peripheral lung regions) as shown below:

97

𝑑𝑋𝑝𝑖

𝑑𝑡=

−3 ∗ 𝐶𝑓 ∗ 𝐷 ∗ 𝑋𝑝0𝑖(23

) ∗ 𝑋𝑝𝑖(13

) ∗ (𝐶𝑠 − 𝑋𝑝𝑑 ∗ 𝑓𝑢𝑙

𝑉𝑝𝑙)

𝑟0𝑖2 ∗ 𝜌

Where Cf = correction factor representing the relative dissolution rate of

formulation B-3.8 µm (= 0.65) and formulation A-4.5 µm (=0.46) with respect to

formulation C-3.7 µm as reference.

Evaluation of the Sensitivity of Peak Plasma Concentration (Cmax) of FP to the Regional Lung Deposition Differences of the DPI Formulations

By combining the semi-physiological central and peripheral lung region

absorption profiles generated above together with the systemic compartment mean pop

PK parameters (see Table 4-1), PK profiles of the three formulations were generated

and compared against the observed data obtained from the clinical study. While

keeping the central, peripheral pulmonary dose and dissolution rate constant, the Cmax

was determined over a range of the regional deposition/ central to peripheral ratio (CP

ratio) = 1:4, 1:3, 1:2, 1:1, 2:1, 3:1 and 4:1 for establishing the relationship between

Cmax and CP ratio. Subsequently, we assessed if one needs to account for regional

deposition (CP ratio) in addition to dissolution rate differences for explaining the

observed differences in the dose adjusted Cmax of the three DPI formulations. The

contribution of dissolution rate differences to dose adjusted Cmax differences was

estimated by integrating relative surface area of formulations (obtained through

transwell dissolution profile modeling as described above) into the semi-physiological

PK model. After accounting for dissolution rate differences between the formulations,

any difference in the dose adjusted Cmax of the formulations was rightly attributed to

the only variable, CP ratio differences between the formulations.

98

Results

The regional lung deposition pattern of formulation C-3.7 µm is shown in Table 4-

3. The fraction of larger particles deposited in central lung region is higher compared to

the peripheral lung region. The fitted central and peripheral lung semi-physiological

absorption profiles (NB + Fick’s law) of formulation C-3.7 µm are shown in Figure 4-2. In

the peripheral lung region, the fitted saturation solubility (Cs) described the observed

pop PK absorption profile reasonably well. The estimated Cs (Table 4-4) was found to

be precise and close to the water solubility of fluticasone propionate reported in the

literature (0.41 to 0.51 mcg/mL). Similarly, the estimated permeability in the central lung

region (Pc) also described the observed pop PK absorption profile reasonably well and

was found to be precise (Table 4-4). The estimated ‘Pc’ was found to be approximately

one-fifth of the peripheral lung permeability indicating that the central lung region has

thicker membranes compared to the peripheral lung region, which agrees with the

anatomy and physiology of these lung regions.

As a consequence of the permeability differences in different regions of the lung,

while the in vivo dissolution profile (in ASL) completely overlaps with the absorption

profile of peripheral lung region, the absorption rate is much slower in the central lung

region (see Figure 4-3). In addition, as shown in Figure 4-4, despite the low solubility of

FP, the high permeability in the peripheral lung region led to short pulmonary residence

time (less than 30 min). On the other hand, longer pulmonary residence time (> 5 h)

was observed in the central lung region due to low permeability of FP in the upper

airways, which primarily contributed to the overall long mean residence time of FP.

The predicted semi-physiological absorption profiles of formulations B-3.8 µm

and A-4.5 µm obtained by applying correction factors to the dissolution rate (with

99

respect to formulation C) are in good agreement with their corresponding pop PK

absorption profiles (see Figure 4-5) indicating that the semi-physiological model can

capture differences in the absorption rate of the formulations reasonably well. Further,

the semi-physiological PK profiles of all the three formulations are in good agreement

with their respective concentration-time profiles obtained from the clinical study (see

Figure 4-6). Thus, the established semi-physiological PK model successfully linked the

regional absorption pop PK estimates to lung anatomy and physiology.

From the PK profiles simulated using the validated semi-physiological model, the

relationship between peak plasma concentration (Cmax) and regional lung deposition

was identified. The Cmax decreased monoexponentially with CP ratio and increased

linearly with the fraction of peripheral lung dose indicating that the PK might be sensitive

to regional lung deposition differences (see Figure 4-7). The observed difference in the

dose-normalized Cmax of formulations C-3.7 µm and A-4.5 µm could be explained only

after adjusting for both dissolution rate (explained 39.8% of the observed difference in

dose-normalized Cmax) and regional lung deposition (explained 60.2% of the observed

difference in dose-normalized Cmax) differences between the formulations confirming

that the PK might be sensitive to central and peripheral regional lung deposition (CP

ratio) differences (see Figure 4-8).

Discussion

In this paper, a semi-physiological PK model was developed to assess if PK is

sensitive to regional deposition differences of FP DPI formulations. Previously, to

describe the systemic PK of FP DPI formulations, the lung was broadly divided into two

distinct regions: central and peripheral lung regions, each region characterized by its

deposited dose and absorption rate (slow absorption presumably from central lung and

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fast absorption presumably from peripheral lung) determined through pop PK analysis

(Drescher et al, unpublished). Contrary to other complex and expensive airway

dosimetry methods (semi-empirical, whole-lung one-dimensional, computational fluid

dynamics three-dimensional and in vivo gamma scintigraphy methods) which commonly

describe aerosol deposition pattern across the 23 generations of Weibull lung model,

pop PK analysis of systemic PK data to identify different regions of lung is much simpler

and straight forward (47–50). At the same time, in the absence of observed lung tissue

concentrations (which usually is the case since the target site in the lung are not easily

accessible for sampling), it was not possible to describe the pulmonary events in

different regions of the lung with higher resolution through pop PK analysis due to

parameter identifiability concerns (51). Hence, in this paper, a link was established

between the empirical Pop PK estimates and lung physiology/anatomy through semi-

physiological PK model to describe the pulmonary events of the three FP DPI

formulations mechanistically.

To develop a semi-physiological PK model comparable to that of the Pop PK

model, both tracheobronchial and bronchiolar regions (i.e. Weibull human lung model

generations 1 to 15) were considered to represent the pop PK central lung region. And

the alveolar region (i.e. Weibull human lung model generations 16 to 23) represented

the pop PK peripheral lung. The pop PK predicted total absorbed lung doses for the

three FP DPI formulations were within 68% to 89% of the deposited total lung doses

predicted from Mimetokis Preludium software through bottom-up approach (data not

shown). Similarly, the pop PK predicted total absorbed lung doses for the three FP DPI

formulations were within 61% to 74% of the in vitro ex-throat doses determined from

101

several anatomical throats, a surrogate for deposited pulmonary dose (data not shown).

This indicates that it is reasonable to use pop PK estimated absorbed regional lung

doses as an input parameter for generating semi-physiological lung absorption profiles.

As shown in Table 4-3, the fraction of larger particles deposited in central lung

region is higher compared to the peripheral lung region. This agrees with the published

literature that small particles are preferentially deposited in the peripheral lung region

through diffusion across the airways (13,52). For generating the semi-physiological

absorption profiles, we assumed that the permeability across lung tissue is conserved

between rats (=0.01368 cm/h) and humans due to non-availability of data from isolated

perfused human lung for ethical reasons (53,54). The estimated saturation solubility

(Cs) of fluticasone propionate (FP) in the airway surface liquid (ASL) was low (0.731

mcg/ml), which can be explained by the high lipophilicity of FP (55,56). The estimated

Cs was slightly higher than the water solubility of FP reported in the literature (0.41 to

0.51 mcg/ml) (55). The slightly higher estimated solubility of FP in the ASL might be due

to the presence of surfactants in the ASL (57). It might also be possible that the particle

size distribution (input parameter for describing Nernst-Brunner equation) obtained from

the aerodynamic particle size distribution (APSD) of the formulation doesn’t reflect the

true APSD of the active pharmaceutical ingredient (FP) or the ASL layer might be

smaller than the particle diameter in some regions of the peripheral lung (51). The

fraction of FP unbound in the ASL was assumed to be equal to one since data on the

binding of FP in the ASL was not available (58).

The estimated permeability of FP in the central lung region was found to be

approximately one-fifth of the alveolar permeability. It is well-known that the permeation

102

rate decreases with the increase in thickness of membranes for neutral small molecules

such as FP that rely on transcellular transport (58). Owing to the well-built thicker

membranes in the central lung region, the estimated central lung permeability was

found to be lower than the alveolar permeability as expected. If we scale the alveolar

permeability as per the thickness of membranes, the predicted central lung permeability

should lie within the range of 6.36E-05 cm/h (since the lung tissue in tracheobronchial

region is 217 times thicker than the alveolar lung tissue) to 0.00152 cm/h (since the lung

tissue in bronchiolar region is 9 times thicker than the alveolar lung tissue). In another

study, it was reported that for drugs primarily transported through transcellular

pathways, the central lung permeability was estimated to be one-tenth of the alveolar

region permeability through PBPK approach (58). However, the estimated central lung

permeability of 0.0027 cm/h is slightly higher than the predicted value (based on scaling

by membrane thickness) and is only one-fifth of the alveolar permeability. It should be

noted that there are currently no established methods for measuring the human central

lung permeability and any discrepancies in the estimated value across different studies

might be attributed to a higher resolution heterogeneity of human lung which was not

feasible to capture in the current model (58).

Despite of having same solubility in the ASL of both central and peripheral lung

regions, the absorption rate of FP from the central lung region is much slower compared

to the peripheral lung region (59). As shown in Figure 4-3, the lower permeability of

central lung region slowed down the absorption of dissolved drug in the central lung

region due to non-sink conditions i.e. the concentration of FP in the ASL was higher

than one-tenth of the saturation solubility of FP (Cs, Figure 4-4) (56). On the other hand,

103

in the peripheral lung region, due to high permeability of FP across the thin membranes

of alveoli, sink conditions (i.e. the concentration of FP in the ASL was always lower than

one-tenth of the saturation solubility of FP) were always maintained resulting in faster

absorption of FP (see Figure 4-3 and Figure 4-4). Because of this differential regional

permeability, it would be much easier to achieve pulmonary targeting with a formulation

that deposits preferentially in the central lung regions as compared to the one that

deposits more peripherally for drugs such as FP (51).

The developed semi-physiological PK model was validated by generating the

absorption profiles of the other two formulations (A-4.5 µm and B-3.8 µm) through pure

simulation (i.e. Cs and Pc parameters were fixed to the values shown in Table 4-4) only

accounting for differences in the dissolution rate by incorporating correction factors in

the model. The dissolution rates of the formulations were measured through a

previously established in vitro transwell dissolution system that closely mimics the lung

lining fluid capacity limited dissolution process occurring in vivo (45,46,55). It has been

previously shown through experimentation that the transwell dissolution system can

capture differences in the dissolution rate of formulations that differ in their APSD (55).

Thus, any differences in the deposition pattern of the formulations was indirectly

accounted by correcting for dissolution rate differences (measured from transwell

dissolution experiments) across the formulations. In fact, any biorelevant dissolution

assay that can capture dissolution rate differences of formulations may be employed for

obtaining the dissolution rate correction factors (57).

The simulated central and peripheral lung semi-physiological absorption profiles

agreed with their respective Pop PK absorption profiles and the fitted/simulated semi-

104

physiological PK profiles described the observed plasma concentration-time profiles of

the three FP DPI formulations well. The simulated PK profiles and the ASL

concentration-time profiles are not entirely smooth owing to the discrete particle size

distribution employed in the semi-physiological model. Had a more continuous

deposition pattern was employed for this purpose, it would have resulted in smoother

PK profiles closely matching the observed PK profiles at the expense of decreasing

computational efficiency of the model. Nonetheless, the Cmax and AUC of the semi-

physiological PK profiles are within 75% to 125% of the observed PK profiles (data not

shown) indicating that the current semi-physiological PK model successfully calibrated

and linked the Pop PK empirical regional lung parameter estimates to lung physiology

and anatomy. This semi-physiological model might be easily extended to other drugs

showing similar solubility as that of FP. However, further analysis would be required to

claim the utility of this model for other drug classes (41).

The semi-physiological PK model simulations (see Figure 4-7) suggested that the

Cmax increased linearly with increase in fraction of peripheral lung deposited dose and

vice-versa (see Figure 4-7). Furthermore, the simulations indicated that the observed

difference in the dose-adjusted Cmax of the formulations could not be explained by

dissolution rate differences (caused due to differences in the microstructure of

agglomerated particles) alone and the regional deposition (CP ratio) adjustment indeed

explained 60% of the observed difference in the dose adjusted Cmax of formulations C-

3.7 µm and A-4.5 µm (see Figure 4-8). In this simulation study based on the observed

clinical study data, 4-fold lower CP ratio for formulation C-3.7 µm (compared to

formulation A-4.5 µm) led to 1.9-fold higher dose adjusted Cmax (see Figure 4-8) for

105

formulation C-3.7 µm, which is much higher than the observed within subject variability

of 28.7% for Cmax in the current clinical study (Hochhaus and Chen et al, unpublished).

It is interesting to see that the dose adjusted Cmax can be used to effectively

distinguish the regional deposition differences of two FP DPI formulations that differ in

their MMAD by only 0.8 µm. However, further Monte Carlo simulation and power

analysis is required to figure out the minimum difference (in the MMAD of FP DPI

formulations) that can be effectively distinguished by PK/dose adjusted Cmax.

It is worthwhile mentioning that in the current study, we couldn’t explore the utility

of dose normalized AUC in detecting the regional deposition differences of the FP DPI

formulations. Initially, we hypothesized that for slowly dissolving drugs like FP,

formulations with higher CP ratio will be removed more by muco-ciliary clearance

(MCC) and will have lower AUC compared to the ones with same pulmonary dose and

lower CP ratio (3). However, as indicated by the NGI studies (stages 2 and 3, Hochhaus

and Chen et al, unpublished), in our study, the amount of centrally deposited drug may

have been similar for the three formulations. Therefore, MCC may have removed

comparable amounts of drug for the three formulations, resulting in similar AUC

estimates after dose normalization (Hochhaus and Chen et al, unpublished). Thus, we

couldn’t identify and mechanistically describe the influence of MCC on the FP DPI

formulations as well as couldn’t investigate the sensitivity of dose normalized AUC to

regional lung deposition differences of the formulations. Nevertheless, our study

confirmed that dose normalized Cmax is sensitive to regional deposition differences

across FP DPI formulations. Hence, PK may be used for providing supportive evidence

in the BE assessment of OIDPs without the need for conducting endpoint PD studies.

106

Conclusion

The regional deposition and absorption rate estimates obtained through Pop PK

analysis for one of the FP DPI formulations (C-3.7 µm) were calibrated and linked to

regional lung anatomy and physiology by establishing a semi-physiological PK model.

The semi-physiological PK model was characterized by differential regional lung

permeability of FP (low permeability in the central lung region and high permeability in

the peripheral lung region). With the support of in vitro dissolution experiments, the

established semi-physiological PK model was validated using the observed PK data of

the other two FP DPI formulations (A-4.5 µm and B-3.8 µm). The semi-physiological

model simulations along with the observed clinical study data confirmed that the dose

adjusted Cmax can detect regional deposition differences across FP DPI formulations.

Therefore, our study and the modeling approach suggested that PK may be used in lieu

of the time consuming and resource intensive PD endpoint studies to support generic

drug development of OIDPs (drug products containing slow dissolving drugs such as FP

as active ingredient).

107

Table 4-1. Mean population pharmacokinetics model estimates of the three fluticasone propionate (FP) dry powder inhaler (DPI) formulations: A-4.5 µm, B-3.8 µm and C-3.7 µm

Formulation Parameter Central lung Peripheral lung

A-4.5 µm Dose (µg) 30.4 8.55 B-3.8 µm Dose (µg) 30.45 28.3 C-3.7 µm Dose (µg) 26.35 30.05 A-4.5 µm Ka (1/h) 0.261 2.557 B-3.8 µm Ka (1/h) 0.423 5.457 C-3.7 µm Ka (1/h) 0.420 5.5

Systemic parameter Value [unit]

Volume of central compartment (V1) 60.4 L

Volume of shallow peripheral compartment (V2) 48.8 L

Volume of deep peripheral compartment (V3) 437 L

Clearance of central compartment (CL) 61.7 L/h

Distributional clearance of shallow peripheral compartment (CLD1) 158 L/h

Distributional clearance of deep peripheral compartment CLD2 50.6 L/h

108

Table 4-2. Semi-physiological PK model parameters obtained from Mimetokis

Preludium software

Parameters related to lung physiology

Central lung:

Surface area (Ac) 4800 cm2

Volume of airway surface liquid (Vcl) 3.063 mL

Volume of lung tissue (Vct) 34.065 mL

Normalized blood flow (Blood flow per tissue volume, Qc) 730 1/h

Peripheral lung:

Surface area (Ap) 4800 cm2

Volume of airway surface liquid (Vpl) 3.063 mL

Volume of lung tissue (Vpt) 34.065 mL

Normalized blood flow (Blood flow per tissue volume, Qp) 730 1/h

Parameters related to drug (fluticasone propionate)

Diffusion co-efficient (D) 0.0204 cm/h

Density (ρ) 1.4 g/mL

Shape factor (s) 1

Fraction unbound in airway surface liquid 1

Unbound tissue/plasma ratio (Kpu) 35.95

Fraction unbound in plasma (fup) 0.0306

Blood to plasma partition co-efficient (Rbp) 0.95

Peripheral lung permeability (Pp) 0.01368 cm/h

109

Table 4-3. Deposition pattern of formulation C-3.7 µm determined using the lung deposition module in the Mimetokis Preludium software

Table 4-4. Estimated parameters of the semi-physiological PK model using the Pop PK derived absorption profiles

Model parameter Mean estimate

% RSE

Saturation solubility of FP in the airway surface liquid (Cs)

0.731 µg/ml

1.51

Permeability of FP in the central lung region

0.0027 cm/h

3.66

Bin ‘i’ 1 2 3 4 5 6 7 8

Aerodynamic

diameter

(daeroi)

9.56 5.37 4.18 2.16 1.52 0.76 0.45 0.02

Fraction of

deposited

dose in

central lung

region (Frci)

0.83% 20.56% 37.89% 30.15% 9.41% 0.82% 0.34% 0%

Fraction of

deposited

dose in

peripheral

lung region

(Frpi)

0% 2.31% 11.61% 53.60% 27.85% 3.72% 0.9% 0%

110

Figure 4-1. Semi-physiological PK model structure

111

Figure 4-2. Comparison of the fitted semi-physiological absorption profiles (NB + Fick’s

law) with that of population PK derived absorption profiles for formulation C-3.7 µm A) in peripheral lung region B) in central lung region

112

Figure 4-3. Comparison of the in vivo dissolution profiles in the airway surface liquid,

ASL (purple color) with that of absorption profiles (red color) in A) peripheral lung region B) central lung region. The orange curve in B) represents the permeation of saturated solution of fluticasone propionate from ASL across the lung tissue

113

Figure 4-4. Concentration-time profiles of dissolved drug in the airway surface liquid of

A) peripheral lung region B) central lung region

114

Figure 4-5. Predicted absorption profiles of formulations A-4.5 µm and B-3.8 µm using

the semi-physiological model in comparison to their respective population PK derived absorption profiles: A) Peripheral lung region absorption profile of formulation A-4.5 µm B) Central lung region absorption profile of formulation A-4.5 µm C) Peripheral lung region absorption profile of formulation B-3.8 µm D) Central lung region absorption profile of formulation B-3.8 µm

115

Figure 4-6. Predicted PK profiles of FP DPI formulations using semi-physiological PK

model in comparison to the observed PK data from the clinical study A) Formulation A-4.5 µm B) Formulation B-3.8 µm and C) Formulation C-3.7 µm

116

Figure 4-7. Semi-physiological PK model predicted relationship between peak plasma

concentration (ng/L) and regional lung deposition of FP DPI formulations

117

Figure 4-8. Semi-physiological PK model simulations showing the sensitivity of dose

normalized Cmax to regional lung deposition differences (or CP ratio differences)

118

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BIOGRAPHICAL SKETCH

Abhinav Kurumaddali was born in Machilipatnam, India in 1991. He received

Master of Pharmacy degree from Birla Institute of Technology, India in 2014. Thereafter,

he joined the research group of Dr. Guenther Hochhaus at the Department of

Pharmaceutics (College of Pharmacy, University of Florida), for pursuing a non-

traditional MS/Ph.D. degree program. His research focused on the evaluation of novel

approaches (statistical, in vitro and pharmacokinetic methods) for establishing

bioequivalence of inhalation drug products. Abhinav has been awarded a fellowship of

the Oak Ridge Institute for Science and Education in 2016 for pursuing his summer

internship at the Office of Generic Drugs, Center of Drug Evaluation and Research,

Food and Drug Administration, Silver Springs, MD. He also gained insights into PK and

PKPD modeling and simulation during different stages of drug development as research

intern at Abbvie Inc., Chicago. Abhinav presented his research at several international

conferences. He received his MS in Biostatistics from the University of Florida in May

2019 and Ph.D. in December 2019.

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