Pharmacometric Modeling in Rheumatoid Arthritis799066/FULLTEXT01.pdf · Rheumatoid arthritis...

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ACTA UNIVERSITATIS UPSALIENSIS UPPSALA 2015 Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy 199 Pharmacometric Modeling in Rheumatoid Arthritis BRIGITTE LACROIX ISSN 1651-6192 ISBN 978-91-554-9221-2 urn:nbn:se:uu:diva-247917

Transcript of Pharmacometric Modeling in Rheumatoid Arthritis799066/FULLTEXT01.pdf · Rheumatoid arthritis...

ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2015

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Pharmacy 199

Pharmacometric Modeling inRheumatoid Arthritis

BRIGITTE LACROIX

ISSN 1651-6192ISBN 978-91-554-9221-2urn:nbn:se:uu:diva-247917

Dissertation presented at Uppsala University to be publicly examined in B42, BMC, Uppsala,Friday, 22 May 2015 at 13:15 for the degree of Doctor of Philosophy (Faculty of Pharmacy).The examination will be conducted in English. Faculty examiner: Dr. Ekaterina Gibiansky.

AbstractLacroix, B. 2015. Pharmacometric Modeling in Rheumatoid Arthritis. Digital ComprehensiveSummaries of Uppsala Dissertations from the Faculty of Pharmacy 199. 68 pp. Uppsala: ActaUniversitatis Upsaliensis. ISBN 978-91-554-9221-2.

Biologic therapies have revolutionized the treatment of rheumatoid arthritis, a commonchronic inflammatory disease, mainly characterized by the chronic inflammation of the joints.The activity and progression of the disease are highly variable, both between subjects andbetween the successive assessments for the same subject. Standardized assessments of clinicalvariables have been developed to reflect the disease activity and evaluate new therapies.Pharmacokinetics-pharmacodynamic (PKPD) models and methods for analyzing the generatedtime-course data are needed to improve the interpretation of the clinical trials’ outcomes, andto describe the variability between subjects, including patients characteristics, disease factorsand the use of concomitant treatments that may affect the response to treatment. In addition,good simulation properties are also desirable for predicting clinical responses for variouspopulations or for different dosing schedules. The aim of this thesis was to develop methods andmodels for analyzing pharmacokinetic and pharmacokinetic-pharmacodynamic (PKPD) datafrom rheumatoid arthritis patients, illustrated by treatment with a new anti-TNFα biologic drugunder clinical development, certolizumab pegol.

Two models were developed that characterized the relationship between the exposure to thedrug and the efficacy ACR variables that represent improvement of the disease; a logistic-type Markov model for 20% improvement (ACR20) and a continuous-type Markov model forsimultaneous analysis of 20% (ACR20), 50% (ACR50) and 70% (ACR70) improvement. Bothmodels accounted for the within-subjects correlation in the successive clinical assessments andwere able to capture the observed ACR responses over time. Simulations from these models ofthe ACR20 response rate supported dosing regimens of 400 mg at weeks 0, 2 and 4 to achievea rapid onset of response to the treatment, followed by 200 mg every 2 weeks, or alternativemaintenance regimen of 400 mg every 4 weeks.

The immunogenicity induced by the biologic drug was characterized by a time to event modeldescribing the time to appearance of antibodies directed against the drug. The immunogenicitywas predicted to appear mainly during the first 3 months following the start of the treatment andto be reduced at higher trough concentrations of CZP, as well as with concomitant administrationof MTX.

The full time-course of sequential events, such as dose-exposure-efficacy relations, is mostaccurately described by a simultaneous analysis of all data. However, due to the complexityand runtime limitations of such an analysis, alternatives are often used. In this thesis, a method,IPPSE, was developed and compared to the reference simultaneous method and to existingalternative methods. The IPPSE method was shown to provide accuracy and precision ofestimates similar to the simultaneous method, but with easier implementation and shorter runtimes.

In conclusion, two PKPD models and one immunogenicity model were developed forevaluation of the response of a biologic drug against rheumatoid arthritis that allowed accurateanalysis and simulation of clinical trial data, as well as serving as examples for how a model-informed basis for decisions about biological drugs can be created.

Keywords: rheumatoid arthritis, PKPD, immunogenicity, ACR, IPPSE, certolizumab pegol

Brigitte Lacroix, Department of Pharmaceutical Biosciences, Box 591, Uppsala University,SE-75124 Uppsala, Sweden.

© Brigitte Lacroix 2015

ISSN 1651-6192ISBN 978-91-554-9221-2urn:nbn:se:uu:diva-247917 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-247917)

The journey permits to open a window and to put ourselves on the right scale. A bit likewhen measuring one centimeter on a map face to the immensity of the world.

This journey has been a good yardstick for me.

Zazie (Rendez-vous en terre inconnue)

Le voyage permet d’ouvrir une brèche et de se replacer à la bonneéchelle. Un peu comme quand on mesure un centimètre sur une carte

face à l’immensité du monde. Ce voyage a été un bon mètre-étalon pourmoi.

Zazie (Rendez-vous en terre inconnue)

List of Papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Lacroix BD, Lovern MR, Stockis A, Sargentini-Maier ML,

Karlsson MO and Friberg LE. A pharmacodynamic Markov mixed-Effects model for determining the effect of exposure to certolizumab pegol on the ACR20 Score in patients with rheumatoid arthritis. Clinical Pharmacology and Therapeutics, 86:387–395 (2009)

II Lacroix BD, Karlsson MO and Friberg LE.

Simultaneous exposure-response modeling of ACR20, ACR50, and ACR70 improvement scores in rheumatoid arthritis patients treated with certolizumab pegol. CPT Pharmacometrics and System Pharmacology, 3:e143. Doi: 10.1038/psp.2014.41 (2014)

III Lacroix BD, Kirby H, Oliver R, Parker G, Friberg LE and

Karlsson MO. A time-to-event model for the immunogenicity of certolizumab pegol in rheumatoid arthritis subjects. In manuscript

IV Lacroix BD, Friberg LE and Karlsson MO.

Evaluation of IPPSE, an alternative method for sequential population PKPD analysis. Journal of Pharmacokinetics and Pharmacodynamics, 39:177–193 (2011)

Reprints were made with permission from the respective publishers.

Contents

Introduction ................................................................................................... 11 Rheumatoid arthritis ................................................................................. 11 

Pathogenesis and Epidemiology .......................................................... 11 Pathophysiology and TNF-α role ........................................................ 11 Treatment ............................................................................................. 14 Classification and clinical assessment ................................................. 18 

Pharmacometrics ...................................................................................... 19 Population methods ............................................................................. 20 PKPD modeling ................................................................................... 21 Dropout modeling ................................................................................ 22 Categorical data modeling ................................................................... 23 Simulations .......................................................................................... 28 

Aims .............................................................................................................. 29 

Materials and methods .................................................................................. 30 Data .......................................................................................................... 30 

Clinical studies .................................................................................... 30 Exposure measures .............................................................................. 32 PD measures ........................................................................................ 34 Covariates ............................................................................................ 34 

Modeling .................................................................................................. 35 Software and data analysis ................................................................... 35 Model building .................................................................................... 36 Variability model ................................................................................. 36 Dropout model ..................................................................................... 36 Model evaluation ................................................................................. 37 Model-based simulations ..................................................................... 37 

ACR20 structural model ........................................................................... 37 ACR20/50/70 structural model ................................................................ 39 Immunogenicity model structure .............................................................. 40 Evaluation of IPPSE ................................................................................. 40 

PKPD approaches ................................................................................ 41 PKPD models ...................................................................................... 41 Model parameters and study design .................................................... 42 Performance measures ......................................................................... 43 

Results ........................................................................................................... 44 Reduced vs. Full joint count ..................................................................... 44 Time effect ............................................................................................... 44 Exposure-response ................................................................................... 45 Covariates ................................................................................................. 47 Dropout .................................................................................................... 47 IPPSE method .......................................................................................... 49 

Precision in parameter estimation ........................................................ 49 Accuracy of PD parameter estimation ................................................. 49 Estimation time .................................................................................... 50 Estimation status .................................................................................. 50 

Discussion ..................................................................................................... 51 

Conclusions ................................................................................................... 58 

Acknowledgments......................................................................................... 59 

References ..................................................................................................... 63 

Abbreviations and definitions

Ab+ Antibody positive ACPA Antibodies to citrullinated protein antigen ACR American college of rheumatology ADA(s) Anti-drug antibody(ies) AUC Area under the curve Cavg Average concentration over the last dosing interval CL/F Apparent clearance Cmax Maximum serum concentration over a dosing interval Cp Predicted individual concentration at time of PD observation CPU Central processing unit CTLA4–Ig Cytotoxic T lymphocyte antigen 4–immunoglobulin CRP C-reactive protein CV Coefficient of variation DMARDs Disease modifying anti-rheumatic drugs ESR Erythrocyte sedimentation rate EULAR European league against rheumatism Fab The fragment antigen-binding of an antibody (the region that

binds to antigens) Fc The fragment crystallizable region of an antibody FDA Food and Drug Administration GM-CSF Granulocyte macrophage colony stimulating factor HAQ-DI Health assessment questionnaire disability index IgG Immunoglobulin class G IIV Inter-individual variability IL Interleukine INF-α interferon α IPP Method for sequential PKPD analysis using individual PK

parameters IPPSE Method for SEQ sequential analysis using individual PK

parameters and their standard errors LIF Leucocyte inhibitory factor LT Lymphotoxine LV Latent variable M-CSF Macrophage colony stimulating factor NSAIDs Non-steroidal anti-inflammatory drugs OFV Objective function value

PEG Polyethylene glycol PK Pharmacokinetic, pharmacokinetics PD Pharmacodynamic, pharmacodynamics PPP&D Method for SEQ PKPD analysis using population PK pa-

rameters and PK data Q2W Every 2 weeks, Q4W Every 4 weeks RF Rheumatoid factor SE Standard error SEQ Sequential method for PKPD analysis SIM Simultaneous method for PKPD analysis SJC Swollen joint count TGFβ Transforming growth factor beta TJC Tender joint count TNF Tumor necrosis factor TTE Time to event VAS Visual analog scale VPC Visual predictive check

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Introduction

Rheumatoid arthritis Rheumatoid arthritis is a common chronic inflammatory autoimmune dis-ease that affects 0.5 to 1% of adults in the industrialized countries, with 5 to 50 per 100 000 new cases annually1,2. It is a systemic disease that may affect many different organs, including the skin, eyes, lung, heart and kidneys, but it is mainly characterized by the chronic inflammation of the joints resulting in painful and deformed joints due to bone erosion, destruction of cartilage and complete loss of joint integrity. The loss of physical function can lead to disability. Patients with rheumatoid arthritis exhibit fluctuating disease course with periods of flares and periods without symptoms, due to the dis-ease itself and the treatment3. The activity and progression are highly varia-ble both between and within patients and standardized assessments of clini-cal variables are necessary to reflect the disease progression3.

Pathogenesis and Epidemiology The reason why the immune system turn against itself in rheumatoid arthritis remain unclear. Environmental factors are thought to trigger the disease pro-cess in genetically predisposed persons9. The relative contribution of genetic factors, evaluated based on twin studies, is about 50%5. Smoking is the main environmental risk factor, it doubles risk of developing rheumatoid arthritis. Multiple evidences indicate that hormones could have a pathogenic role: the disease is three times more common in women than in men, the prevalence increases with age and achieve its maximum in women older than 65 years1, pregnancy may improve the disease, and breastfeeding worsen it. The geo-graphical distribution seems also to be dependent on different genetic risks and environmental exposure: the disease is more common in Northern Eu-rope and North America compared with parts of the developing world, such as rural West Africa1.

Pathophysiology and TNF-α role In the state of chronic inflammation, the balance between the pro-inflammatory and the anti-inflammatory mechanisms that control the in-flammatory process is deregulated. The inflammation remains unchecked,

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causing the recruitment of inflammatory cells and self-perpetuation of in-flammation, which results into cellular damages, in case of rheumatoid ar-thritis primarily the destruction of cartilage and bones10-12 (Figure 1).

Figure 1. Deregulation of the inflammatory process in rheumatoid arthritis

The cascade of inflammatory process involves a large number of cytokines. Cytokines are small peptides that have very potent biological action because they can be produced by almost any cells in the body and act on high affinity receptors present on other cells. They mediate several biological processes including inflammation, tissue repair, cell growth, fibrosis, angiogenesis and immune response12. Cytokines usually have a local action, and a large num-ber of pro- and anti-inflammatory cytokines are present in the synovium of the inflamed joints (Table 1).

Table 1. Pro-inflammatory and anti-inflammatory cytokines in RA joints12-15

Pro-inflammatory cytokines Anti-inflammatory cytokines

TNFα, IL-1, LT, IL-6, GM-CSF, M-CSF, LIF, IL15, IFN-α, IL-2, IL-12

IL-4, IL-10, IL-13, IL-1 receptor antagonist, soluble TNF-receptor, TGFβ

LT = lymphotoxine, INF-α = interferon α, GM-CSF = Granulocyte macrophage colony stimu-lating factor, M-CSF = Macrophage colony stimulating factor, LIF = Leucocyte inhibitory factor, TGFβ= transforming growth factor beta

The overproduction and overexpression of the cytokine TNFα play a central role in the inflammatory cascade. Elevated levels of TNFα are observed both in the serum and in the joints of rheumatoid patients. TNFα is a pleiotropic protein produced essentially in the synovium of the inflamed joints, and has a major role in both the inflammation and the bone resorption16,17 (Figure 2). On one hand, TNFα induces the production of other pro-inflammatory cyto-kines, including IL1 and IL6 as well as the production and the release of

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chemokines that attract leukocytes from the blood into the inflamed tissue. On the other hand, TNFα induces proteolytic and metalloproteinase enzymes leading to the destruction of cartilages and activates the resorptive activity leading to the destruction of the bones18.

Figure 2. TNFα actions relevant to the pathogenesis of rheumatoid arthritis. Copy-right © 2008, American Society for Clinical Investigation18.

Figure 3. Comparison of normal and rheumatoid joints. Reprinted by permission from Macmillan Publishers Ltd: Nature Reviews Immunology (Feldman15) © 2002

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Rheumatoid arthritis progresses in 3 stages (Figure 3): 1. The swelling of the synovial lining causes pain, warmth, stiffness, red-

ness and swelling around the joint; 2. The rapid division and growth of cells (pannus) causes the synovium to

thicken; 3. The inflamed cells release enzymes that may digest bone and cartilage,

causing the involved joint to lose its shape and alignment, leading to more pain, and loss of movement.

Treatment The medical treatment of rheumatoid arthritis has improved greatly in the 2000’s. The benefit of treating the patients early with effective drugs to pre-vent the disease progression was recognized. The treatment started to be initiated at an earlier stage of the disease with more aggressive approach, with the aim to achieve an early and persistent reduction in the inflamma-tion3,19. Therefore, it is essential when developing new therapies against rheumatoid arthritis to demonstrate a fast onset of the clinical response, e.g. this could be achieved by the use a loading dose to provoke a rapid diminu-tion of the inflammation. The number of therapeutic options also increased greatly with the advent of new biological therapies targeting specific molec-ular mechanisms and the diversity of rheumatoid arthritis was acknowl-edged, with different treatment to be administrated for individual patients at various time points5. The main treatments used in rheumatoid arthritis are summarized in Table 2.

Treatment of symptoms Pain and stiffness are treated with non-steroidal anti-inflammatory drugs (NSAIDs). Analgesics reduce pain, and disease flares are managed using corticosteroids9. NSAIDs are no longer the first line treatment against rheu-matoid arthritis because of they are only symptomatic treatments that do not modify the course of the disease, have limited efficacy and some gastrointes-tinal and cardiac side effects1.

Disease modifying anti-rheumatic drugs (DMARDs) The DMARDs denomination encompasses a collection of heterogeneous treatments that have the potential of modifying the evolution of the disease. They remain the mainstay and first line treatment in rheumatoid arthritis20,1. Methotrexate is the main DMARDs, followed by sulfasalazine and lefluno-mide. DMARDs may be combined in order to achieve a better disease con-trol, especially in severe disease9,21.

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Table 2. Main treatment used in rheumatoid arthritis

Medication Effect Use

Analgesics & NSAIDs - Acetaminophen - Aspirin - Ibuprofen, ketoprofen, naproxen - COX-2 inhibitors

- Analgesics relieve pain; - NSAIDs relieve pain and reduce inflammation9.

Symptomatic treatment. NSAIDs are no longer the first line treatment.

Corticosteroids - Methylprednisolone - Prednisolone

Relieve inflammation and reduce swelling, redness, itching and allergic reactions.

Used for severe flares and when disease does not re-spond to NSAIDs and DMARDs.

DMARDs - Methotrexate - Leflunomide - Sulfalazine - Azathioprine, cyclosporine - Hydroxychloroquine - Gold sodium thiomalate

Relieve pain and swelling Slow joint damage.

May be used over the disease course. Take a few weeks or months to have an effect Mechanism of action is not completely understood.

Biologics - anti-TNF: etanercept, in-fliximab, adalimumab - anti-IL1: anakinra

Selectively block cytokines. For patients with an inade-quate response to DMARDs. May be prescribed in combi-nation with methotrexate.

NSAIDs = non-steroidal anti-inflammatory drugs DMARDs = disease modifying anti-rheumatoid arthritis drugs

Biological agents The enhanced understanding of the pathogenic pathways drove the develop-ment of treatments targeting specific molecules and pathways5. This revolu-tionized the care of rheumatoid arthritis22.

TNFα became naturally the primary target because of its key position at the top of the pro-inflammatory cascade15. TNF inhibitors are usually given to patients with active rheumatoid arthritis who did not achieve a satisfactory response with conventional DMARDs9. They are generally prescribed in combination with methotrexate1. The combination has been proven to be more efficacious than anti-TNF or methotrexate taken alone. Initially, the concomitant administration of methotrexate was intended to reduce the for-mation of antibodies against the biologic drug9,23, but the complementarity of the two treatments is also due to the specific effects of methotrexate, that inhibits the adenosine metabolism and T-cells activation, and affects the folate synthesis5. In 2007, five anti-TNF biologics were available on the market for the treatment of rheumatoid arthritis: etanercept (Enbrel®), a TNF receptor-Fc fusion protein, approved by

FDA at the end of 1998; infliximab (Remicade®), a chimeric IgG1 monoclonal antibody, ap-

proved by FDA at the end of 1999;

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adalimumab (Humira®), a human monoclonal antibody, approved by FDA at the end of 2002;

and two other anti-TNF drugs were on clinical development: golimumab (Simponi®), a human monoclonal antibody certolizumab pegol (Cimzia®),

This thesis work was initiated when phase III clinical trials for certolizumab pegol became available and needed to be analyzed to support the submission of the drug to the health authorities. Certolizumab pegol is an engineered, humanized antibody Fab fragment with specificity for TNFα, that is conju-gated to polyethylene glycol (PEG), a water soluble polymer24. This drug does not neutralize TNFβ, a related cytokine, and does not activate comple-ment or kill cells via antibody-dependent cellular toxicity.

Certolizumab pegol differs from the existing anti-TNF drugs essentially by its structure, as the only Fc-free molecule (Figure 4). The addition of the PEG was used as a mean to increase the terminal elimination half-life of the drug to approximately 14 days for all dosage levels tested. It contributes to achieve more constant and sustained plasma concentrations25-27. The phar-macokinetics of certolizumab pegol was characterized by a predictable dose-related plasma concentrations with a linear relationship between the dose administered and the maximum serum concentration (Cmax) and the area under the drug plasma concentration versus time curve (AUC). The bioavail-ability is approximately 75% when the drug is administered subcutaneously. PEG is also used to reduce the immunogenicity of certolizumab pegol by preventing immune recognition26,27, which needs to be confirmed based on the outcome from the clinical trials.

Figure 4. The five anti-TNF agents approved for the treatment of rheumatoid arthri-tis. Permission obtained from NPG © van Vollenhoven, R. F. Nat. Rev. Rheumatol. 7, 205–215 (2011).

Apart from the class of anti-TNF, other drugs targeting IL1 (anakinra, Ki-neret®), T-cells (abatacept, Orencia®) and B cells (rituximab, Rituxan®, MabThera®) have enriched the therapeutic arsenal, while other drugs such as anti-IL6 therapies were still under development.

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Immunogenicity All biologic treatments have the potential to provoke an unwanted immuno-genic reaction leading to the production of antibodies directed against the drug (anti-drug antibodies, ADA). Immunogenicity of biologics is a concern both for efficacy and safety reasons. Unwanted immune response to the drug may lead to: a change in the drug exposure, as evidenced by low drug concentrations; a loss of target engagement; a loss of efficacy, as measured by the clinical endpoints; an increase in immunologically-based adverse events, such as anaphy-

laxis and cross-reactive neutralization of endogenous proteins mediating critical functions (e.g., neutralizing antibodies to therapeutic erythropoi-etin cause pure red cell aplasia by also neutralizing the endogenous pro-tein)28.

Many factors are thought to influence the formation of ADAs (Table 3)26.

Table 3. Main factors influencing the formation of ADAs26

Factors Characteristics Description

Drug-related Aminoacid sequence

The differences in the sequence between the therapeutic and the endogenous protein promote ADA formation.

Fc fragment The presence of epitopes in the drug increas-es its immunogenic potential.

Immune complex The drugs that lead to formation of large immune complexes might result in increased immunogenicity.

Aggregates and particles Aggregates and particles introduced during the drug production and purification process can induce immune activation.

Patients-related Underlying disease

Patients with highly active immune system, i.e. with higher baseline disease activity have increased risk.

Genetic variation Some genotypes have been associated with antibody production.

Treatment-related Route of administration Intravenous administration is thought to be generally less immunogenic than intramus-cular or subcutaneous.

Dose High enough dose might mediate exhaustion of the immune response.

Treatment schedule Short-term therapy or long term treatment with intermittent administration may trigger the immune response.

Duration of treatment The risk of immunogenicity might be in-creased with increasing duration of treat-ment.

Combination therapy Immunosuppressant co-medications such as methotrexate prevent the activation of the immune system.

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Classification and clinical assessment The rheumatoid arthritis classification criteria developed by the American Colleague of Rheumatology (ACR) in 19874 was used to select patients with establish rheumatoid arthritis for entering clinical trials on which this thesis work was performed. The criteria includes: 1. Morning stiffness in and around joints lasting at least 1 hour before max-

imal improvement; 2. Soft tissue swelling (arthritis) of 3 or more joint areas observed by a

physician; 3. Swelling (arthritis) of the proximal interphalangeal, metacarpophalange-

al, or wrist joints; 4. Symmetric swelling (arthritis); 5. Rheumatoid nodules; 6. The presence of rheumatoid factor; 7. radiographic erosions and/or periarticular osteopenia in hand and/or

wrist joints.

Criteria 1 through 4 must have been present for at least 6 weeks. Rheumatoid arthritis is defined by the presence of 4 or more criteria.

Rheumatoid arthritis progresses with fluctuations. Frequent standardized assessments of the disease activity are necessary to evaluate the disease pro-cess. Assessment criteria include disease activity and inflammation, damages to the joints, disability induced by the disease, comorbidity, psychological, social and economic consequences3. The evaluation can take different forms according to the objective pursued, whether it is to evaluate the patient dis-ease course, the efficacy and toxicity of a treatment, or to evaluate the differ-ences between groups of patients, in clinical practice or during clinical trials.

Indices of clinical activity have been developed that combine multiple ac-tivity measures into a single score, in order to allow for comparison between clinical trials, to get an unambiguous interpretation of the disease activity and to increase the statistical power of clinical trials3. Several clinical scales have been developed, among which the most important are the American College of Rheumatology (ACR) core data set30 from which is derived the main efficacy endpoint in rheumatoid arthritis clinical trials and the DAS2831 that is used routinely in clinical practice. The two indexes differs mainly in that the ACR core set is the support for measures of the improvement of the disease from baseline, while the DAS28 is an absolute measure of the dis-ease activity.

The ACR core data set consists in seven measures including three scores assessed by the physician, three scores assessed by the patient and one bio-logical measure, as summarized in Table 430. Measure of improvement in rheumatoid arthritis is defined based on the core set of measures. The ACR20 response, generally used as the efficacy benchmark in clinical trials,

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is achieved if a decrease of at least 20% in both the tender and the swollen joint counts, as well a decrease of at least 20% in at least three of the five other measures over the baseline assessment is observed32. Higher level of improvement are defined based on similar definition with 50 and 70% im-provement over baseline33,34. The relevance of the different levels of re-sponse is discussed in more detail in the discussion section.

Table 4. ACR core data set

Assessor Disease activity measure Method of assessment

Physician Tender joint count Assessment of 68 joints Swollen joint count Assessment of 66 joints Global assessment of disease activity 10 cm VAS or Likert scale measure Patient Assessment of pain 10 cm VAS or Likert scale measure Assessment of physical function Any validated self-assessment instrumenta

Global assessment of disease activity 10 cm VAS or Likert scale measure Biology Acute phase reactant ESR or CRP

VAS = visual analog scale ESR = erythrocyte sedimentation rate CRP = C-reactive protein aincluding the following instruments : the Arthritis Impact Measurement Scales (AIMS), the Health Assessment Questionnaire (HAQ), the Quality (or Index) of Well Being, the McMas-ter Health Index Questionnaire (MHIQ) and the McMaster Toronto Arthritis Patient Prefer-ence Disability Questionnaire (MACTAR).

Pharmacometrics

Pharmacometrics is a continuously growing disciple that contributes to more rational and efficient drug development36-39, influencing regulatory and ther-apeutic decisions40. The discipline has evolved and its definition expanded with time. While the initial focus was on population pharmacokinetic (PK) analyses, it was later described as:

“the science of developing and applying mathematical and statistical methods to characterize, understand and predict a drug’s pharmacokinetic, pharmaco-dynamic, and biomarker-outcome behavior”41.

More recently an even broader definition has been proposed, that better illus-trates the multi-disciplinary perspective:

“the branch of science concerned with mathematical models of biology, pharmacology, disease, and physiology used to describe and quantify interac-tions between xenobiotics and patients, including beneficial effects and side effects resultant from such interface”42.

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During drug development, pharmacometric methods are used to integrate the information from massive amount of generated data and various clinical trials, to learn and confirm prior knowledge along the development, to sup-port internal drug development and regulatory decisions, to fill the gaps that might appear in the clinical development program and to predict and extrap-olate (e.g. study designs, dosing regimens…).

Population methods When analyzing the clinical scores collected during clinical trials, it is im-portant to account for the fact that observations over time are coming from the same individual42,44. In the population approach, data from all individuals are analyzed simultaneously. In consequence, fewer observations points are needed per individual to analyze the data, and the approach allows for de-scribing the variability in the population. Two types of parameters are esti-mated: the fixed effects that describe the structural model shared by all indi-viduals and the variances of the random effects that describe the overall var-iability. Hence these models are referred to as mixed-effects models.

The observed response (e.g. the concentration or the clinical score) can be described as shown in Equation 1.

Equation 1

,

where yij is the jth observation of the ith subject, the function f( ) is a linear or non-linear function describing the individual prediction based on the vec-tor of estimated parameters Pi as function of the independent variables xij (e.g. the time for PK models, the time and concentration for a PD model). The random effect εij describes the residual error that account for the dis-crepancy between the individual model predictions and the observations. The values of εij are assumed to be normally distributed with the estimated variance σ2 (Figure 5). The residual error encompasses analytical assay er-rors and model misspecifications.

Figure 5. Residual variability in mixed effects models

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The inter-individual variability (IIV) is another source of variability. The part of IIV that can be explained by known observable factors (available covariates) such as demographics, disease-related factors, concomitant med-ications or other predictors are part of the structural model in the function f( ) (Equation 1). The remaining unexplained IIV, whether due to lack of identi-fied predictor or true random variability is estimated in the model as follows (Equation 2).

Equation 2

∙ ∙ 1 η η

where pki is the kth individual parameter in Pi and θk is the typical value of pk. The random effect ηki describes the difference between the individual parameter estimate and the typical population parameter estimate; it is as-sumed to be normally distributed with the estimated variance ωk

2 (Figure 6), and is commonly parameterized as exponential, proportional or additive error (Equation 2). The exponential function is frequently used for biological systems, as it constrains parameters values to be positive, which is often physiologically plausible.

Figure 6. Inter-individual variability (IIV) in mixed effects models

PKPD modeling Characterizing the exposure-response relationship is a key component of the drug development, as highlighted in the FDA guidance on Exposure-Response relationship : “Exposure-response information is at the heart of any determination of the efficacy and effectiveness of drugs.” 45 In the con-text of clinical development, the pharmacokinetic-pharmacodynamic (PKPD) modeling of exposure-response data consists in the characterization

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of the relationship between the drug effect (the PD variable) and the drug exposure (PK component).

The marker for exposure can be of different type, from treatment (e.g. drug vs. placebo) and dose (dose-response analysis) to measures from the drug concentration-time profile (predicted concentration at the clinical ob-servation time, peak or trough concentration over the dosing interval, steady-state concentration, time above a minimum effective concentration, etc.) and secondary PK parameters (area under the curve [AUC], cumulative AUC, etc.). The second component of the exposure-response model, the clinical response, can be a continuous or a discrete variable (categorical, count). The type of data determines the mathematical approach for the anal-ysis.

The PKPD modeling can either be performed simultaneously, in one step where both drug concentrations and PD measurement are fitted at the same time, or sequentially, where first a model is develop that fit the PK data and then a model to fit the PD data. The simultaneous approach (SIM) is consid-ered the gold standard. Sequential methods (SEQ) differ in the way the PK condition the PD parameter estimation. The approach that uses both the es-timated PK population parameters and the PK data (PPP&D) perform the best among SEQ methods. This method shows low bias in the estimation of PD parameters with similar standard errors as for the SIM method, and saves about 40% computation time. The SEQ method that uses the individual PK parameters (IPP) is commonly used, probably for practical reasons. It has computation-time advantages but its inferior performance suggests that using the individual PK parameters (posterior Bayes estimates) is losing some PK information relative to the actual PK data46. A newer version of NONMEM, the software that was used to perform the analyses included in this thesis, became available shortly after the start of this thesis work. This version (NONMEM 7.1) included new estimations methods, but also other new fea-tures, including the automatic output of a table file that incorporates the standard errors (SE) of the parameter estimates. This new feature made it possible to use that information to develop an alternative SEQ method for performing PKPD analysis and was the basis for the methodological assess-ment of this approach presented in this thesis.

Dropout modeling

The dropout model considers the early withdrawal of subjects from clinical trials leading to incomplete data (right-censored). The dropout rate varies with time, as well as across clinical trials and indications. It can exceed 50% under certain circumstances47. In the statistical literature, the dropout is usu-ally described as “missing completely at random” (MCAR: the dropout does not depend on observed or unobserved values of the variable that is ana-

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lyzed, the dependent variable), “missing at random” (MAR: the dropout is dependent on the observed, but not the unobserved value of the dependent variable), and MNAR (the dropout is dependent on unobserved measure-ments). The MNAR and MAR are referred to as informative dropout and cannot be ignored during the analysis48.

Modeling the informative dropout not only aims at characterizing the dropout time course or at identifying potential covariates/patients character-istics that lead to increased dropout risk; it may also improve the PKPD analysis and be crucial for accurate model evaluation. Ignoring informative dropout can lead to biased parameter estimates50, even if this was shown not to have a major impact on the prediction of the PD variables. In addition, dropout is essential to make accurate simulations from the model49. There-fore the informative dropout shouldn’t be ignored during the analysis. The dropout can either be an integrated part of the PKPD model or a modeled as a separate component.

Categorical data modeling Categorical variables are variables that can take only a limited number of possible, usually pre-defined, values, as opposed to continuous variables that can take an infinite number of values51. Categorical data can be of three types: binary if the data are dichotomized (e.g. “responder” or “non-responder”), nominal in absence of natural ordering (e.g. sleeping states) or ordinal (e.g. grade of severity of pain). Clinical efficacy and toxicity are often measured as binary or ordered categorical data, where subjects are assigned to a particular level of the score at each assessment.

For example, the ACR core set of measure was dichotomized as 3 binary responses with the following levels: “ACR20 responder” vs. “ACR20 non-responder”, “ACR50 responder” vs. “ACR50 non-responder” and “ACR70 responder” vs. “ACR70 non-responder”. The ACR20, ACR50 and ACR70 scores may also be viewed as ordered categorical variables with four levels : “ACR20 non-responder”, “ACR20 but not ACR50 responder”, “ACR50 but not ACR70 responder” and “ACR70 responder”. The dropout can also be considered as a binary variable (“non-dropped out” vs “dropped out”) or an additional levels in a categorical score (“ACR20 responder” vs. “ACR20 non-responder” vs. “dropped out”).

Logistic model Categorical data modeling differs from continuous data analysis in that the observed variable is not the value of the variable itself but the likelihood of observing the variable, e.g. for a binary variable the probability of having “effect” or “no effect”. By consequence, the residual error variability be-comes. As the probability scale is bounded between 0 and 1, a link function is used to estimate the parameters describing the probability of the scores on

24

a non-bounded scale (-∞;+∞). The logit transformation in which the cumula-tive distribution of the responses is assumed to be logistically distributed, is the most common link function (Equation 3).

Equation 3

1,

⇔ ,

1 ,

where the function f( ) is the linear or non-linear function describing the probability of the score based on the vector of estimated parameters P (a, b, …) as function of the independent variables X (e.g. time, covariates). The IIV term is included as an additive term in the logit function (Equation 4).

Equation 4

1

Therefore, binary data (with scores “0” and “1”) are modeled as shown in Equation 5.

Equation 5

∝ η ⟺∝

1 ∝

1

where p1i is the individual probabilities of observing score “1” and p0i indi-vidual probabilities of observing score “0” (e.g. “1” for responder and “0” for non-responder). The intercept parameter α describes the baseline proba-bility of observing score “1” and the function g( ) describes the covariate relationship, including placebo, drug and other explanatory covariates, such as demographics, concomitant medications, markers for disease severity.. effects. Other link functions can also be applied such as the probit or com-plementary log-log, corresponding to different assumptions about the distri-bution of the response variable52,53.

The model for binary data can be extended to a categorical outcome with more than two categories. There are N categories instead of two, therefore there will be N-1 probabilities to model instead of one52. The proportional odds model for mixed-effects analysis of PKPD data was first proposed in 1994 to analyze a 4-degree pain scale54. In this approach the same effects of an explanatory variable is assumed for all cumulative probabilities corre-

25

sponding to the various levels of the categorical scores55. This assumption may not be appropriate, especially when the categorical score reflects the outcome for a composite outcome44. Some approaches have been proposed that allow more flexibility44,55,56, e.g. to estimate a separate vector of parame-ters for each response level.

One limitation of the logistic model lies in the assumption that each data point is independent of all other data points, which may not be true in case of serial correlations. At least two approaches were proposed to address this weakness, the latent variable (LV) and the Markov approach. These ap-proaches are presented below, and a more extensive comparison is debated in the discussion section.

Latent variable model The latent variable (LV) approach has been developed as a mean to imple-ment more mechanistic thoughts to discrete or ordered categorical data. For example, the underlying, unobserved disease severity can be described by an indirect response model57. The continuous unobservable underlying variable is mapped to binary or ordered categorical variables based on estimated threshold values (Figure 7). This approach has been applied for modeling the ACR20 response in rheumatoid arthritis subjects treated with a JAK3 inhibitor57 where the indirect response model may represent the level of in-flammation.

Figure 7. An illustration depicting the mapping between the latent variable scale and the probability scale. When the mean of the latent variable falls below a threshold, γ, the amount of the latent variable distribution below the threshold increases. The fraction of the distribution below the threshold corresponds to the probability of a positive response (z = 1). Copyright © 200757, reprinted with kind permission from Springer Science and Business Media Springer.

26

Markov model The Markov approach accounts for the correlations between subsequent observations from the same subject. For example, if the number of observa-tions within a certain time frame is increased, this will not necessarily multi-ply the amount of information gained but the observations may depend on each other over this time interval e.g. reporting the status “asleep” vs. “awake” every minute instead of every hour will not multiply the observa-tions by 60 as at each minute the likelihood is great that the subjects has not changed status from the previous minute. Ignoring this dependency may lead to an overestimation of the IIV and prevent from simulating realistic indi-vidual time-courses of the modeled clinical score, e.g. for sleep data too frequent transitions between the “asleep” and the “awake” states, that are unlikely to be accurate (Figure 8).

The approach is similar to the logistic model but the probabilities of tran-sitions between the different stages are defined, rather than the probability of each of the stages. It was first applied for non-linear mixed effects modeling to model sleep data60-63. This type of model was the starting point for the ACR20 model developed in this thesis work (Paper I), the details of the model are presented in the methods section. The Markov model can be of first order if the transition probability is conditioned on the value of the pre-ceding state only, or on higher order in case the transition probability is con-ditioned on two or more of the preceding states53.

Figure 8. Example of nighttime observations of awake (=0) or sleep (=1) every 5 minutes in an insomniac patient (©Pharmacometric Research Group, PKPD model-ing of Continuous and Categorical data in NONMEM 7 course, Berlin, 2010)

Another type of Markov model was proposed to accommodate data with varying time interval between the observations, where the influence of the preceding states decreases as time between observations increases64. This

27

was starting point for the ACR20/50/70 model developed in this thesis work (Paper II). The details of the model are presented in the methods section.

Time to event model Time to event (TTE) models are used to analyze the time duration from entry into a study, or time from drug administration, until the response (“event”) happen, therefore this approach was deemed appropriate to characterize the time to appearance of antibodies (Paper III). The data are censored in case the event had not been observed at the end of the observation time. This type of analysis has traditionally been performed to describe time to death, hence the name of “survival analysis”. The time course of the probability of sur-vival, S(t), is called the survivor function. Generally, the survivor function is calculated from the integral of the hazard with respect to time (Equation 6).

Equation 6

Pr

where S(t) is the probability of survival (i.e. not having an event) at time t, T is a random variable denoting the time of the event and H(t) the cumulative hazard. During modeling of TTE data, the distribution of T is characterized by the hazard function (h(t)), which is the instantaneous rate of occurrence of the event (Equation 7).

Equation 7

lim→

|

with | the conditional probability that the event will occur in the interval [t, t+dt) given that it has not occurred before, and dt is the width of the interval66. The survival function S(t) may therefore be writ-ten as shown in Equation 8, in which the simplest possible survival distribu-tion corresponds to a constant risk over time.

Equation 8

where λ is the estimated constant hazard. Other common distributions are the Weibull or Gompertz distributions68, but the hazard can take any form as appropriate based on the data to analyze.

28

Simulations The PKPD models developed during drug development and for regulatory purposes can be exploited through simulation. The clinical outcomes may be simulated over a large population with specific characteristics or as clinical trials with specific study designs. Clinical trial simulations are used to design powerful, robust, informative and efficient clinical trials44,67,68. It may be used for example to study the impact of different study designs, different dosing strategies, the selection of different study populations44, to extrapo-late to different populations…

Simulations are used to support drug development as well as regulatory decisions. The simulations settings and assumptions must be described on a case by case basis in order to be tailored to answer the specific question of interest. As described above, the PKPD modeling is thought and performed in such a way that accurate simulations can be are performed, e.g. the inclu-sion of a dropout model or the use of Markov models may have a large im-pact on the conclusions that can be drawn from the simulations.

29

Aims

The aim of this thesis was to develop methods and models for analyzing pharmacokinetic (PK) and pharmacokinetic-pharmacodynamic (PKPD) data from rheumatoid arthritis patients, illustrated by treatment with a new anti-TNFα biologic drug under clinical development, certolizumab pegol. The focus was on modeling the efficacy categorical ACR variables that represent improvement of the disease over baseline assessment, used to evaluate the efficacy of new anti-rheumatic therapies in clinical trials, and to evaluate different methods for performing PKPD analyses.

The specific aims were: To develop a Markov model to characterize the time-course of the

ACR20 clinical outcome (response vs. non-response) that captures the within-subject correlations in the successive clinical assessments during the clinical trials.

To develop a Markov model to characterize the three levels of ACR improvement over baseline (ACR20, ACR50 and ACR70) that captures time-varying intervals for the dependency of the previous status of re-sponse on the clinical assessment, in order to characterize higher levels of response (ACR50, ACR70) that are more meaningful for clinicians and more desirable for patients than the ACR20 response.

To develop a model to characterize the immunogenicity directed against

the test drug, a feature that is specific to biologics and may impact both the PK and the PD of the drug.

To present an alternative method for performing sequential PKPD and to

evaluate its performance towards precision and accuracy of PD model parameters estimation, compared to the reference simultaneous method and other sequential approaches.

30

Materials and methods

Data Clinical studies The same database was used to perform all the modeling included in this thesis. Data were available from 2380 subjects suffering from rheumatoid arthritis, from five double-blind placebo-controlled phase II and phase III clinical trials. Subjects were treated for periods lasting from 12 weeks up to 1 year, with every 2 or every 4 weeks (Q2W or Q4W) dosing, alone or in combination with methotrexate; 1747 subjects received certolizumab pegol at doses ranging from 50 to 800 mg (including non-label dosages) and 633 patients received placebo. The global design of the included studies and amount of available data are summarized in Table 5, inclusion criteria and concomitant drug medications are summarized in Table 6.

Table 5. Study design and available data

Study Duration(weeks) Control Active doses Dosing

schedule Formu-lation

No of subjects

total/drug

Dropout frequency(%)

drug/PBO 1 8 Placebo 50, 100, 200,

400, 600, 800Q4W Liquid,

pH5.5320/239 11/37

2 24 Placebo 400 Q4W Lyo 219/111 32/73 3 24 Placebo

+MTX400 Q4W Lyo 243/124 21/45

4 52 Placebo +MTX

200,400 Q2W Lyo 979/780 32/78

5 24 Placebo +MTX

200, 400 Q2W Liquid, pH4.7

619/493 28/87

PBO = placebo , Q4W = every 4 weeks, Q2W = every 2 weeks, MTX = methotrexate

The dosing, PK sampling and PD observation times are summarized in Fig-ure 9. PK assessments included both the measurement of plasma concentra-tions of certolizumab pegol and anti-certolizumab pegol antibodies (ADAs). The ADA status was assessed at pre-specified visits and data were interval-censored, i.e. the interval during which the ADA appeared was known, but not the exact time when subjects turned antibody positive (Ab+). For the ADA analysis, subjects who had not turned Ab+ at the end of the trial were right censored at their last visit. In studies 4 and 5, subjects who were non-

31

responders at both week 12 and week 14 visits were to be withdrawn at week 16 and were given the option of entering an open-label extension study.

Table 6. Inclusion criteria and concomitant drug medications

RA diagnosis/ disease activity Medication history Concomitant drugsb

1 Diagnosis of RAa. Active disease at screening as defined by: ≥ 6 tender joints , ≥ 6 swollen joints and 1 of the follow-ing: ≥45 min duration of morning stiffness or ESR(c) ≥ 28 mm/hr.

History of inadequate re-sponse or intolerance to at least 1 DMARD.

Discontinued all DMARD therapy for at least 1 month prior to first dose of study medication.

2 Diagnosis of adult-onset RAa of at least 6 months duration. Active disease at screening and baseline as defined by: ≥ 9 tender joints (68 joint count), ≥ 9 swollen joints (66 joint count) and 1 of the following: ≥45 min duration of morning stiffness, ESR ≥ 28 mm/hr or CRP(c)>10 mg/L.

History of failure to respond (i.e. lack of efficacy or intol-erance) to at least 1 DMARD.

Discontinued all DMARD therapy.

3 Adult onset RAa of at least 6 months duration Active disease at screening and baseline as defined by: ≥ 9 tender joints, ≥ 9 swollen joints and 1 of the following: ≥45 min duration of morning stiffness ESR ≥ 28 mm/hr or CRP>10 mg/L.

Partial responders to MTX. Had received MTX for at least 6 months and been on stable dose of MTX between 15 and 25 mg/week for at least 8 weeks prior to 1st dose of study medication.

Remained on a stable methotrexate doses for the study dura-tion. Discontinued all other DMARDs for at least 28 days prior to first dose of study medication.

4, 5

Diagnosis of adult-onset RAa of at least 6 months duration but not longer than 15 years prior to screening. Active disease at screening and baseline as defined by: ≥ 9 tender joints, ≥ 9 swollen joints and 1 of the following: ESR ≥ 30 mm/hr or CRP>15 mg/L

Incomplete responders to MTX. Had received treat-ment with MTX (with or without folic acid) for at least 6 months prior to the baseline visit, with the dose having been stable for at least the 2 months prior to the baseline visit.

Remained on a stable methotrexate for the study duration. No other DMARDs was permitted. The minimum dose of MTX had to be equivalent to 10 mg weekly.

aRA diagnosis based upon American College of Rheumatology 1987 Revised Criteria. bcommon design element’ If the patient was taking NSAID or COX-2 therapy, the patient was expected to be on a stable dosage throughout the double-blind treatment period. No other concomitant DMARD therapy was permitted. If the patient was taking oral corticosteroid therapy, the patient was expected to remain on a stable dosage of ≤10 mg/day prednisolone equivalent, throughout the double-blind treatment period. Patients taking parenteral cortico-steroids were not permitted CRP = C reactive protein, DMARD = disease-modifying anti-rheumatoid drug, ESR = eryth-rocyte sedimentation rate, MTX = methotrexate, RA = rheumatoid arthritis

32

Figure 9. Theoretical study schedule of dosing and assessments

Exposure measures Plasma concentrations of certolizumab pegol were determined using a ligand (TNF) binding enzyme-linked immunosorbent immunoassay (LB ELISA) method. The lower limit of quantification was 0.41 μg/mL (precision 29% coefficient of variation (CV), accuracy 78% for the lower limit of quantifica-tion samples). The overall assay precision was 3.1% CV and the overall ana-lytical recovery of each of the quality control samples, representing the intra-assay accuracy, was 99.2%.

A one-compartment disposition population pharmacokinetic model with a zero-order input into a depot compartment and subsequent first order absorp-tion to the central compartment characterized the certolizumab pegol con-centration profile (UCB, unpublished data). The model included inter-individual variability on the apparent clearance (CL/F), apparent distribution volume, absorption rate constant, and infusion time to the depot compart-ment, as well as inter-occasion variability on CL/F. The final model included the effects of ADAs and bodyweight on CL/F. The presence of anti-antibodies had the largest effect, it was associated with a 2.91-fold increase in CL/F resulting in a 60% decrease in AUC, a 46% decrease in Cmax and a 82% decrease in Cmin. Extreme body weights of 40 kg and 120 kg were predicted to have an effect of approximately ±30% on CL/F relatively to a 70 kg reference body weight.

Individual certolizumab pegol–exposure measurements were derived from the population PK model, using the empirical Bayes post hoc estimates from NONMEM (Figure 10). Two exposure variables were computed and evalu-ated as potential explanatory variables for the exposure–response relation-ship to ACR scores, the predicted individual concentration at the time of PD observation Cp and the average concentration over the last dosing interval Cavg. Cp and Cavg were set at 0 for placebo data. Cavg ranged from 1 to 213 μg/mL and Cp ranged from 0.4 to 174 μg/mL across all doses and stud-ies. The typical steady state value for the proposed treatment regimens of 200 mg Q2W and 400 mg Q4W was 23.2 μg/mL.

33

Figure 10. Pharmacokinetic profile of a typical 70 kg rheumatoid arthritis subject, derived from the population PK model. Load of 400 mg at weeks 0, 2 and 4 fol-lowed by a maintenance treatment of 200 mg Q2W or 400 mg Q4W.

Antibodies to CZP were detected in plasma samples with a screening ELISA using a double-antigen sandwich (bridge) format. The assay was validated using a rabbit polyclonal antibody to certolizumab pegol as reference stand-ard, which had been affinity purified using protein A sepharose beads. Sam-ples were diluted 1/10 before assay and the level of measured ADA, which describes the magnitude of the immune response, was expressed in arbitrary units/mL, where 1 unit/mL is equivalent to 1 μg/mL of the rabbit standard. The lower limit of quantification for this assay is 0.6 units/mL for undiluted samples. The overall assay precision was 6.03% CV and the overall analyti-cal recovery of each of the QC samples, representing the intra-assay accura-cy, was 69.2%. For the analyses, subjects are considered Ab+ at the first occurrence of a measure of ADA concentration above a threshold value of 2.4 units/mL onwards. The proportion of Ab+ subjects by study and treat-ment is summarized in Table 7.

0 2 4 6 8 10 12 14 16 18 20 22 24

01

02

03

04

05

0

Time (weeks)

CZ

P c

on

cen

tra

tion

( g

/mL

)Load/ 200 mg Q2WLoad/ 400 mg Q4W

CZ

P c

once

ntra

tions

g/m

L)

Time (weeks)

Load/ 200 mg Q2WLoad/ 400 mg Q4W

0 2 4 6 8 10 12 14 16 18 20 22 24

0

10

2

0

30

40

50

34

Table 7. Proportion of Ab+ subjects by study and treatment

Study Treatment Concomitant MTX Proportion of Ab+ (%)

1 50 mg Q4W (3 doses) No 64.1 100 mg Q4W (3 doses) No 60.0 200 mg Q4W (3 doses) No 60.0 400 mg Q4W (3 doses) No 20.5 600 mg Q4W (3 doses) No 12.8 800 mg Q4W (3 doses) No 5.32 400 mg Q4W (24 weeks) No 22.53 400 mg Q4W (24 weeks) Yes 4.84 200 mg Q2W (52 weeks) Yes 11.7 400 mg Q2W (52 weeks) Yes 2.65 200 mg Q2W (24 weeks) Yes 9.3 400 mg Q2W (24 weeks) No 2.0

PD measures At each visit, the disease activity was assessed based on the ACR core set of measure, and subjects were classified as responder or non-responder for the 3 target levels of improvement over baseline (ACR20, ACR50 and ACR70). The assessment of disease activity was based on the ACR core set of data including the following measurement tools: Tender joint count: assessment of 68 joints (28 joints for study 1); Swollen joint count: assessment of 66 joints (28 joints for study 1); Physician’s global assessment of disease activity: 10 cm VAS (a 5 points

Likert scale was used in studies 2 and 3); Patient’s assessment of arthritis pain: 10 cm VAS; Patient’s assessment of physical function: HAQ-DI score (Health As-

sessment Questionnaire Disability Index); Patient’s global assessment of disease activity: 10 cm VAS (a 5 points

Likert scale was used in studies 2 and 3); Acute phase reactant: CRP.

Covariates The potential effects of demographic factors, disease severity, concomitant medications and medication history were investigated during the exposure-response modeling (Table 9). The potential effect of race was not tested be-cause of the limited number of non-Caucasians (~7%).

35

Table 8. Covariates

Category Covariate median (mix-max)a % subjects by categoryb

Patient-related Age 53 (18-83) years

Bodyweight 72 (41-164) kg Gender Females (81%); Males (19%) Geographical regions Eastern Europe (31%); Northern

Europe and baltic states (25%); Western Europe (20%); North America (15%); Central and South America (6%); Asia/Oceania (3%)

Disease-related Disease duration at entrance 6 (0.3-47) years Baseline reduced tender joint count 17 (0-28) Baseline reduced swollen joint count 14 (0-28) Baseline CRP 15 (0.2-273) mg/L Physician’s assessment of disease

activity65 (14-100) mm

Patient’s assessement of disease activity

64 (6-100) mm

Patient’s assessment of physical function

1.6 (0-3)

Patient’s assessment of arthritis pain 65 (0-100) mmConcomitant medications

Methotrexate dose at baseline 10 (0-30) mg/week

Use of corticosteroids 39% (46.3% on placebo; 37.6% on drug treatment)

Use of NSAIDs 60% (62.9% on placebo; 59.2 % on drug treatment

Use of analgesics 16% (16.9% on placebo; 15.6 % on drug treatment

Previous medi-cations

Number of previous DMARDs other than MTX

1 (0-9)

afor continuous covariates, bfor categorical covariates

Modeling Software and data analysis All analyses in this thesis were performed using the software NONMEM, version VI level 1.0 (ACR20 modeling, paper I), version 7.1.2 and 7.3.0 (ACR20/50/70 model, paper II; Immunogenicity model, paper III), launched with PsN70. PsN was used for performing the VPC and bootstrap procedures. S-Plus, version 6.2 and R version 2.8.171 to 2.15 were used for data man-agement purposes and graphic outputs, with the package Xpose72 for the immunogenicity model. R was also used to generate the datasets and NON-MEM control files and to perform the statistical analysis for the simulation study (IPPSE evaluation, paper IV). Simulations were performed in NON-MEM and in Trial Simulator 2, version 2.2.

36

The ACR data were analyzed by nonlinear mixed-effects modeling. The Laplacian method, which used a second-order expansion around the empiri-cal Bayes predictions of the inter-individual random effects, was used in NONMEM to approximate the marginal likelihood.

Model building The model building for the two ACR exposure-response models (papers I and II) were initiated with the modeling of the placebo data. Functions of increasing complexity, such as linear, Emax, Hill and polynomial were test-ed to describe the time effect on the estimated transition probabili-ties/transfer rate constants. After addition of data from drug-treated patients, drug effects models were evaluated, using either a treatment flag, the dose, the predicted concentration Cp or Cavg as marker for certolizumab pegol exposure. During model building, efforts were made to keep the models as simple and parsimonious as possible by sharing the parameters for different transition probabilities/transfer rate constants when this was meaningful (i.e. similar parameter estimates and no significant increase in the objective func-tion value [OFV] when sharing the parameters). Equations retained in the final model are presented in the results section.

For all models (papers I, II and III), covariates were included in the mod-els based on their statistical significance, clinical effect and improvement in the VPC plots.

Variability model The IIV was estimated for the main ACR model parameters (Equations 10 and 12). The ηk,i, representing the random effect around parameter k for sub-ject i, was assumed to have a normal probability distribution of mean zero and variance ω2; its Bayes predictions allowed for subject-specific predic-tions of the corresponding transition probability.

No random effect around the dropout probabilities was estimated because patients could only drop out once during the trial, resulting in less than 1 observation per individual. This was also the case for the immunogenicity modeling where the appearance of ADAs was considered a unique event.

Dropout model Dropout was considered in the ACR modeling, either integrated in the model as an additional level of the categorical score, i.e. “ACR20 responder” vs. “ACR20 non-responder” vs. “dropped out” (paper I) or as a separate logistic model for binary data, i.e. “not-dropped out” vs. “dropped out” (paper II).

37

Model evaluation Because the model estimated the probability of a score and not a prediction of the score itself, residuals were not available for evaluating the goodness of fit. Model selection was based on changes in the NONMEM objective func-tion value assessed using a likelihood ratio test for nested models. The pre-dictive performances of the models were assessed through visual predictive checks (VPC). The proportions of ACR responders was simulated from the models and compared to the observed proportions of response. In case of early dropout in the original data set, additional rows reproducing the theo-retical observation scheme were added in order to mimic the trials and allow subjects to drop out at any time, according to model simulations. For the time to event modeling of immunogenicity data, VPC of Kaplan-Meier plots representing the evolution of the survival with time were produced.

Model-based simulations Simulations from the models were performed in TS2 (paper I) and NON-MEM (paper II) in order to compare the time courses of ACR response and dropout for various dosing regimens, e.g. with and without the use of a load-ing dose, and 200 mg Q2W and 400 mg Q4W maintenance treatment regi-mens.

ACR20 structural model At each visit, each subject was assessed as an ACR20 responder (score = 1), an ACR20 non-responder (score = 0), or a dropout (score = 2). The structural model described the transition probabilities between these three scores, i.e. the probability for a subject being in a particular state at a given visit condi-tioned on the score at the previous visit (Figure 11). These transition proba-bilities were defined using 2 digits, the first one representing the current score and the second one the score at the previous visit. At each time point, the sum of the probabilities corresponding to the possible transitions from the previous state remains equal to 1 (Pr10 + Pr00 + Pr20 = 1; Pr01 + Pr11 + Pr21 = 1). Therefore four probabilities were estimated (Pr10, Pr20, Pr10, Pr21) and the remaining ones (Pr00, Pr11) were deduced from them.

38

Figure 11. Transitions between the three possible states (ACR20 non-responder, ACR20 responder and dropout, defined by the scores 0, 1 and 2, respectively).

A model based on the data from placebo-treated subjects was first devel-oped. After addition of data from certolizumab pegol-treated subjects, drug-effect models were evaluated on top of the time course defined by the place-bo-treated subjects. Transition probabilities were described by logit func-tions (Equation 10).

Equation 10

1

, ,

1

where φk reflects the baseline logit score of the kth transition after the first dose of study medication and θk the corresponding typical population proba-bility operator. fpk(tij) and fdk(q(t)ij) denote respectively the time and addi-tional drug effects on the transition probabilities, tij being the time for jth observation of ith subject and q(t)ij the corresponding exposure measure-ment. Covariates were added as linear terms in the logit functions, with con-tinuous covariates being centered on their mean values in the data set (Equa-tion 11).

Equation 11

⋯ for categorical covariates

39

⋯ for continuous covari-

ates.

ACR20/50/70 structural model The ACR improvement scores were considered as categorical scores with 4 levels: ACR20 non-responder (ACR-NR, score = 0), ACR20 but not ACR50 responder (ACR20-50, score = 1), ACR50 but not ACR70 (ACR50-70, score = 2), and ACR70 responder (score = 3). The probabilities of the scores were modeled using a continuous-time type Markov model as compartment amounts, where the transition rate constants are estimated (Equation 12, Figure 12). At the time of observation, the actual score is known, i.e. the probability of observing this score is equal to 1. In the dataset, the compart-ment corresponding to the observed score is turned on, e.g. for a subject assessed as ACR20-50, compartment 2 is attributed an amount of 1 and compartments 1, 3 and 4 are attributed an amount of 0.

Figure 12. Transition model for the four ACR scores based on the clinical responses ACR20, ACR50 and ACR70.

Equation 12

0∙ Pr 1 ∙ Pr 0

1∙ Pr 0 ∙ Pr 2 ∙ Pr 1

2∙ Pr 1 ∙ Pr 3 ∙ Pr 2

3∙ Pr 2 ∙ Pr 3

with ∙ exp , and , , ,

where Pr(0) to Pr(3) are the probability of the scores from ACR20-NR to ACR70, the Kp are the transfer rate parameters between the compartments where the first digit of the rate parameter represents the current score and the second digit the preceding score (e.g. K21 can be read as the transfer rate to

40

score 2 given current score of 1). Kp,0 reflects the baseline value of the pth transfer rate parameter at the time of the first dose of study medication, gp(t) and hp(qij) the time and drug effects on the transfer rate, t the continuous time for the jth observation of ith subject and the corresponding exposure meas-urement for the jth observation of ith subject. The predicted concentration at the time of observation, Cp, was selected as marker for drug exposure based on the OFV.

Covariates were added on all the transition rate constants. Continuous and categorical covariates were introduced as showed in Equation 13.

Equation 13

, ∙ ∙

, ∙ 1 , , , ⋯

where θcov is the estimated covariate effect, CONT the continuous covariate value and CONTmed the median of the covariate in the dataset; θcov,CATx are the estimated categorical covariate effects, CATx = 1 for the corresponding covariate, CATx = 0 otherwise.

Immunogenicity model structure A model describing the time to appearance of ADA was developed. The probability of an individual to survive to time t was described by a paramet-ric survival function (Equation 14).

Equation 14

where h(t) is the hazard function characterizing the instantaneous risk of becoming Ab+, given that the individual had no event until t and H(t) is the cumulative hazard function. Various functions for describing the shape if the hazard function were tested during the model building.

Evaluation of IPPSE IPPSE is an alternative proposed method for sequential PKPD analysis. The ability of this method to estimate PD parameters with respect to bias and precision was assessed through a simulation study. Similar methodology and experimental setup were used for this analysis as used in a previous publica-tion comparing simultaneous (SIM) versus sequential (SEQ) approaches for

41

PKPD analysis46. Data were simulated from a population PKPD model and a specific study design, and were analyzed using the four methods evaluated. These steps were replicated 200 times in order to generate reliable statistics on the performance measures.

PKPD approaches Drug concentrations and effects measures were analyzed by non-linear mixed effect model as two stages models, including IIV and residual varia-bility. The SIM approach, where the sets of PK and PD parameters are esti-mated simultaneously (i.e. accounts for the uncertainties in both types of measures and allows the drug effect data to influence the fit of the PK mod-el) was compared to three different sequential methods. With the SEQ meth-ods, the sets of PK and PD parameters are estimated separately: first a PK model is fitted to the concentration data, and in a second step a PD model is fitted to the effect measurements, conditioned on the PK. The sequential methods differ according to the way the information about individual PK is propagated to the PD estimation step: The IPP method assumes that the individual PK parameter estimates are

known without uncertainty. The PD parameter estimation is based on the PD data and the posthoc individual PK parameter estimates.

The IPPSE method considers that the individual PK parameter estimates are known with uncertainty. The PD parameter estimation is based on the PD data, the posthoc individual PK parameter estimates and the SE of the individual PK parameter estimates.

The PPP&D method assumes that the population PK parameters are known and propagation of the individual PK information is through the PK raw data. The PD parameter estimation is based on the PD data, the population PK parameter estimates and the PK data.

PKPD models The PK data were simulated from a one-compartment model following a single bonus dose and the PD data were simulated from a direct Emax model (Equation 15).

Equation 15

, ∙ ∙

,∙ ,

50 ,

42

The clearance CLi, volume of distribution Vi and concentration to reach half of the maximum effect C50i were assumed to be constant within the ith indi-vidual and to differ randomly between individuals. Individual parameters were assumed to be independent and log-normally distributed with mean CL, V and C50 and variances ωCL

2, ωV2 and ωC50

2. No IIV was considered for the maximum estimated effect Emax in the PD model in order to reduce the risk of over-parameterization of the model. No covariance between CLi, Vi and C50i was assumed. The residual errors in observed concentrations (Cpij) and responses (Eij) consisted of both proportional and additive components (Equation 16).

Equation 16

, 1

, 1

where the random error terms ε1Cpij, ε2Cpij, ε1Eij and ε2Eij were assumed to be independent and normally distributed with mean 0 and variances σ1Cp

2, σ2Cp2,

σ1E2 and σ2E

2, respectively.

Model parameters and study design The PKPD design (total number of subjects, mean numbers of PK and PD observations by subjects within a replicates) and model parameters values for each of the 200 replicates were sampled from uniform distributions using the latin hypercube sampling package in R73, except the parameters CL, V and Emax that were set to the same typical value across replicates. The rang-es of possible values are presented in Table 8. The number of PK and PD observations for each subject were drawn from normal distributions around the sampled mean number of PK and PD observations and sampled accord-ing a scheme that ensured a reasonable distribution of the samples over the time interval.

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Table 9. Design and model parameters

Category Parameter Value Sampling

Study design Number of subjects [10;50] Fixeda Average number of PK observations per subject [2;7] LHSb

Average number of PK observations per subject [2;7] LHSb

Sampling times [0;10] In a list Parameters Clearance 3.46 Fixed Volume of distribution 10 Fixeda Emax 10 Fixeda C50 [1;5] LHSb

ωCL2, ωV

2 and ωC502 [0.01;0.09] LHSb

σ1Cp2, σ1E

2 [0.01;0.09] LHSb

σ2Cp2, σ2E

2 [0.04;0.25] LHSb a Fixed, scale factor, b LHS, uniformly distributed

Performance measures The accuracy and imprecision of the estimation of the PD parameters were evaluated using the signed and absolute errors of the parameter estimates, overall and by PK and PD observations. The mean and the median across the 200 replicates were calculated (Equation 17).

Equation 17

| |

where ParTrue is the true value and ParEst the estimated value of the pa-rameter.

The CPU time needed to fit the PD models was computed by replicate and the relative time saved with the SEQ methods compared to the SIM method was computed. The proportion of successful convergence of the estimation and successful completion of the covariance were calculated and the reasons for non-success in these two aspects were investigated.

44

Results

Reduced vs. Full joint count The full assessment of tender joint counts in the ACR core set of measure is based on the evaluation of 68 joints, and 66 joints for the swollen count. However, in study 1, a reduced 28 joint subset was used, that omit the joint located in the lower extremities (this count is used in the disease activity score DAS28). The similarity between the ACR response calculated based on the full and reduced joint counts was confirmed by the comparison of the ACR20, ACR50 and ACR70 responses computed based on the reduced 28 and the full 68/66 joint counts from studies 2 to 5. Results showed a good agreement between the scores computed using the full and the reduce counts: 95% agreement for ACR20, 97% agreement for ACR50 and 98% for ACR70, which was reassuring for pooling the data from study 1 with the data from studies 2 to 5 (Table 10).

Table 10. Comparison of the assessment of ACR response based on the reduced vs. full joint counts.

Result ACR20 ACR50 ACR70

Agreement between the reduced and the full counts 94.9% 96.7% 97.9% Underestimation of response with reduced count a 3.6% 2.1% 1.4% Overestimation of response with reduced count b 1.6% 1.2% 0.7% aAssessed “non-response” based on the reduced joint count while “response” based on full joint count, bAssessed “response” based on the reduced joint count while “non-response” based on full joint count.

Time effect The time was the first explanatory variables included in all models, for de-scribing the time-course of the ACR responses and the time to appearance of ADAs.

In the ACR20 model, time effect was described by a linear function on the logit scale for the probability of becoming a responder, and a non-linear Emax relationship for the probability of reverting back to the non-responder state (Equation 18).

45

Equation 18

∙ 7

t ∙7

50 7

where s10 represents the slope of the linear relationship and the time origin was rescaled to account for the first ACR20 outcome from baseline (Time = 0) being assessed one week after the first dosing, i.e. typically at day 7. ET5001 represents the time to reach half of the maximum transition probabil-ity E01.

In the continuous-time Markov model for ACR20, ACR50 and ACR70, linear relationships described the time effects on the estimated transfer rate parameters (Equation 20) and a Hill function on the logit scale described the effect of time on dropout (Equation 22).

The time course of the hazard for developing ADAs was estimated using a step function with constant hazard parameters estimated over pre-defined monthly time intervals. The resulting hazard estimated for the whole dataset was high during the first months after the start of the dosing with a maxi-mum effect at month 3 and decreased to achieve a low and constant value from month 5 onwards.

Exposure-response Increased exposure to certolizumab pegol significantly increased the proba-bility of becoming an ACR20 responder (paper I) and achieving a higher level of ACR response (paper II) while it decreased probability of dropping out (paper I) and developing ADAs (paper III).

In the ACR20 model, Cavg was retained in the final model as the expo-sure measure to relate to the clinical response. The effect of Cavg on the transitions probabilities was incorporated into the logit expressions with Emax relationship that were found to share a common potency parameter (help-maximal effective concentration, 16.8 μg/mL) but differed with respect to the magnitude of the maximum effect Emax. The logits for the two drop-out probabilities decreased linearly with increasing Cavg and were found to share a common shape parameter (Equation 19).

46

Equation 19

where q(t)ij is the Cavg for the jth observation of the ith subject and s2x repre-sents the slope of the linear effect of Cavg on the dropout probabilities from responder and from non-responder states.

In the continuous-type ACR20/50/70 model, an Emax relationship with positive Emax value (on K10) and linear functions with positive slopes (on K21 and K32, common slope) described the effect of the drug concentration on upward transfer rate constants. Emax relationships with negative esti-mates of Emax described the drug effect on downward rate parameters (K01, K12, K23, common Emax). The Kp were restricted to be positive by setting the lower boundaries of the initial parameter estimates (Equation 20).

Equation 20

, ∙ 1 ∙ ∙ 1 ∙ ∙ for K10, K01,

K12 and K23;

, ∙ 1 ∙ ∙ 1 ∙ ∙ for K21 and K32

where sltp represent the slope of the linear relationship to continuous time and and sldp the slope of the linear relationship to concentration, Emaxp is the maximum change in the pth transfer constant value as function of the exposure measure and EC50 the concentration to reach half of the maximum effect related to Cp, common to the relevant transfer rate parameters.

In the immunogenicity time to event model, Ctrough was the most influ-encial covariate affecting the time to appearance of ADAs. The hazard was reduced when higher trough concentration were achieved, in the range of predicted Ctrough (the hazard should be null in the absence of drug). It was incorporated in the model in an exponential term affecting the hazard (Equa-tion 21).

Equation 21

∙ ∙

where SLE is the estimated effect on the hazard.

47

Covariates The covariates included in the final models are summarized in Table 11, and the ranges of the covariates are presented in Table 8. Covariates

The ACR20 model was improved by incorporation of two Markov ele-ment of order greater than one: the ACR20 response state at the antepenul-timate visit (second-order Markov element) and the average ACR20 re-sponse since the start of the trial. Subjects with a history of response were found to have higher probabilities of remaining responders and of transition-ing back to response in the event they temporarily reverted to non-response. The probability of remaining a responder also increased if the subject was already a responder at the antepenultimate visit. With regards to dropout, subjects with a history of response tended to remain in the trial, provided that they continued to respond. However, such subjects also had a higher probability of dropping out immediately after reverting to non-response.

The concomitant administration of MTX was the second best covariate in the immunogenicity TTE model, it was added on top of the Ctrough effect that was estimated to be higher in the presence of MTX. Some bias remained in the fitting of a few treatment regimens. As no other significant explanato-ry covariate (such as the frequency of dosing, the formulation or the use of concomitant medications) was identified, specific study effects were incor-porated in the model for studies 2 and 3.

Dropout The dropout was evaluated as an integrated part of the ACR20 Markov mod-el, as described in the above sections (paper I). It was characterized using a logistic model in the ACR20/50/70 analysis. The increase in dropout with time from the start of the trial was described by a Hill function on the logit scale, where the time to reach half of the maximum dropout was estimated to approximately 3 weeks. ACR50 and ACR70 responders were less likely to drop out than ACR20 responders, while ACR20 non-responders had the highest probability of dropping out (Equation 21).

Equation 22

∙ 20 ∙ 50 ∙ 70

1

48

where φ reflects the baseline (time=0) logit score of the dropout, EmaxT the maximum change in the logit related to time, T50 the time to reach half of this maximum change. The parameters θACR20, θACR50 and θACR70 reflects the effects of previous ACR outcome (ACR20 = 1 if the patient was an ACR20 but not ACR50 responder and 0 otherwise, similarly for ACR50-70 and ACR70).

Table 11. Summary of the models’ variables

Dependent variable Explanatory variable Parameter Description

Drug concentrations Bodyweight CL/F ±30% for 40-120 kg relative to 70 kg

ADA status CL/F 2.91 fold increaseACR20 Time P10 Linear relationship on the logit scale P01 Emax relationship on the logit scale Cavg P10, P01 Emax relationship on the logit scale P20, P21 Linear relationship on the logit scale Average PACRa P01, P21 for higher history of response P10, P20 for higher history of response Second. ACR20b P10 for responders at antepenultimate

visit Baseline CRP P10 for high vs. low baseline CRP Baseline TJC P10 for high vs. low baseline TJC Age P01 in older vs. younger subjects Region P01, P20,

P21 for North Americans

Baseline pain P01 for max. vs. min. baseline pain Disease duration P20 for longer vs. shorter duration Gender P21 for menACR20/50/70 time K10, 21, 32 Linear function with positive slope time K01, 12, 23 Linear function with negative slope Cp K10 Positive Emax function Cp K21, K32 Linear function with positive slope Corticosteroids K10, 21, 32 with concomitant administration Baseline SJC28 K10, 21, 32 with high vs. low SJC Age K01, 12, 23 for higher vs. lower age Region K10, 21, 32 in Central and South America,

North America, Western Europe in Northern Europe

Time to ADA ap-pearance

Time Step function

Ctrough / MTX h(t) with higher Ctrough, higher with concomitant MTX treatment

Study h(t) in study 2 and 3 Baseline SJC28 K10, 21, 32 with high vs. low SJC aAverage of previous ACR20 response since the start of the trial, bantepenultimate ACR20 score, Cavg = average drug concentration over the dosing interval, CL/F = apparent clearance, Cp = predicted drug plasma concentration, CRP = C-reactive protein, Ctrough = trough plas-ma concentration, MTX = methotrexate, SJC = swollen joint count, SJC28 = reduced swollen joint count evaluated on 28 joints, TJC = tender joint count.

49

IPPSE method Precision in parameter estimation The precision of the estimation of the PD model parameters (based on as-sessment of absolute errors) was similar for the SIM, IPPSE and PPP&D method, better than the IPP method (Figure 13). The variance component VarC50 was badly estimated in all cases, but benefited the most from the estimation with IPPSE, PPP&D and SIM approaches over IPP (median of the absolute error 60 vs. 100%). The trend of imprecision in the PD parame-ter estimates by number of observations in the dataset was also similar for the SIM, IPPSE and PPP&D methods. The concentration to reach half of the maximum effect, C50, was the parameter that was most dependent on the number of PK and PD observations in the dataset, while Emax was insensi-tive to this design feature. For the estimation of VarC50, the means of the absolute errors increased markedly for sparse PK data, while the median values remained constant, indicated some very influential runs had very poor estimates of the variance component under this settings (with the IPP meth-od, both the mean and the median of VarC50 estimation absolute error were affected by data sparsity).

Figure 13. Mean and median absolute errors of PD parameters obtained with the FOCE I estimation method, SEQ vs. SIM methods. Grey circles represents the IPP, grey squares the PPP&D and black triangles the IPPSE method. Empty symbols represent the means and filled symbols the medians.

Accuracy of PD parameter estimation All parameters were most accurately with the SIM, IPPSE and PPP&D methods over IPP (based on assessment of signed error, Figure 14). Bias in the estimates of the variance parameters were reduced with these 3 methods, but was still affected by influential runs, as evidenced by higher means of signed errors (around 50%). The signed errors for C50 are slightly higher for the SEQ methods then for the reference SIM.

The IPPSE approach presented globally a similar trend for the accuracy of PD parameter estimation by number of PK and PD observations as PPP&D

50

and SIM, even though PPP&D was generally the SEQ method closest to SIM with respect to mean of the signed errors. The bias for IPP consistently deviated the most from the reference bias obtained with SIM. For the estima-tion of VarC50, similarly as the absolute errors (imprecision), the means of the signed errors increased markedly for space PK data, while the median values remained constant, indicated some very influential runs had very poor estimates of the variance component under this settings (with the IPP meth-od, both the mean and the median of VarC50 estimation signed error were affected by data sparsity).

Figure 14. Mean and median signed errors of PD parameters obtained with the FOCE I estimation method, SEQ vs. SIM methods. Grey circles represents the IPP, grey squares the PPP&D and black triangles the IPPSE method. Empty symbols represent the means and filled symbols the medians.

Estimation time Sequential methods saved 86% [83;88] for IPP, 61% [55;67] for IPPSE, and 39% [32;45] for PPP&D methods over the SIM method (median [p25;p75] for the 200 runs.

Estimation status All runs converged successfully with the IPP and IPPSE methods. One run for the SIM and 3 runs for the PPP&D did not converge successfully. The SEQ methods had the highest frequency of success in estimating one or more variance components and providing standard errors of the estimates; IPP achieved the highest rate of success (74%), followed by IPPSE (68%) and PPP&D (66%) while it was only 58% with the SIM method. The success of covariance estimation decreased with sparse PD data, but only SIM was affected by sparse PK data.

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Discussion

In this thesis, PKPD data from rheumatoid arthritis clinical trials were ana-lyzed, including PK (immunogenicity) and PKPD analyses, dropout model-ing, and methods for performing PKPD analyses were evaluated.

The two pooled exposure-response analyses established the relationships between the exposure to the new anti-TNFα drug certolizumab pegol and the ACR improvement scores (ACR20, ACR50 and ACR70). The ACR20 score (as a dichotomous variable) was selected for the first model (paper I) as it was the primary efficacy variable in the included clinical trials. ACR20 was recommended by the ACR as a tool to standardize outcomes in rheumatoid arthritis trials32 and became a key criterion for regulatory decision by the US Food and Drug Administration as the efficacy benchmark in rheumatoid arthritis clinical trials74. Compared to more stringent criteria such as ACR50 and ACR70, it was shown in 1998 to achieve highest discriminatory capacity to distinguish active treatment from placebo control, while higher scores best reflected patient satisfaction75,76. The ACR20 Markov mixed effect model developed in this thesis was successfully used to support the registration of certolizumab pegol among the health authorities, including FDA and Euro-pean Agency for the Evaluation of Medicinal Products (EMEA, now Euro-pean Medicines Agency [EMA]), as well as the labeling with regards to dos-ing regimens. Simulations were performed from the model that helped to support the proposed label maintenance treatment of 200 mg Q2W or 400 mg Q4W and the use of a loading dose at weeks 0, 2 and 4. The model and simulations from the model assisted communication of the certolizumab pegol treatment regimens85,86.

With the advent of more effective therapy, the outcome of clinical trials shifted towards higher response to treatment and in clinical trials conducted after 1997, similar discriminant capacities were identified for ACR20 and ACR50 to distinguish active versus control treatment77. In addition, 20% improvement does not represent the optimal clinical progress that is ex-pected from the new drugs tested in clinical trials; it is not a meaningful clin-ical response for rheumatologist. The ACR50 and ACR70 responses are more desirable target for the patient and provide additional qualitative in-formation compared to ACR2076,77. Therefore, in a second step, these higher thresholds of responses were considered (Paper II). While a stand-alone model similar as the ACR20 model was developed for ACR50, this showed some limitations, for example the dropout driven by study design could not

52

be implemented79. Another aspect is that dichotomizing the ACR assessment into binary variables discards information80. Characterizing the three thresh-olds of 20, 50 and 70% improvement, i.e. 4 levels of response ranging from ACR20 non-responder to ACR70 responder, is gaining more information from the same amount of collected data (ACR core set of measures). A dif-ferent type of model was proposed for this purpose, in order not to dramati-cally increase the number of categories with the possible number of transi-tions and to accommodate varying time intervals between observations.

The two ACR models were developed with the objective to account for the dependency of the successive ACR assessments recorded repeatedly over time for each individual, hence the use of the Markov approach. In models where this within-subject variability is not taken into account, the IIV is overestimated and therefore the model-predicted number of transition be-tween the responder and the non-responder stages within each individual is higher than the observed one (Figure 15). The autocorrelations within the data was evidenced during the modeling of the ACR20, where the inclusion of first order and higher-order Markov element improved the fit of the model (antepenultimate score, average score since the start of the trial). These ele-ments allowed the characterization of the sustained response to drug treat-ment : patients with an history of response were more likely to remain re-sponder or to turn responder again, even if they occasionally failed to re-spond.

The main characteristics of the two types of models are summarized and commented in Table 12. The primary difference between the two Markov approaches lies in that the continuous type Markov model does not assume time homogeneity, but the influence of the preceding score decreases with time between observations, and therefore is better at extrapolating to situa-tions with different dosing and observation schedules. On a practical point of view, the continuous Markov model structure is very intuitive and therefore easy to implement in the software NONMEM, but the formatting of the da-taset is more complicated, both for the estimation and the simulation step. The difficulties lies in that the observation are turned into compartment amounts, e.g. if the score “ACR20 but not ACR50” is observed / simulated, the compartment 2 is to be turned on with amount set to 1 and all other com-partments turned off with amount set to 0. This continuous-type model is implemented as differential equations, the computational run time may in-crease significantly with the amount of data, especially if numerical difficul-ties arise in the integration routine.

53

Table 12. Main characteristics of the two types of Markov models developed to characterize the ACR scores

Characteristic Logistic-type Markov (ACR20, paper I)

Continuous-type Markov model (ACR20/50/70, paper II)

Endpoints Primary endpoint used as benchmark in clinical trials. This type of model can be ex-tended to ordered categorical data with Markov elements.

Includes higher level of ACR response, providing additional information.

Model structure Logistic model for the transi-tion probabilities.

Compartment-type model.

Model parameters Transition probabilities. Increasing the number of cate-gories could lead to a dramatic increase in the number of mod-el parameters (it may be re-duced if not all transitions exist in the data)61,63.

Transfer rate constants. More parsimonious, not all possi-ble transitions have to be deter-mined with a separate model parameter.

Markov type The transition probability is conditioned on the value of the preceding state whatever the time is between 2 observations. Markov elements of greater order were incorporated (the dependency may vary with time61).

The influence of the preceding state decreases with time. Better at extrapolating to situa-tions with different dosing and observation schedules.

Dropout Integrated in the model as implemented here.

Modeled separately in a joint model. Could be integrated to the model if the data allows.

Implementation in NONMEM

In $PRED given that no time-varying covariates are used. Possibly easy to implement and short to run.

In $DES (differential equations). Intuitive to implement, may be computationally intense.

Formatting of the data (NONMEM)

Dropout incorporated as an additional score.

2 types of data for the joint model as implemented here (ACR, dropout); the compartments corresponding to the observed score must be turned on.

The Markov approach has been extensively compared with the LV approach in the literature as various models for modeling ACR scores have been pro-posed50,58,59,82 (including Papers I and II in this thesis). The main characteris-tics of both types of models are described in Table 13. The LV approach has the appeal to use a more pharmacologically founded continuous function that can be to describe the underlying unobserved variable, such as the indirect response model that was implemented to describe the ACR20 score57. Pa-rameters from such models are easier to interpret compared with the transi-tion probabilities on the logit scale or the transfer rate constants in the two types of Markov models. Following the initial implementation57, the LV model was applied to model simultaneously the three ACR levels ACR20,

54

ACR50 and ACR70. The approach has been subsequently improved, first to be more parsimonious and to be able to predict a probability of 0 at time = 0, which make sense for variables representing an improvement over base-line58, second to allow meaningful interpretation of intercept terms for char-acterizing placebo steady-state probabilities59. The main claim of the Markov approach over the LV approach is that it accounts for within-subject correla-tion of the observations, while the autocorrelation is characterized by the between subject random effect in the current implementation of LV models. This was illustrated in Paper I by applying the LV model that had been de-veloped for modeling the ACR20 response in rheumatoid arthritis subjects treated with a JAK3 inhibitor57 to our data. The estimated parameter esti-mates were similar to those in the original LV publication and the LV model predicted ACR20 response well, but it overestimated the movements be-tween the “ACR20 responder” and the “ACR20 non-responder” states (Figure 15). The LV approach has later been extended to accommodate cor-relations within longitudinal data with a method that uses the correlations between the latent residuals to address extra-correlation and predict fewer transitions, but this method is not easy to utilize because it still need to be implemented in currently available software packages84.

Figure 15. Predictive check by transition for the reduced Markov Model (1st order, no covariates – Black-shaded areas) and the LV model with 1st order Markov ele-ments (Red-shaded areas). Shaded area represents 90% PI (250 replicates), black points represents observed data.

55

Table 13. Main characteristics of the Markov vs. LV models developed for charac-terizing ACR scores and general comments

Characteristic Markov models (logistic-type ACR2082 and con-tinuous type ACR20/50/7083)

LV models (ACR2057 and ACR20/50/7058, 59)

Parameterization Transition probabilities on the logic scale / transfer rate con-stants.

Indirect response model, mapped to the probability of the scores (other type of continuous models may be used).

Parameter interpre-tation

Not straight forward82,83. It is difficult to understand how each model parameter influences the overall response rate58. Simulations should be done to help the interpretation.

The parameters such as Emax and EC50 are meaningful 57. The model predicts directly the probability of a positive response for the average subject58.

Within-subject correlations

Markov elements of first or higher order82 / influence of the preced-ing state decreases with time83.

Included in the IIV random ef-fect59

Number of parame-ters

The continuous model is more parsimonious than the logistic model for increased number of response levels. It has a large flexibility by allowing different covariates and drug effects for each transition rate.

Parsimonious, while flexibility can be added by fitting separate intercepts for the different thresh-olds57.

Dropout Integrated in the model or added in a separate model.

Not included in the initial mo-dels57, 58. Added in a separate model50.

In our data, most of the observed dropout was due to lack of improve-ment/disease deterioration (91% of the dropout on placebo treatment and 70% of the dropout on drug treatment). Therefore the dropout was included in the PKPD models with the same approach, using Markov elements. In the ACR20 model, this was implemented by addition of a third score represent-ing dropout (non-reversible transition to dropout, Figure 11). In the continu-ous Markov model, the dropout may similarly have been implemented as an additional compartment with transfer rate constants. However in our dataset, dropout events were recorded at the same time points as ACR observations. Therefore, a logistic regression model for dropout was developed and im-plemented as a separate model, including first order Markov elements to account for last observed score before the subject left the trial.

Immunogenicity became a concern with the advent of biologic therapies because it may impact both the safety and the efficacy of the drugs. The analysis of immunogenicity is currently restricted by the limitation in the available analytical methods. The assays such as ELISA can usually not detect ADAs that are in complex with the drug, therefore high concentra-tions of circulating drug may hide the presence of ADAs and the reported measure of ADA may be underestimated87,88. In addition, the measurement of ADA is semi-quantitative, there is no universal standard and lack of con-

56

sistency in reporting the immunogenic response. Therefore, ADA data can-not be compared between different assays or products87,89. The immunogen-icity was taken into account in the PKPD modeling, using covariates in the population PK model where the presence of ADAs was associated with a 2.91 fold increase in the apparent clearance. However this did not character-ize the immunogenicity. A time to event model was developed for this pur-pose, which related the formation of observable ADAs (given the limitations of the analytical bioassays as explained above) to the drug exposure and the level of concomitant methotrexate. The previously developed population PK model was used to derive the drug exposure parameters.

In Paper IV, the IPPSE method was proposed as an alternative method to perform PKPD analysis sequentially. IPPSE accounts for the uncertainty in the individual parameter estimate, relaxing the value of the parameter esti-mate that condition the PD parameter estimation. It had previously been shown that the IPP method that conditions the PD parameter estimation on the individual PK parameters implied the loss of some valuable information about the individual PK46. The PPP&D and the IPPSE methods are both proposed to overcome this weakness of sequential analyses, with the indi-vidual PK information propagated through the raw data (PPP&D) or the individual PK parameters estimates and their SEs (IPPSE). The two methods performed similarly and resulted in not much less precise and accurate pa-rameter estimates than the simultaneous method (SIM). The improvement provided by the PPP&D over the IPP method showed that the PK observa-tions contain subject specific information that is helpful in the PD fitting. The population parameters used in this method are typically estimated with better precision than the individual post-hoc parameters used in the IPP method and are less biased in sparse data analyses. The improvement pro-vided by the IPPSE method over IPP showed that the accounting for the uncertainty in the first-state PK parameter estimates allows to retrieve most of the information relative to the actual data that is missing in the simplistic IPP approach. The main advantages of the SEQ approach over SIM are the decreased run times and the higher stability when estimating the PD model parameters. Both PPP&D and IPPSE methods attempt to find a useful bal-ance between the benefit of the IPP method and the performance of the method to adequately estimate the PD parameters. With this respect, the rate of success with the SIM method was not only sensitive to the low number of available PK observation in the dataset, but also the superiority of PPP&D and IPPSE over SIM increased with increased number of PD observations. The run times were shorter with IPPSE compared to PPP&D, with an aver-age of 61% vs. 39% time saved over SIM, which may justify the choice of this approach when time saving is critical and/or run time is elevated, for example if the dataset is huge. The IPPSE method could also be applied to other situations than PKPD sequential analysis, in the situation where a first set of parameters are estimated and has to be fixed for the second part of the

57

analysis, allowing to relax the value of the parameter estimates and not con-sider that it is known without any error. This could be for example a PK analysis where the parameters characterizing the PK after single dose cannot be estimated simultaneously with the parameters characterizing the PK after multiple dose, or for an analysis where a PK or PD variable is driving an outcome such as dropout or survival. This approach may have been applied here for the immunogenicity modeling (Paper III), where the individual PK parameters and their standard errors from the initial PK step may have been used, rather than the individual PK observations and the PK model parame-ters. However this approach was not applied for the analysis of immunogen-icity because the model was implemented in such a way that the PK and immunogenicity could be evaluated simultaneously. The objective – not implemented here – was to incorporate not only the drug exposure effect on the time to appearance of ADAs, but also in turn the presence of ADAs on the PK in a dynamic way instead of a binary covariate.

58

Conclusions

Two Markov models were developed for characterizing the time course of the ACR20 and the ACR20/50/70 improvement scores in rheumatoid arthri-tis clinical trials. Both models accounted for the within-subjects correlation in the successive clinical assessments observed during the trials and were able to capture both the observed ACR responses and the observed propor-tions of transitions between the ACR responder states. Exposure-response relationships were successfully established, that related the exposure to the anti-TNFα biological drug certolizumab pegol and the ACR improvement scores. The two models showed good properties for simulating the propor-tion of response and the transitions between the different states.

The ACR20 model included higher level of Markov elements that ac-counted for the history of response. The dropout also depended on the expo-sure to the drug and the history of response to the treatment. The model was useful to explore dosing regimens that were included in the labeling.

The ACR20/50/70 model characterized higher levels of response (ACR50 and ACR70) that are more meaningful for clinicians and more desirable for patients than the ACR20 response. The simultaneous analysis of the 4 levels of ACR was performed to use the data more efficiently and gain more in-formation from the ACR set of measures. The model accounted for the de-pendency in the observations, where the influence of the preceding observa-tion decreases when the time between observations increases. The models may be utilized in drug development to characterize and simulate expected ACR assessments under various settings and assumptions, and to derive clinically meaningful outcomes. This approach is applicable to model any ordered categorical score where consecutive observations are dependent.

Immunogenicity is a characteristic that is specific to biologic drugs. The time to event model characterized the time to appearance of antibodies di-rected against the drug. The immunogenicity was predicted to appear main-ly during the first three months of therapy and to be reduced with higher exposure to the drug, as well as with concomitant administration of metho-trexate.

The IPPSE method for sequential analysis of the PKPD data is a promis-ing alternative for PKPD analysis. It combines the advantages of the refer-ence simultaneous analysis method with regards to good precision and low bias of parameter estimates with the advantage of the sequential IPP methods with short run times and easy implementation.

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Acknowledgments

Ce que nous sommes est aussi le témoignage des personnes que nous avons admirées et aimées, qui nous ont instruit et influencés...

Lluis Claret (violoncelliste) à Kilian Jornet (amoureux des montagnes, athlète)

Who we are is also the testimony of the people we admired and loved,

who taught and influenced us ….

Lluis Claret (violoncelliste) to Kilian Jornet (mountain lover, athlete)

The work presented in this thesis was carried out at the Department of Pharmaceutical Biosciences, Faculty of Pharmacy, Uppsala University, Sweden. Financial support was provided by UCB Pharma. I have received help and encouragements from numerous people without whom I could not have completed this thesis work. Many thanks to:

My main supervisor Lena Friberg for always remaining positive and calm while helping me to find solutions to progress in my work. You always pushed me to give my best and impressed me with your scientific expertise, your availability and your human behavior.

My deputy supervisor Mats Karlsson for accepting me in this program and bringing your magic touch and innovative ideas in each of the projects. Also thanks for integrating me in the group activities.

My deputy supervisor from UCB, Laura Maier (head of clinical M&S group) for your trust, your passion and your encouragements. My half-time seminar remains a good memory, you showed such an enthusiasm to see one of your team member reaching this step!

My line management at UCB who made this PhD program possible: Thomas Senderovitz (head of the Global Exploratory Development department GED) and Armel Stockis (head of the Pharmacometrics group) for initiating the collaboration with the university. Magnus Sjögren and Duncan Mc Hale, former and current head of GED for your continuous support, even across the changes at UCB. Ruth Oliver (head of clinical M&S group) for defend-

60

ing this program and allowing me to continue despite the industry and re-sources constrains.

Armel, also for the « Aphorisms of an old monkey » (auquel on n’apprend pas à faire des grimaces). Your witticisms always reach their targets, you were the only one capable to make us laugh during s difficult days at UCB.

All members of the various Cimzia teams and sub-teams to whom I partici-pated. All UCB reviewers and the UCB publication teams for your under-standing and increased flexibility towards academic needs.

Mark (coauthor of paper I) and Hishani (coauthor of paper III), it has been a pleasure working with you.

Gerry, the best clinical pharmacologist I could have dreamed to work with: thanks for sharing your deep knowledge of Cimzia, for your availability and your openness to M&S. Your guidance and opinions were always of added value.

Kajsa for your efficient and kind help with the technical questions. Maud for the great IT support at UCB. Not only you listened to our needs, but also you understood what we were doing! To quote Armel: ‘You are our true PsN: you are a pearl and you speak nonmem !’

Emilie and Alexandre, the Lyon connection, for great time in Uppsala and at PAGE meetings… our long discussions (around sushis?) rebuilding the world. A special thanks to Emilie for all our fruitful discussions on our mod-eling projects. It learnt a lot from you! (un tantinet scolaire ? ;-) )

Åsa for all the fun, including the good souvenirs watching the Winter Olym-pic Games (although we did not have the same favorites). Gaël, Camille, Jan-Stefan, Rocio, Joy, Ami, Elodie and Paul for nice entertainment time and discussions (and Camille, also for sharing your philosophical doubts!). Joe for organizing an unforgettably bike trip from Uppsala to Herränge… and return!

Nathalie for being such a great support all the time. You are always availa-ble to provide advices, to cheer me up and help me gain some confidence that I will complete this PhD eventually!

« Les rebelles du Cimzia », Christophe and Laetitia for the data manage-ment, the dataset programming support, and the memory of the Cimzia stud-ies (and there is more to come!).

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All other colleagues from the PMX group and the department for always warmly welcoming me in Uppsala, whether I was visiting for 4 months or 2 days. A special thanks to Angelica, Martin, Elin, Salim, Emilie S., Anne-Gaëlle, Siv, Irena, Britt and Marina for nice fika and lunch discussions. And of course all participants to the Yukiko Wednesday’s sushi lunches!

All my former and current colleagues and friends from UCB GED. Despite the storms we have been through, a great team spirit was always present. Etienne, for the transmission of your work on Cimzia. Colleagues from Monheim and in particular Brunhild, Jochen, Dirk and Jan-Peer for the good but too short collaboration. Elisabeth, Laurence and Véronique D. for the nice lunch breaks and discussions about everything apart work... Veronique C. for all the fun and crazy ideas (I like your sheeps), I miss you! Dominique, the king for putting ideas into equations. Miren, Rocio and Pa-van for the excellent collaboration over the channel.

All the persons who initiated me to the pharmacometric discipline and made me want to continue in the field: France Mentre, Sylvie Retout and Emman-uel Comets for an unforgettable year of master (DESS). Pascal Delrat and Christian Laveille from Servier for the kind initiation to NONMEM.

My friends for always supporting me and forgiving me when I was not available while travelling, for your visits to Sweden and Belgium and for always being with me in the important events of my life: Florence (best and only partner for the practical works during pharmacy studies), Ella-Pauline, Tamara, Christelle, Dani.

My parents, maman et papa, for always being proud of me and supporting me whatever my choices. My sisters Caroline and Marie and my brother François for remaining so close despite the distance.

Frédéric, for your patience and for helping me escape the PKPD world. Thanks for all the fun and crazy sport competitions we made together (Lin-digö-Ultra, Namur-Raid…), and for the entertaining visits of Sweden includ-ing a fantastic tour of the best mini-golfs of the country (the winner is defi-nitely Falun Lugnet, with honors!).

Mes deux amours, Frédéric and Antoine for reminding me what is most im-portant in life, and for your invaluable contributions to this thesis:

“- Bootstraps? Are these the straps to tighten your cross-country ski-boots? - Adadadada... dada !”

(Feb 2014, ski holidays, Le Grand Bornand, France)

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Image © Natmatiss au féminin www.natmatiss.com Carrière – Management – Leadership

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