ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2019

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Pharmacy 267

Pharmacometric Models toImprove the Treatment andDevelopment of Drugs againstTuberculosis

ROBIN J. SVENSSON

ISSN 1651-6192ISBN 978-91-513-0598-1urn:nbn:se:uu:diva-379359

Dissertation presented at Uppsala University to be publicly examined in B21, BMC,Husargatan 3, Uppsala, Friday, 3 May 2019 at 09:15 for the degree of Doctor of Philosophy(Faculty of Pharmacy). The examination will be conducted in English. Faculty examiner: PhDAndreas Krause (Department of Clinical Pharmacology, Idorsia Pharmaceuticals Ltd).

AbstractSvensson, R. J. 2019. Pharmacometric Models to Improve the Treatment and Developmentof Drugs against Tuberculosis. Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Pharmacy 267. 77 pp. Uppsala: Acta Universitatis Upsaliensis.ISBN 978-91-513-0598-1.

With 10 million new infections yearly, tuberculosis has a major impact on the human well-being of the world. Most patients have infections susceptible to a first-line treatment with atreatment success rate of 80%, a number that can potentially be improved by optimising thefirst-line treatment. Besides susceptible disease, each year half a million patients are infected bytuberculosis with resistance to first-line treatment where only 50% of patients get cured. Thus,new drugs against resistant tuberculosis are desperately needed but given the inefficiency ofdeveloping new anti-tuberculosis drugs, enough new drugs will not reach patients in time. Theaim of this thesis was to develop pharmacometric models to optimise the development and useof current and future drugs for treating tuberculosis.

A population pharmacokinetic model for rifampicin, the most prominent first-line drug, wasdeveloped and later used for developing exposure-response models followed by clinical trialsimulations. The developed exposure-response models were based on liquid culture data andwere expanded to describe the relationship between liquid culture results and a new biomarker,the molecular bacterial load assay which is a quicker alternative to liquid culture and is alsocontamination-free.

The in vitro-derived semi-mechanistic Multistate Tuberculosis Pharmacometric (MTP)model was applied to clinical rifampicin and clofazimine colony forming unit datasets. Thisnovel application of the MTP model allowed detection of statistically significant exposure-response relationships between rifampicin and clofazimine for the specific killing of non-multiplying, persister bacteria. Furthermore, the MTP model was compared to conventionalstatistical analyses for detecting drug effects in Phase IIa. If designing and analysing PhaseIIa using the MTP model, the required sample size for detecting drug effects can be lowered.An improved design and analysis of pre-clinical treatment outcome assessments was developedwhich increased the information gain compared to a conventional design yet kept the animal useat a minimum. Lastly, a therapeutic drug monitoring approach was suggested based on updatedtargets for rifampicin, a framework easily expandable to second-line drugs.

In conclusion this thesis presents the development of pharmacometric models which willstreamline both the development and use of drugs against tuberculosis.

Keywords: Pharmacokinetics, Pharmacodynamics, Biomarkers, Rifampicin, Clofazimine,Therapeutic drug monitoring, Time-to-event, Time-to-positivity, Molecular bacterial loadassay

Robin J. Svensson, Department of Pharmaceutical Biosciences, Box 591, Uppsala University,SE-75124 Uppsala, Sweden.

© Robin J. Svensson 2019

ISSN 1651-6192ISBN 978-91-513-0598-1urn:nbn:se:uu:diva-379359 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-379359)

När ett problem förefaller vara akut är det första man börgöra inte att skrika vargen kommer utan att organisera data.

[When a problem appears to be acute, the first thing one

should do is not to cry wolf but to organise data.]

Hans Rosling

List of Papers

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

I Svensson RJ, Aarnoutse RE, Diacon AH, Dawson R, Gillespie

SH, Boeree MJ, Simonsson USH. (2018) A population pharma-cokinetic model incorporating saturable pharmacokinetics and autoinduction for high rifampicin doses. Clin Pharmacol Ther, 103(4):674-683

II Svensson RJ, Svensson EM, Aarnoutse RE, Diacon AH, Daw-son R, Gillespie SH, Moodley M, Boeree MJ, Simonsson USH. (2018) Greater early bactericidal activity at higher rifampicin doses revealed by modeling and clinical trial simulations. J In-fect Dis, 218:991-999

III Svensson RJ, Sabiiti W, Kibiki GS, Ntinginya NE, Bhatt N, Davies G, Gillespie SH, Simonsson USH. Model-based rela-tionship between the molecular bacterial load assay and time-to-positivity in liquid culture. Submitted.

IV Svensson EM, Svensson RJ, te Brake LHM, Boeree MJ, Hein-rich N, Konsten S, Churchyard G, Dawson R, Diacon AH, Kibiki GS, Minja LT, Ntingiya NE, Sanne I, Gillespie SH, Hoelscher M, Phillips PPJ, Simonsson USH, Aarnoutse RE. (2018) The potential for treatment shortening with higher ri-fampicin doses: relating drug exposure to treatment response in patients with pulmonary tuberculosis. Clin Infect Dis, 67(1):34-41

V Svensson RJ, Simonsson USH. (2016) Application of the mul-tistate tuberculosis pharmacometric model in patients with ri-fampicin-treated pulmonary tuberculosis. CPT Pharmacomet-rics Syst Pharmacol, 5(5):264-273

VI Faraj A, Svensson RJ, Diacon AH, Simonsson USH. Drug ef-fect of clofazimine on persisters explain an unexpected increase in bacterial load from patients. Submitted

VII Svensson RJ, Gillespie SH, Simonsson USH. (2017) Improved power for tuberculosis Phase IIa trials using a model-based pharmacokinetic-pharmacodynamic approach compared with

commonly used analysis methods. J Antimicrob Chemother, 72(8):2311-2319

VIII Mourik BC,* Svensson RJ,* de Knegt GJ, Bax HI, Verbon A, Simonsson USH, de Steenwinkel JEM. (2018) Improving treatment outcome assessment in a mouse tuberculosis model. Sci Rep, 8(1):7514

IX Svensson RJ, Niward K, Davies Forsman L, Bruchfeld J, Paues J, Eliasson E, Schön T, Simonsson USH. Individualised dosing algorithm and personalised treatment of rifampicin for tubercu-losis. Submitted

Reprints were made with permission from the respective publishers. *The authors contributed equally to this work

Contents

Introduction ................................................................................................... 11 New and improved therapies against TB are needed ............................... 11 Tuberculosis pathology and disease ......................................................... 12 Tuberculosis biomarkers .......................................................................... 12 Treatment ................................................................................................. 13

First-line treatment............................................................................... 13 Second-line treatment .......................................................................... 14 Therapeutic drug monitoring ............................................................... 15

Tuberculosis drug development ............................................................... 16 Pharmacokinetics and pharmacodynamics ............................................... 18 Pharmacometrics ...................................................................................... 18

Non-linear mixed effects model .......................................................... 19 Pharmacometric models for tuberculosis ................................................. 20

Pharmacokinetic models ...................................................................... 20 Pharmacodynamic models ................................................................... 21

Aims .............................................................................................................. 24

Methods ........................................................................................................ 25 Clinical data.............................................................................................. 25

Pharmacokinetic and pharmacodynamic monotherapy data of high-dose rifampicin (Paper I-II) ................................................................. 25 Joint dataset of molecular bacterial load and time-to-positivity (Paper III) ............................................................................................ 25 Culture conversion data (Paper IV) ..................................................... 26 Rifampicin colony forming unit data (Paper V) .................................. 27 Clofazimine and pyrazinamide pharmacokinetic and colony forming unit data (Paper VI) ............................................................................. 27 Therapeutic drug monitoring data for rifampicin (Paper IX) .............. 27

Animal data .............................................................................................. 27 Software ................................................................................................... 28 Model development .................................................................................. 28

Modelling of time-to-positivity of high-dose rifampicin (Papers I and II) .................................................................................................. 29 Modelling of molecular bacterial load data (Paper III) ....................... 29 Modelling of culture conversion data (Paper IV) ................................ 30

Modelling of colony forming unit data (Papers V-VI) ........................ 30 Modelling of treatment outcome data in mice (Paper VIII) ................ 31

Evaluation of sample size for tuberculosis Phase IIa trials (Paper VII) ... 31 New Bayesian therapeutic drug monitoring targets for high-dose rifampicin (Paper IX) ............................................................................... 35

Application of targets to patient data ................................................... 35

Results and discussion .................................................................................. 36 Model for time-to-positivity of high-dose rifampicin (Papers I-II) .......... 36 Model for molecular bacterial load (Paper III) ......................................... 40 Model for culture conversion data (Paper IV) .......................................... 45 The Multistate Tuberculosis Pharmacometric model applied to colony forming unit data (Papers V and VI) ........................................................ 47 Sample size requirements for Phase IIa tuberculosis trials (Paper VII) ... 53 Model for treatment outcome in mice (Paper VIII) .................................. 54 Overview of developed models ................................................................ 56 Framework for model-based therapeutic drug monitoring for tuberculosis (Paper IX) ............................................................................. 58

Conclusions and perspectives ....................................................................... 61

Populärvetenskaplig sammanfattning ........................................................... 64

Acknowledgements ....................................................................................... 67

References ..................................................................................................... 70

Abbreviations

AUC0-24h the area under the plasma concentration-time curve during 24 hours

CFU colony forming units CL clearance Cmax the highest plasma concentration during 24 hours DS-TB drug-susceptible tuberculosis EBA early bactericidal activity F fast multiplying bacteria IIV inter-individual variability i index for individual IOV inter-occasion variability j index for observation LRT likelihood ratio test MBL molecular bacterial load MCMP Monte Carlo mapped power MDR-TB multi drug-resistant tuberculosis MIC minimum inhibitory concentration MTP Multistate Tuberculosis Pharmacometric N non-multiplying bacteria NCA non-compartmental analysis OFV objective function value PD pharmacodynamic PK pharmacokinetic PKPD pharmacokinetic-pharmacodynamic PPC posterior predictive check RZME rifampicin, pyrazinamide, moxifloxacin and ethambutol RZMH rifampicin, pyrazinamide, moxifloxacin and isoniazid RpZHE rifapentine, pyrazinamide, isoniazid and ethambutol RUV remaining unexplained variability S slow multiplying bacteria TB tuberculosis TDM therapeutic drug monitoring TSCC time to stable culture conversion TTE time-to-event TTP time-to-positivity VPC visual predictive check

WHO World Health Organization x independent variable y dependent variable, observation ε epsilon, residual η eta, individual level random effect θ theta, population fixed effect

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Introduction

New and improved therapies against TB are needed Tuberculosis (TB) is a main cause of death due to an infectious disease.1 In 2017, 1.6 million people died from TB (including TB/HIV co-infection) and 10 million people got infected with TB.

Most of the 10 million are drug-susceptible TB (DS-TB) cases which mean that they are susceptible to first-line drugs. Drug-susceptible patients can be successfully cured with a standard six month TB regimen in 95% of patients in trial settings2–4 and in 80% of patients in programmatic settings.1 Apart from DS-TB, the 10 million also contain 500 000 cases with resistance to isoniazid and rifampicin, termed multi-drug resistant TB (MDR-TB). This subset of patients are significantly harder to treat where 18-20 months of treatment are most often required and only about 50% of patients get cured in programmatic settings.1 The World Health Organization (WHO) has an-nounced MDR-TB a global public health crisis.5 Relevant actions are urgent-ly needed to reduce the impact of MDR-TB in the world. A prioritised action is to quickly bring new drugs against MDR-TB to patients. This prioritisa-tion had an apparent effect as there are now multiple new drugs against TB in clinical development, in addition to bedaquiline6 and delamanid7 which are already on the market with conditional approvals. However, sufficiently many of these candidates are not likely to reach the patients in time since the current TB development programme is too inefficient. Another prioritised action is to prevent further development of MDR-TB through optimisation of the treatment of DS-TB; the 20% of DS-TB patients that get treatment failure from the first-line treatment under programmatic settings is an unac-ceptably large figure. It is unacceptable not only because the patients will have continued suffering because they are still sick but they are also put at a great risk of developing MDR-TB. Reducing the 20% would thus contribute to an overall lower risk for patients to develop MDR-TB. In other words, there is a great need for new drugs to treat MDR-TB as outlined above but at the same time the need for improving the first-line treatment cannot be ne-glected.

This thesis suggests novel pharmacometric tools that can be used to streamline the current TB drug development and optimise the first-line treatment which can contribute to a lower global impact of MDR-TB.

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Tuberculosis pathology and disease Tuberculosis is caused by Mycobacterium tuberculosis primarily affecting the lung, known as pulmonary TB which will be the focus of this thesis. The chain of events from the point of infection until active, established disease with associated symptoms is complex and not fully understood.8 Tuberculo-sis can exist in a latent disease form where patients are symptom-free carri-ers of TB and activation of latent TB can lead to active TB. Much of the development of a TB infection is caused by interactions between the immune systems of patients and the TB bacterium. It is believed that the immune system can be of both benefit and harm to the patient; on the one hand a hampered immune system elevates the risk of activation of latent TB into active TB which suggests that a working immune system can suppress active TB in some patients. On the other hand, the granulomas or lesions, which are reservoirs for TB within the human lung are partly composed of immune cells which acts as a protective barrier for the bacteria which makes it diffi-cult for e.g. drugs to reach the bacteria.9 The time from actual infection to established TB is usually unknown but is known to appear late in a clinical infection.10 Established infections are usually in a stationary phase where the bacterial load determined in sputum is known to be stable, i.e. not increasing nor decreasing over time, in absence of drug treatment.11

As stated above, the immune system can provide the bacteria with a pro-tective barrier which makes treatment difficult but there are other, more im-portant bacterial factors that make bacterial killing through drug treatment even more difficult. Tuberculosis bacteria are known to exist in different states, or subpopulations, including multiplying (i.e. growing) and non-multiplying states.12 Many antibiotics have an ability to kill multiplying bac-teria whereas non-multiplying bacteria are known to be tolerant against most antibiotics.13 Non-multiplying bacteria have shifted down most metabolic processes inside the bacterial cell and become dormant where antibiotics are seldom active and thus, this subpopulation is also termed persisters. To tar-get both multiplying and non-multiplying (persistent) subpopulations are essential for successful TB treatment.14 Drugs that mainly kill multiplying bacteria are termed bactericidal drugs. Drugs with an ability to kill non-multiplying bacteria are said to have sterilising activity. An important issue with non-multiplying bacteria is that they are difficult to detect using cul-ture-based quantification methods which creates a challenge; how do we kill something we can’t see?

Tuberculosis biomarkers The current standard biomarkers for quantifying the TB bacterial load is the colony forming unit (CFU) assay on solid media and time-to-positivity

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(TTP) in liquid media.15 The CFU assay do not quantify non-multiplying bacteria16–20 and non-multiplying bacteria has also been shown to comprise the majority of TB bacteria in clinical sputum samples.21 In contrast to CFU on solid media, methods based on liquid culture are considered a better op-tion to detect non-multiplying bacteria.22 The TTP biomarker is more sensi-tive in detecting non-multiplying bacteria than CFU.23 Analysis of clinical data of matched CFU and TTP observations revealed that TTP captured a subpopulation of TB that is invisible on CFU.24 It is unclear if this TTP-specific subpopulation represents all or just parts of a spectrum of non-multiplying bacteria. It is difficult to determine exactly what TTP captures in relation to CFU since the biomarkers are so different - CFU being a continu-ous, direct measurement of bacterial load whereas TTP is a time-to-event variable which is an indirect measurement of bacterial load (high CFU gives short TTP and vice versa).

Both CFU and TTP are culture-based where long waiting times (days to weeks) until results can be read out and risk of culture contamination limit the use of these biomarkers.25 An alternative to culture-based methods is the molecular bacterial load (MBL) assay26 which is quick (~4 hours) and has a negligible risk of contamination. The MBL assay is based on 16S rRNA quantification using quantitative polymerase chain reaction. Since TB con-tain this type of rRNA, it makes MBL a continuous, direct measurement of bacterial load.27 Since MBL is non-culture based it is hypothesized that it may be able to quantify non-multiplying TB.28 The MBL biomarker has been compared with TTP in clinical trials where correlations of -0.525 and -0.828 have been reported. These correlations are not really informative regarding what subpopulations MBL are reflective of in relation to TTP. To establish a more informative link between MBL and TTP would enhance the under-standing of what MBL captures but achieving this probably requires a more sophisticated way of analysing data than mere correlation coefficients, such as a model-based approach.

Apart from interpreting biomarkers as quantitative numbers, as described above, it is possible to interpret the data as a positive or negative result known as culture conversion.

Treatment First-line treatment Drug-susceptible patients are treated with a standard regimen29 consisting of six months of rifampicin (10 mg/kg) and isoniazid (5 mg/kg) supplemented by pyrazinamide (20 mg/kg) and ethambutol (15 mg/kg) for the first two months of treatment.

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Rifampicin is crucial since it targets multiplying and non-multiplying bac-teria.14 The mechanism of action is inhibition of DNA-dependent RNA pol-ymerase inside the bacterium which is central for basic metabolism.30,31 Ri-fampicin has sterilising activity and can reduce occurrence of relapse.32 When introduced, rifampicin reduced the required treatment from 12 to 9 months (adding pyrazinamide reduced the time to six months).33 The rec-ommended 10 mg/kg dose was chosen due to fear of toxicity and high cost.34 This way of selecting a dose is not up to date with current standards. Several studies exploring high-dose rifampicin35–43 conclude that a higher dose may be more effective but the exact dose must be determined. Current data sug-gests a dose around 35 mg/kg. This is given an encouraging improvement in time to culture conversion during 12 weeks for 35 vs 10 mg/kg rifampicin.42 Note that this was based on a conventional statistical analysis where no link was established between the response and rifampicin pharmacokinetics (PK). In short-term data, no statistically significant exposure-response relationship of 35 mg/kg has been established, which was also based on conventional statistics.38

Pyrazinamide is able to prevent relapse due to the ability to kill slow-growing bacteria.44 Pyrazinamide acts by being converted into pyrazinoic acid inside TB bacteria where pyrazinoic acid accumulates and eventually kills TB. Pyrazinamide killing is limited to acidic conditions.

Isoniazid has activity against multiplying bacteria by targeting the bacte-rial cell wall synthesis.45 Ethambutol has no role for killing bacteria and is instead known to be able to inhibit bacterial growth.46

Second-line treatment Treatment of MDR-TB is more complex than treating DS-TB. Several new regimens for treating MDR-TB are under investigation and treatment guide-lines may change once results become available.47 Current guidelines for treating MDR-TB suggest treatment durations of 18-20 months in most pa-tients.48 The duration can be individualised based on individual treatment response where treatment should be continued for 15-17 months after culture conversion. Treatment should preferably be injectable-free and consist of all Group A drugs, if possible both Group B drugs and add Group C drugs to complete the regimen according to Table 1.

Bedaquiline treatment is to be discontinued after 6 months. A standard-ised short MDR-TB regimen can also be considered where kanamycin, mox-ifloxacin, clofazimine, ethionamide, pyrazinamide, ethambutol and isoniazid are given for 4-6 months followed by five months of moxifloxacin, clo-fazimine, pyrazinamide and ethambutol (known as the ”Bangladesh” regi-men49).

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Table 1. Groups of drugs recommended by WHO for treatment of multi-drug re-sistant tuberculosis (MDR-TB) Group Remark Drug

A Include all three drugs Levofloxacin or moxifloxacin Bedaquiline Linezolid B Include at least one drug Clofazimine Cycloseride or terizidone C Add to complete the regimen and when

medicines from groups A and B cannot be used

Ethambutol Delamanid Pyrazinamide Imipenem-cilastatin or meropenem Amikacin Ethionamide or prothionamide p-aminosalicylic acid Table adapted from WHO48 In contrast to the 18-20 month treatment, this shorter regimen involves daily intravenous injections (kanamycin) for 4-6 months which has to be taken into consideration since it requires access to educated health care personnel and the injections are also painful for patients. Both the longer injectable-free and shorter treatment contains clofazimine which had a lower priority in the past. Inclusion of clofazimine makes sense due to the ability of clo-fazimine to decrease time to culture conversion50 and occurrence of re-lapse.49 Exactly what type of TB subpopulations that clofazimine kills is not well understood. Short-term monotherapy data in DS-TB patients have not led to better understanding of what subpopulations clofazimine kills since a numerical increase in CFU was seen (which suggests the opposite to bacteri-al killing).51 The ability to kill non-replicating bacteria has been demonstrat-ed in vitro.52 There are several reports of potential mechanisms of action for clofazmine53,54 including membrane destabilization and/or and an indirect effect through immunomodulation.55

Therapeutic drug monitoring The treatment guidelines described above suggest a ”one-dose-fits-all” ap-proach. Note that patients get dosed on a mg/kg basis which means that, technically patients with different body weight will not get exactly the same dose, but seen to the mg/kg every patient gets the same dose. An alternative to this approach is therapeutic drug monitoring (TDM)56 also known as per-sonalised medicine which most commonly means to measure plasma con-centrations of a drug in an individual patient to identify too low drug expo-sures (lack of efficacy) or too high drug exposures (toxicity). This is fol-lowed by appropriate dose adjustments in the individual patient. Therapeutic drug monitoring is occasionally used for TB treatment.57 For first-line drugs,

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TDM is mostly used for rifampicin which can be explained by studies that have linked low rifampicin exposure to treatment failure.58,59 Rifampicin also has complex and highly variable PK60 which are other reasons for perform-ing TDM. Current rifampicin TDM targets aim at achieving peak or two hour concentrations above 8 mg/L.57,61 This target was derived from studies based on 10 mg/kg rifampicin.57,58,62–65 The future rifampicin dose will likely be higher than 10 mg/kg (as described above) and thus updated TDM targets for rifampicin would be relevant.

When performing TDM, PK samples are usually collected with sparse sampling where it can be difficult to derive PK parameters of interest with reasonable precision and bias using non-compartmental analysis (NCA) based methods. Parameters of interest include e.g. the highest plasma con-centration during 24 hours (Cmax) or the area under the plasma concentration-time curve during 24 hours (AUC0-24h). An appropriate alternative for sparse sampling is model-based TDM, also termed TDM coupled with Bayesian forecasting. For this method NCA is replaced by a population PK model which increases the quality and amount of PK information.

Model-based TDM has been applied to rifampicin66,67 but the current ex-amples are too simplistic which will be evident at higher rifampicin doses; previous models rely on linear PK which may be incorrect for rifampicin which has dose-dependent PK.38,60 For doses near 10 mg/kg rifampicin, line-ar models work well68,69 but for high-dose rifampicin linear models will un-der-predict the exposure resulting in too high dose recommendations. Fur-thermore, rifampicin has high inter-occasion variability (IOV) in PK which also poses problems for TDM which should be handled properly70 to in-crease the likelihood of successful implementation of model-based TDM for rifampicin. The current examples of model-based TDM do not handle the high IOV of rifampicin.66,67 Furthermore, the current approaches for rifam-picin only work on PK data collected two weeks after treatment initiation whereas it would be preferable to have a model-based TDM approach that can be applied on data collected on any treatment day including day one.

Apart from rifampicin, a model-based TDM methodology can be applied to MDR-TB treatment which could be a potential way of reducing the high proportion of patients failing treatment (~50%). Of note, personalised medi-cine should ideally not be performed only based on PK but could also in-clude biomarker data. This is problematic since the current standard culture-based methods (CFU and TTP) are too slow for a TDM setting. Thus, quick-er biomarkers such as MBL are warranted.

Tuberculosis drug development The ultimate endpoint for TB is relapse-free cure at least 6 months after end of treatment which is studied in Phase III trials.71 Phase III trials include one

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or two combinations of drugs which are chosen based on Phase IIb trials. Phase IIb trials focus on the first 8-12 weeks of treatment and include a few different drug combinations. The endpoint is e.g. proportion of patients with culture conversion at end of trial. Repeated biomarker measurements, PK information and use of pharmacometric models are conventionally not con-sidered when analysing Phase IIb data.

Phase IIb is preceded by Phase IIa which is usually monotherapy trials, often including different doses of a drug given for 7-14 days.71 Sputum and plasma blood samples are usually collected to determine both PK and phar-macodynamics (PD) of the drug. The aim of Phase IIa is to show a drug ef-fect but Phase IIa can also be relevant for dose selection for Phase IIb. Phase IIa is important for decision-making regarding further development and are usually analysed focusing on comparing the difference in mycobacterial load, known as early bactericidal activity (EBA) between day 0 and 14 using traditional statistical tests e.g. ANOVA72 and/or using regression-based analyses taking longitudinal CFU measurements into account.73 Phase IIa can also be based on TTP where regression-based methods often are applied to repeated TTP data.74–76 The regression-based methods are empirical, aim-ing at describing trends of the data rather than getting insight into underlying mechanisms that caused the patterns in the data. Phase IIa trials usually in-clude 10-15 patients per study arm.77,78 Given this sample size, it has been shown that many Phase IIa trials fail to show statistically significant drug effects or differences between study arms.

Prior to Phase IIa, pre-clinical studies are performed including several ex-periments including in vitro and in vivo studies.71 The pre-clinical focus of this thesis is treatment outcome assessments in mice, which is the most common way to study treatment outcome pre-clinically.79 Conventionally, such an experiment is conducted by first measuring mycobacterial killing of a regimen during early treatment in small groups of mice (n=3-5) and sec-ondly, larger groups of mice (n=12-30) are studied after end of treatment for 1-3 different treatment lengths.80–85 This design has some drawbacks. For example it is unclear if the first part of the design evaluating early bacterial killing has relevance for treatment outcome and may therefore be exces-sive.86,87 Secondly, the last part of the design includes so few time-points that it will not give good information on how treatment length correlates with outcome for a regimen which is crucial information for designing future studies.

In summary, pre-clinical and clinical studies for TB generally require high number of study subjects but at the same time results of the studies often read out as inconclusive and uninformative. Thus the development path is slow, expensive and inefficient. Ways to streamline the development is urgently needed to be able to deliver new drugs to patients in time. For ex-ample, reducing the sample size would save precious time (especially for patient studies). Furthermore, more informative ways of analysing studies to

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not render them uninformative would also be of benefit to allow for rational decision-making.

Pharmacokinetics and pharmacodynamics Within clinical pharmacology the concepts of PK and PD are central. Phar-macokinetics describes how a drug is absorbed, distributed and eliminated throughout the body. Mostly, this is limited to the plasma compartment but it may also include other tissues or organs such as the site of action. For TB the exposure achieved in the lung, inside granulomas or lesions or even in-side TB cells may be considered more relevant than the plasma compart-ment.9 However, the focus of this thesis is limited to plasma PK. Of note, it has been shown for most anti-TB drugs that they achieve considerable expo-sures in the lung and granulomas.88

If a drug has a meaningful mechanism of action then the drug exposure leads to a response which is described by PD. Pharmacodynamics for TB can mean change in biomarkers but it can also be defined as bacterial killing of different subpopulations of TB. Pharmacodynamics can also refer to toxicity.

How the PK affects PD is described by pharmacokinetic-pharmacodynamic (PKPD) relationships. Different types of PKPD relation-ships exist and what is considered most relevant is situation-dependent. It is relevant to have a PKPD relationship based on continuous drug concentra-tions if different dosing regimens are to be considered because it allows pre-diction of the PD response for any dose regimen. However, this approach requires an established PK model. For other situations the PK can be includ-ed as a summary measure such as Cmax or AUC0-24h which limits the use for simulating new dose regimens but can simplify the implementation of the PKPD relationship. Since PK is the driver for PD it means that misspecifica-tions in PK become carried over to PD. Thus, it is crucial to define PK properly before establishing any PKPD relationship.

The concept of PKPD relationships is not widely acknowledged within TB drug development which can partly explain why the development is inef-ficient. Knowledge of a PKPD relationship can aid decision-making for fur-ther development and dose selection. If the PKPD relationship is included in a pharmacometric framework it can be used for simulation which is very valuable for drug development as described in the next section.

Pharmacometrics Pharmacometrics is an inter-disciplinary science that combines mathematics, statistics, pharmacology and physiology. Within pharmacometrics, mathe-matical models are applied to various biological systems to quantitatively

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describe components of the system. The models are classified as non-linear mixed effects models where “mixed” refers to that the parameters of the model are a mix of fixed effects parameters and random effects parameters. Fixed effects parameters describe the general trend of the data. Random ef-fects parameters describe the variability of the data. The concepts of PK and PD are also present within pharmacometrics where the development of PK models, PD models and PKPD models are common. Pharmacometric models can also be referred to as PKPD modelling, population modelling or model-ling and simulation. A principal use of pharmacometric models is better un-derstanding of a biological system by interpreting the estimated parameters of the model. Different models can be compared and tested against each other to e.g. determine the most likely mechanism of action of a drug. Mod-els can also be used for simulation purposes to e.g. simulate different doses for the next planned study to help choosing appropriate doses.

Non-linear mixed effects model A pharmacometric or non-linear mixed effects model is usually defined by differential equations or an analytical equation. The model includes a struc-tural model whose parameters describe the general tendency in the popula-tion, e.g. a population value of clearance (CL). Another component is the stochastic, or variability model describing variability in the population. The variability can refer to variability in structural model parameters between individuals e.g. inter-individual variability (IIV) in CL, or it can refer to variability in structural parameters between occasions e.g. IOV in CL. A third type of variability is the remaining unexplained variability (RUV), or the residual error which describes the remaining variability in the data which was not described by IIV or IOV. A pharmacometric model also consists of a covariate model describing the relationship between patient covariates and model parameters e.g. the effect of body weight on CL. A general non-linear mixed effects model for continuous data observations (yi,j) can be described by: , = , , + , where yi,j is the j:th observation of the i:th individual. f is a function describ-ing the individual prediction based on the independent variables xi,j including e.g. dose and time. The model also includes εi,j which describes the residual variability, i.e. the deviation between the individual prediction and the ob-servation and is assumed to follow a normal distribution. A parameter vector θi describes individual model parameters. The elements of the vector can be derived according to the following for exponentially distributed parameters: = × e

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where θp is the population value of the parameter and ηi is the i:ths individu-als deviation from the population value θp and is assumed to follow a normal distribution.

For models used for categorical data (i.e. binary data) the non-linear mixed effects model is defined differently. The model defines a probability (p) to observe a certain response, yi,j, given independent variables (xi,j) and parameters according to: , , , ) Time-to-event (TTE) models are another type of model which characterise the time to the occurrence of an event. The first step for defining a TTE model is to define a hazard hi(t), the individual instantaneous probability for an event to occur according to: ℎ ( ) = ( , , )

where the hazard depends on a function, f, described by independent varia-bles (xi,j) and a set of individual parameters (θi). Next, the hazard is used to calculate the survival, Si(t), which is the probability to remain event free (i.e. to “survive” occurrence of the event) over time according to: ( ) = ( ) Finally, the probability, gi(t) for having an event at time t can be calculated by the following: ( ) = ( ) × ℎ ( )

Pharmacometric models for tuberculosis Pharmacometric models for TB are uncommon compared to other disease areas. This section summarizes the current landscape of PK and PD models with relevance to this thesis.

Pharmacokinetic models For PK there are published population pharmacokinetic models for many TB drugs including all first-line drugs.89–92 However, as the field moves into a high-dose rifampicin paradigm there may be a need to review and potentially update the population PK for rifampicin. In a PK study of high-dose rifam-picin (including up to 35 mg/kg) it became evident that rifampicin has dose-dependent PK (which is in addition to the previously described time-varying PK of rifampicin89). Most existing population PK models for rifampicin do not include dose-dependent PK, see e.g.68,69. One model includes saturable PK93 but was based only on data from 10 mg/kg rifampicin. Since doses up to 35-40 mg/kg have been studied it is relevant to develop a rifampicin popu-

21

lation PK model on observations from actual higher doses to better charac-terise the dose-dependency in PK.

For drugs against MDR-TB it is not always the case that population PK models exist, such as for clofazimine.94 It would thus be relevant to develop a clofazimine PK model considering that clofazimine got an increased priori-ty for treatment of MDR-TB.48

Pharmacodynamic models For TB there exist several clinical PD models in the literature where the models with relevance to this thesis will be described in this section. How-ever, a general drawback with almost all the existing models is that they are very empirical and lack PKPD relationships. Pharmacometric PKPD models are beneficial for drug development as evident for other disease areas. For example in HIV, acute stroke and diabetes, semi-mechanistic PKPD model-ling is more powerful for detecting drug effects for Phase II trials compared to conventional statistical methods which allows for a reduction of the sam-ple size.95,96 This aspect has not been explored for TB.

Models for time-to-positivity There are several empirical models for TTP where the TTP is treated as con-tinuous type data without any PKPD relationship74–76 which is a common way of analysing Phase IIa data. For a short-term high-dose rifampicin trial an empirical modelling approach was applied and even extended to link rate of change in TTP to rifampicin exposure but no statistical significant expo-sure-response relationship was found.38 This was despite that the exposure-response of high-dose rifampicin is evident in multiple in vitro and animal studies.97–100 Testing alternative, more mechanistic ways of analysing TTP data to see if it can increase the ability of detecting exposure-response rela-tionships is warranted to increase the ability of making correct decisions.

Time-to-positivity has also been modelled using semi-mechanistic TTE modelling101 also including an example where the approach was extended to describe bedaquiline exposure-response.102 However, a mutual drawback of the semi-mechanistic and empirical models is that no model includes proper handling of contaminated TTP samples. Furthermore there are no models that link TTP to another continuous type of biomarker such as MBL. To co-model TTP with e.g. MBL would allow for better understanding of how TTP links to the underlying bacterial load.

Models for molecular bacterial load Since MBL is a new biomarker the number of previously developed PD models is limited. Filling this gap is relevant since models could be very useful to e.g. analyse future clinical trials involving MBL. To date there is only a single empirical model for MBL which is a bi-exponential model.26

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Models for colony forming units For CFU data the conventional way of analysing clinical data is by empirical models based on mono- or bi-exponential models.72,73 These models are de-scribing the patterns of the data without any mechanistic link to the underly-ing subpopulations of TB bacteria. In addition, the models are usually lack-ing PKPD relationships.

For CFU there exists a semi-mechanistic pharmacometric model, the Multistate Tuberculosis Pharmacometric (MTP) model.103 The MTP model is a semi-mechanistic model for TB describing three different states or sub-populations of TB including multiplying and non-multiplying bacteria (Figure 1). The non-multiplying bacteria are not visible as CFU i.e. CFU only represents the sum of the multiplying bacteria (comprising fast- and slow-multiplying bacteria). The model has been applied to in vitro and ani-mal CFU data where the exposure-response was established between rifam-picin PK and drug effects on the different TB subpopulations including the non-multiplying state.103,104 The MTP model has not been applied to clinical data. To apply it to clinical data and explore it as a tool to analyse clinical data could be of value. It is a framework that includes exploration of expo-sure-response and it can allow for detection of drug effects on non-multiplying bacteria which are difficult to detect.

Figure 1. The Multistate Tuberculosis Pharmacometric (MTP) model. F, fast-multiplying state; S, slow-multiplying state; N, non-multiplying state; kG, growth rate of fast-multiplying state bacteria; Bmax, system-carrying capacity; kFSlin, time-dependent linear rate parameter describing transfer from fast to slow-multiplying state; kSF, first-order transfer rate between slow and fast-multiplying state; kFN, first-order transfer rate between fast and non-multiplying states, kSN, first-order transfer rate between slow and non-multiplying states, kNS, first-order transfer rate between non-multiplying and slow-multiplying states. Adapted from Clewe et al.103

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Models for culture conversion Culture conversion data is generally not subject to any modelling. Instead, culture conversion data is usually analysed by comparing culture conversion by end of trial105 or time to culture conversion42 between study arms using traditional statistical tests. Nevertheless, examples exist where modelling has been applied to culture conversion data such as Imperial et al.106 However, the analysis method in Imperial et al was Cox regression which is a semi-parametric approach. A fully parametric TTE approach, i.e. hazard model-ling has been shown to have higher power than semi-parametric models.107 Furthermore, parametric TTE modelling allows for better inclusion of time-varying covariates such as PK.107

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Aims

The overall aim of this thesis was to develop pharmacometric models to optimise the development and use of current and future drugs for treating TB The specific aims were:

• To develop tools for model-based TB drug development and deci-sion-making

• To give design recommendations for clinical and pre-clinical TB studies

• To propose an individualised treatment approach for TB using TDM coupled with Bayesian forecasting

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Methods

Clinical data All clinical data used within this thesis were conducted according to Good Clinical Practice and approved by local ethics committees including in-formed consent from the patients. However, one exception to this was the data used in Paper V since at the time of conduct of the trial (1966-1977),72 no formal ethical review board or written consent process existed. The prin-cipal investigator of the trial has ensured that there were no restrictions for re-using the data for the purpose of this thesis. Furthermore an irreversibly anonymised version of the data was used which was approved by the UK National Research Ethics Service.

Pharmacokinetic and pharmacodynamic monotherapy data of high-dose rifampicin (Paper I-II) For Papers I-II, data from the multiple dose rising PanACEA HIGHRIF1 trial38 was used. The trial included 83 patients divided into six dose arms that received daily doses of 10 (control group, n=8), 20 (n=15), 25 (n=15), 30 (n=15), 35 (n=15) or 40 (n=15) mg/kg rifampicin during two weeks. In the first week rifampicin was administered alone (monotherapy) whereas after seven days isoniazid, pyrazinamide and ethambutol in standard doses were added. Pharmacokinetics were included on days 7 and 14 with rich plasma concentration sampling of rifampicin. The PK information was used in Paper I. The trial included quantification of the bacterial load using TTP in liquid culture (BD Bactec MGIT 960 Mycobacterial Growth Indicator Tube sys-tem; Becton-Dickinson, Sparks, MD) collected daily at baseline and for the first 7 days of the trial and thereafter on days 9 and 14. The TTP data from the monotherapy part of the data (i.e. the first week of the trial) was used in Paper II.

Joint dataset of molecular bacterial load and time-to-positivity (Paper III) The data for Paper III consisted of repeated longitudinal matched measure-ments of MBL and TTP. The dataset included 105 DS-TB patients with the data coming from three different sites in Africa including 20 patients from

26

Malawi, 53 patients from Mozambique and 32 patients from Tanzania. The Tanzania data was a subset from the MAMS-TB trial42 (the same study that was used for Paper IV). All patients received the four drugs of the standard first-line treatment combination, i.e. rifampicin, isoniazid, pyrazinamide and ethambutol. The doses of all individual agents were the standard ones apart from the rifampicin dose which was 35 mg/kg in 12 patients whereas the remaining 93 patients received 10 mg/kg rifampicin. Sputum, which was used to quantify the bacterial load, were collected at baseline and weekly until week 12 for Tanzania, baseline, weeks 2, 4, 6, 8 and 12 for Malawi and at baseline and weeks 1, 2, 4, 8 and 12 for Mozambique. The TTP was de-termined according to Paper II where contamination for TTP was determined in 85 patients. The MBL was determined as described previously.28

Culture conversion data (Paper IV) The model in Paper IV was developed on culture conversion data from DS-TB patients from the PanACEA MAMS-TB trial.42 The dataset included 336 patients divided in a 2:1:1:1:1 ratio to treatment arms described in Table 2 where the control regimen included twice as many patients as the experi-mental arms.

Table 2. Assigned treatments to MAMS-TB data

Arm Rifampicin dose (mg/kg)

Isoniazid dose (mg/kg)

Pyrazinamide dose (mg/kg) 4th drug

Control (R10HZE) 10 5 25 15-20 mg/kg ethambutol 1 (R35HZE) 35 5 25 15-20 mg/kg ethambutol 2 (R10HZQ) 10 5 25 300 mg SQ109 3 (R20HZQ) 20 5 25 300 mg SQ109 4 (R20HZM) 20 5 25 400 mg moxifloxacin R; rifampicin, H; isoniazid, Z; pyrazinamide, E; ethambutol, Q; SQ109, M; moxifloxacin

The treatment length was six months for all arms. The experimental arms were treated with the combinations and doses listed in Table 2 for the initial three months and were thereafter assigned to the same treatment as the con-trol arm for the remaining three months of treatment. Sputum samples were gathered to determine culture conversion at baseline, weekly for 8 weeks and at weeks 10, 12, 14, 17, 22 and 26. Culture conversion was determined in both liquid media (similar to the dataset for Paper II) and using solid culture with Löwenstein-Jensen medium. The data was in the form of time to stable culture conversion (TSCC) defined as the time until two repeated negative cultures were obtained in a patient. Rifampicin plasma concentrations were determined from 20 patients in each arm with a rich PK sampling curve on day 28.

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Rifampicin colony forming unit data (Paper V) For Paper V, CFU data were used from rifampicin-treated DS-TB patients which was a subset from a previously published trial.72 The data included 23 patients divided into four arms including an untreated negative control group (n=4) or rifampicin monotherapy in daily doses of 5 (n=3), 10 (n=8) or 20 (n=8) mg/kg during 14 days. Sputum sampling for determination of CFU were performed at baseline and every second day of the trial. The data did not include any covariates or PK information.

Clofazimine and pyrazinamide pharmacokinetic and colony forming unit data (Paper VI) The data that was used for Paper VI was a subset of an existing Phase IIa trial51 which included DS-TB patients treated with clofazimine or pyra-zinamide as monotherapy. The total sample size (after subsetting) was 29 where patients received either clofazimine (n=14) or pyrazinamide (n=15) for a duration of 14 days. Clofazimine was given as daily administrations of 300 mg the first three days and then 100 mg daily. Pyrazinamide was given as daily doses of 1500 mg throughout the 14 days. Colony forming unit data was collected at baseline and daily for the whole trial. Plasma concentrations of each drug were sampled with sparse sampling on days 1, 2, 3 and 8 and with rich sampling on day 14.

Therapeutic drug monitoring data for rifampicin (Paper IX) A part of Paper IX involved the use of clinical data from a previously pub-lished study108 where data on PK and minimum inhibitory concentrations (MICs) were determined from TB patients in a routine care setting. For Pa-per IX, a subset of the original study was used including only patients with pulmonary DS-TB treated with the standard first-line regimen. The PK data was collected with sparse sampling on weeks 2, 4 and 12. The MICs were determined at baseline.

Animal data For Paper VIII, treatment outcome data from mice were used. The mice were BALB/c mice infected intratracheal application of Mycobacterium tubercu-losis Beijing strain. The protocols were approved by Erasmus MC animal ethics committee and also in accordance with the Dutch Animal Experimen-tation Act and the EU Animal Directive 201/63/EU. Mice were divided to receive regimens of varying treatment lengths consisting of either i) rifapen-tine, pyrazinamide, isoniazid and ethambutol (RpZHE), ii) rifampicin, pyra-

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zinamide, moxifloxacin and ethambutol (RZME) or iii) rifampicin, pyra-zinamide, moxifloxacin and isoniazid (RZMH). The study was designed to include n=3 mice per treatment length per regimen, also including one back-up mouse per regimen. The treatment lengths studied for each regimen ranged from 2-6 months with two weeks increments, i.e. a total of 9 different treatment lengths. Treatment outcome was determined by sacrificing the mice three months after end of treatment by determining the mycobacterial presence on solid culture from homogenised lung.

Software The pharmacometric analyses within this thesis were performed in NON-MEM 7.3 or 7.4.109 Estimation methods that were employed included first-order method, conditional first-order estimation, Laplace and importance sampling (IMP). The development of models and creation of several model diagnostics including visual predictive checks (VPCs) were assisted by PsN.110,111 Visual predictive checks are diagnostic plots that compare simu-lated and observed data in the same plot. For continuous data (such as PK or CFU observations), the observed outer and 50th (i.e. the median) percentiles of observed data were plotted together with confidence intervals for the cor-responding model-predicted percentiles, based on repeated simulations from the model. For TTE data, Kaplan-Meier VPCs were made where the ob-served Kaplan-Meier curves were compared with the confidence interval of the simulated Kaplan-Meier curves based on repeated simulated datasets. Although VPCs were mainly used to guide model development, the good-ness-of-fit for some models presented in this thesis were shown as posterior predictive checks (PPCs). Posterior predictive checks are similar to VPCs except that that the underlying dependent variable were post-processed into a secondary variable such as performing a PPC for AUC0-24h rather than a VPC for the underlying drug concentrations for a PK model. The VPCs and sever-al other diagnostic plots were generated using Xpose110,112 which is a pack-age for the statistical software R.113 R were also used for data management and graphical analyses.

Model development For all models developed in this thesis different criteria were used to guide model selection. However, common criteria for all model development were improvements in objective function value (OFV), diagnostic plots and preci-sion in parameters. For selecting models based on improvement in OFV, the likelihood ratio test (LRT) was used at the 5% significance level, except for Paper III where the 1% significance level was applied. When guiding model

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selection based on improvement in diagnostic plots, the most frequently used diagnostic was the VPC. For guiding model selection based on precision, what was considered too low precision were situation-dependent, e.g. for a model developed on a small dataset generally lower precision could be ac-cepted compared to larger datasets. Precision in estimated parameters were obtained using the bootstrap procedure or the covariance step in NONMEM.

Modelling of time-to-positivity of high-dose rifampicin (Papers I and II) In Paper I, a PK model was developed on plasma concentration measure-ments for rifampicin up to 40 mg/kg. The starting point for modelling was a previously published rifampicin PK model89 which included an enzyme turn-over model describing auto-induction of rifampicin, where the elimination of rifampicin increased over time. Alternative structures to describe absorption, distribution and non-linear elimination and bioavailability were explored during the model development. The developed PK model was used to per-form clinical trial simulations for an unexplored 50 mg/kg rifampicin dose for the PKPD model developed in Paper II.

For Paper II, a TTE model was developed on the TTP data from the same patients38 as in Paper I. The starting point for the model development was derived from a previous model.102 Briefly, the structure included three com-ponents including i) a sputum model describing change of bacterial load in sputum, ii) a mycobacterial growth model representing growth in the liquid culture and iii) a TTE/hazard model which linked the growth in liquid cul-ture to a probability of a positive TTP signalling event. During TTE model development rifampicin exposure-response was explored by testing AUC0-24h as a covariate for mycobacterial killing in the sputum model. For the final model, clinical trial simulations to predict mycobacterial killing of 50 mg/kg rifampicin were performed.

Modelling of molecular bacterial load data (Paper III) In Paper III, a model was built on a combined TTP-MBL dataset. The start-ing point for developing the model was taken from expanding Paper II to describe MBL data. The two biomarkers were linked via the sputum model where the prediction of bacterial load was the prediction of MBL. The way that a change in bacterial load in sputum had an impact on TTP was handled in the same way as described for Paper II. Data on TTP contamination was included in the data used for Paper III and thus an additional component to describe contaminated TTP was developed. There were also a high number of negative TTP samples (in contrast to Paper II) in the data. Different ap-proaches towards handling negative TTP data were explored including right-

30

censoring within the TTE approach (the common way of handling negative samples for survival modelling) and also by handling negative TTE samples with a designated sub-model as proposed in another TTP model.102

Modelling of culture conversion data (Paper IV) In Paper IV, a TTE model for culture conversion (TSCC) data was devel-oped which included exploration of rifampicin exposure-response. The first step was to develop a PK model which was done by re-applying the model from Paper I. All parameters were re-estimated and limited model develop-ment was performed including the testing of patient covariates. Since PK was only available in 97 of the 363 patients, the PK model was used to im-pute rifampicin exposure in patients without PK data.

To model the TSCC data, a TTE approach was taken where different haz-ard distributions including constant, Weibull and surge functions were test-ed. In addition, patient covariates including model-predicted individual ri-fampicin Cmax or AUC0-24h were tested. Model development was focused on TSCC data based on liquid culture, but a model was also developed on TSCC from solid culture as a sensitivity analysis.

Modelling of colony forming unit data (Papers V-VI) Papers V and VI were based on CFU data and was modelled using the semi-mechanistic MTP model.103 The MTP model described the existence of three subpopulations of TB including fast (F), slow (S) and non-multiplying (N) states reflecting multiplying, semi-dormant and persister subpopulations of TB, respectively and were described using the following differential equa-tions (without any drug effects included): = × + + × + × − × − × = × + × − × − × = × + × − ×

where kFS = kFS,Lin × t. Letters “k” with subscripts describes transfer rates between the subpopulations with the first letter describing the origin of the transfer and the second letter describing the direction. The kFS,Lin parameter multiplied by time (t) in days after infection is a time-dependent transfer going from F to S. The fast-multiplying bacterial growth rate is described by kG, and Bmax is the system carrying capacity which defines the total (F+S+N) bacterial density at stationary phase.

The MTP model was used as a disease model, mainly driven by the nega-tive control group included in Paper V, where the time-point of infection was

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assumed to be 150 days prior to start of treatment (i.e. the model was pre-run for 150 days in each subject). At 150 days after infection, the MTP model predicts stationary phase where CFUs are stable, which is also the case in patients.11 All MTP model parameters were fixed to the parameter estimates derived in vitro,103 apart from Bmax which was re-estimated which described the baseline level of CFU in the patients.

Drug effects were tested as exposure-response relationships between con-tinuously predicted concentrations of the modelled drug and killing, or inhi-bition of growth for the subpopulations, defined as effect sites. The expo-sure-response relationships included linear, Emax and “on/off” (i.e. all or nothing) effect models. The effect sites were tested alone and in combination to conclude the mechanism of action of rifampicin (Paper V), clofazimine and pyrazinamide (Paper VI).

Modelling of treatment outcome data in mice (Paper VIII) In Paper VIII a binary model (i.e. logistic regression model) was developed to describe either of the two outcomes cure and treatment failure. First, a data-driven model development step was performed to determine the most appropriate relationship between treatment length and cure. For this step data from all three regimens (RpZHE, RZME and RZMH) were used assuming that each regimen had similar effect. The tested models included linear and Emax relationships between treatment length and cure. In a second step it was explored if the relationship established in the first step was different between the three regimens. This was explored by testing models where treatment-specific parameters of the relationship in the first step were estimated.

Evaluation of sample size for tuberculosis Phase IIa trials (Paper VII) A simulation-estimation study was performed in Paper VII exploring how the study power changes when analysing Phase IIa trials using the MTP model (according to Papers V and VI) compared to empirical regression-based models, t-test or ANOVA to analyse CFU data. The Monte Carlo Mapped Power (MCMP) method114 was used to determine the required sam-ple size required to achieve 90% power at the 5% significance level accord-ing to the different approaches. The MCMP method was used due to an im-provement in speed compared to stochastic simulation and re-estimation.

For the MTP model the LRT was used taking into account data from all dose groups of the test agent simultaneously. For the empirical model-based approaches, mono- and bi-exponential models were applied to all CFU measurements from patients on the highest dose. The t-test compared the

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point estimate of change from baseline CFU at day 14 for the highest dose of the study drug to the value of 0 (meaning no change in CFU after 14 days). The ANOVA compared the changes from baseline CFU on day 14 between all doses of the test agent.

Colony forming unit data vs time were simulated for four hypothetical drugs using the MTP model; Drugs A and B inhibited growth of F and had killing of S and N where drug B had 50% lower potency, Drug C had killing of N and Drug D had killing of S (Figure 2). The PKs were set to hypothet-ical values representing a drug with short half-life (Table 3). Data were sim-ulated for a 14-day monotherapy trial including four dose arms (100, 200, 300 and 400 mg) with daily doses of study drug also including rifampicin as a control group (Figure 3). The simulated design included CFU measure-ments at baseline and on days 1, 2, 3, 4, 5, 6, 7, 9 and 14.

Figure 2. Overview of the Multistate Tuberculosis Pharmacometric (MTP) model including the mechanism of action for Drugs A to D. The mechanism of action was different for the different drugs where the subpopulations that each drug was able to kill or inhibit growth for is indicated by dashed arrows. Drugs A and B had the same mechanism of action where Drug B were only half as potent. Abbreviations; Abs; absorption compartment, F; fast-multiplying bacteria, S; slow-multiplying bacteria, N; non-multiplying bacteria (for other abbreviations see Figure 1 and Table 3)

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Table 3. Pharmacokinetic and Multistate Tuberculosis Pharmacometric (MTP) pa-rameter values used for simulations in Paper VII Parameter Description Value IIV* Multistate Tuberculosis Pharmacometric model parameters

kG (days-1) Fast-multiplying bacterial growth rate 0.206 -

kFN (days-1) Transfer rate from F to N 8.98·10-7 - kSN (days-1) Transfer rate from S to N 0.186 - kSF (days-1) Transfer rate from S to F 0.0145 - kNS (days-1) Transfer rate from N to S 0.00123 - kFSLin (days-2) Time-dependent transfer rate

from F to S 0.00166 -

F0 (ml-1) Initial bacterial number of F 4.11 - S0 (ml-1) Initial number of S 9770 -

Bmax (ml-1) System carrying capacity per ml sputum 2.61·109 152

Drug pharmacokinetic parameters CL/F (L·h-1) Oral clearance 8.00 30.7

- -

V/F (L) Apparent volume of distribution 60.0 ka (h-1) Absorption rate constant 1.00 Exposure-response parameters

FGon/off Fractional inhibition of growth of F

Drug A 1.00 - Drug B 0.50 - Drug C - - Drug D - -

SDk (L·mg-

1·days-1) Second-order S death rate

Drug A 0.240 60 Drug B 0.120 60 Drug C - - Drug D 0.240 60

NDk (L·mg-

1·days-1) Second-order N death rate

Drug A 0.127 75 Drug B 0.064 75 Drug C 0.127 75 Drug D - -

Residual error parameters

ε (CV%) Additive residual error on log scale for all samples 110 -

εrepl (CV%) Replicate-specific additive re-sidual error on log scale 23.1 -

*IIV expressed as percentage coefficient of variance (%CV) IIV; inter-individual variability

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Figure 3. Typical simulated change from baseline in colony forming units (CFU) after start of treatment for drugs A-D, respectively for once daily (OD) dosing.

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New Bayesian therapeutic drug monitoring targets for high-dose rifampicin (Paper IX) New Bayesian TDM targets were proposed in Paper IX based on Cmax and AUC0-24h and also taking MIC into account. The targets were derived using the rifampicin PK model developed in Paper I. To derive the targets, a dose of interest of 35 mg/kg was chosen as a first step. The 35 mg/kg dose was chosen because this dose is well tolerated and has potential for better effica-cy than 10 mg/kg.38,42 From the 35 mg/kg dose a target range was defined by performing typical model-based simulations of AUC0-24h at steady state using the PK model from Paper I according to the following. The lower range was the mid-point between steady state AUC0-24h for 30 and 35 mg/kg and the upper range was the mid-point between 35 and 40 mg/kg. Furthermore, Cmax-based targets were derived similarly. In addition to the AUC0-24h- and Cmax-based targets described so far, MIC-based targets were derived by dividing the corresponding PK only targets by a MIC of 0.125 mg/L which represents the median MIC in the general TB population. The 0.125 mg/L value was derived from the literature.115

Application of targets to patient data The targets were applied to a patient dataset108 where individual PK parame-ters were estimated based on the observed rifampicin plasma concentrations for each patient as a first step. This estimation step included IOV. The next step was to simulate steady state AUC0-24h and Cmax for increasing doses of rifampicin, including 600, 900, 1200, 1500, 1800, 2100, 2400, 2700 and 3000 mg doses for each individual. The dose with an associated AUC0-24h or Cmax inside the Bayesian TDM target was the predicted individual dose. Sim-ilarly, the predicted AUC0-24h/MIC and Cmax/MIC were calculated for the same doses and the dose that fell inside the target was the individually pre-dicted dose.

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Results and discussion

Model for time-to-positivity of high-dose rifampicin (Papers I-II) The structure of the final rifampicin PK model is shown in Figure 4 with final parameter estimates in Table 4. It included saturable (Michaelis-Menten) elimination in addition to a dose-dependent bioavailability. Dose-dependency in volume was not explored as data on protein binding shows that rifampicin do not show saturation in protein-binding for rifampicin up to 40 mg/kg.116 Absorption was described by an absorption transit compartment model117 and the disposition was characterised by a single compartment. The auto-induction was described using an enzyme turn-over model.89 The final model described the observed data well (Figure 5).

Figure 4. Final rifampicin pharmacokinetic model. Dose enters an absorption com-partment (Abs) through a number (NN) of transits in a transit compartment where the transfer rate between compartments are described by NN+1 divided by the mean transit time (MTT). The fraction of the dose that enters the system is dose-dependent where higher doses give higher fraction. The absorption rate constant (ka) describes how fast the drug moves from Abs to the central compartment, Cp. An enzyme turn-over model describes increase in elimination due to auto-induction where AENZ is the relative amount of enzyme, whose production increase at a rate of kENZ and to an extent described by an Emax model based on the plasma concentration of rifampicin.

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Table 4. Parameter estimates (90% confidence interval based on a 1000 sample bootstrap) from the final rifampicin pharmacokinetic model

Parameter Estimate IIV IOV

Vmax (mg/h/70 kg) 525 (430-564) 30.0 (24.7-40.9) - Corr Vmax-km (%) 38.9 (4.34-72.2) - - km (mg/L) 35.3 (29.9-39.1) 35.8 (30.1-38.4) 18.9 (16.7-21.7) V (L/70 kg) 87.2 (83.1-95.4) 7.86 (6.98-9.17) - ka (h-1) 1.77 (1.50-1.92) 33.8 (30.1-38.4) 31.4 (27.7-36.9) MTT (h) 0.513 (0.478-0.613) 38.2 (34.7-44.7) 56.4 (48.8-62.6) NN 23.8 (20.6-26.4) 77.9 (71.8-88.9) - Emax 1.16 (1.14-1.17) - - EC50 (mg/L) 0.0699 (0.0523-0.0761) - - kENZ (h-1) 0.00603 (0.00587-0.00622) - - F450 mg 1 FIX - 15.7 (13.4-18.0) Fmax 0.504 (0.429-0.574) - - ED50 (mg) 67.0 (57.1-80.5) - - ε (%) 23.6 (19.3-26.4) - - IIV; inter-individual variability, IOV; inter-occasion variability, Vmax; maximal elimination rate, km; rifampicin concentration at which the elimination is half-maximal, V; volume of distribution, ka; absorption rate constant, MTT; mean transit time, NN; number of transits, Emax; maximal increase in enzyme production rate, EC50; rifampicin concentration at which half the Emax is achieved, kENZ; first-order rate constant for enzyme pool degradation, F450 mg; relative bioavailability for a rifampicin dose of 450 mg, Fmax; maximal increase in relative bioavailability, ED50; difference in rifampicin dose from 450 mg at which half the Fmax is achieved

Figure 5. Posterior predictive check (PPC) for non-compartmental analysis (NCA)-based area under the plasma concentration-time curve between 0 and 24 hours (AUC0-24h). The solid line is the median observed AUC0-24h and the upper and lower dashed lines are the upper and lower range. The dark shaded area is a 95% confi-dence interval (CI) of the simulated median and the upper and lower lightly shaded areas are the CI of simulated upper and lower range. The CIs were calculated from 1000 simulated datasets.

38

The final model for TTP of high-dose rifampicin included a statistically significant exposure-response relationship between rifampicin AUC0-24h and bacterial killing. Baseline TTP was a significant covariate on the baseline bacterial load in sputum (B0,sputum). The final model included a single bacteri-al subpopulation whose bacterial growth rate decreased with time on treat-ment. The final model described increase in TTP well (Figure 6) and simula-tions of 50 mg/kg showed a further increase in TTP beyond 40 mg/kg (Figure 7). The final parameter estimates are shown in Table 5.

Figure 6. Posterior predictive check (PPC) for median observed (solid lines) vs simulated (shaded areas, 90% prediction interval from 1000 simulations) time-to-positivity (TTP).

Figure 7. Simulated median day 7 increase in time-to-positivity (TTP) vs rifampicin dose. Shaded areas are 90% prediction intervals (1000 simulated trials). No model fit was performed for creating the plot, observed data (solid line) were overlaid.

39

Table 5. Parameter estimates from the final time-to-event (TTE) model

Model, parameter Description Estimate (90% confi-dence interval)a

Sputum modelb

B0,sputum (risk×day-1) Baseline bacterial load 1.40 × 10-4 (1.67 × 10-5-8.78 × 10-4)

θTTP Effect of baseline TTP on B0 -7.13 (-9.30 to -5.15)

kkill (L×h-1×mg-1×day-1) First-order rifampicin bacterial kill rate 1.42 × 10-3 (8.06 × 10-4 – 2.06 × 10-3)

Mycobacterial growth modelb kG,b (day-1) Baseline bacterial growth rate 4.90 (3.18-6.52) kG,ss (day-1) Steady-state bacterial growth rate 2.74 (1.57-3.78)

kG,k (day-1) Rate constant for decrease of bacterial growth rate 0.580 (0.387-0.870)

Bmax (risk×day-1) Maximal bacterial load in liquid container 0.523 (0.459-0.665) aFrom a 1000 sample bootstrap, bMathematical structure for the final model: ( ) = , × ( ) × × × (sputum model), = , + , − , × (1 − , × ) × ( − ( ) ) × ( ) (mycobacterial

growth model), ℎ( ) = ( ) (hazard model)

TTP; time-to-posivity, tt; time on treatment, TTPbaseline; TTP at baseline, AUC0-24h; rifampicin exposure, Bc; bacterial number in liquid culture, tc; time in liquid culture, h; hazard

The presented rifampicin PK model is the first PK model developed on data from high-dose rifampicin including doses up to 40 mg/kg where the model described the observed data well. In particular, the model described the AUC0-24h well, meaning that the PK model was valid to use for clinical trial simulations for the TTE model which included an exposure-response rela-tionship based on AUC0-24h.

Most previous rifampicin PK models do not include saturable PK (such as68,89) and will likely not be valid to describe PK of high-dose rifampicin given the non-linear increase in exposure at higher doses. One model exists which includes saturable PK93 but was developed only on data from 10 mg/kg rifampicin and needs to be evaluated against actual data from higher doses before it can be used to describe the PK of high-dose rifampicin. Apart from clinical trial simulations (performed in Paper II), the PK model can be used e.g. as input for PKPD modelling and for performing TDM for high-dose rifampicin.

The developed TTE model for high-dose rifampicin showed a statistically significant exposure-response for the EBA of rifampicin which was not pos-sible to identify using conventional statistics.38 This shows that it can be advantageous to use pharmacometric modelling instead of conventional sta-tistics. The model was able to reproduce the trends of the observed data well (Figure 6) and when simulating the response from a 50 mg/kg dose, it showed an expected increase in response compared to 40 mg/kg (Figure 7).

40

Model for molecular bacterial load (Paper III) The joint model for TTP and MBL data had the same general structure as the model presented in Paper II but with added sub-models to allow for descrip-tion of contaminated TTP samples and MBL data. The MBL sub-model was needed in order to allow prediction of MBL data where the predicted bacte-rial load in the sputum model was set as the prediction of MBL. Further-more, a sub-model for handling negative TTP samples was included with a similar implementation as another semi-mechanistic TTE model for TTP data.102 The structure of the final MBL-TTP model is shown in Figure 8 with the final parameter estimates shown in Table 6. The model described all aspects of the observed data well as shown in Figure 9 for TTP vs MBL, TTP vs time and MBL vs time.

The sputum model described bacterial kill and consisted of two mycobac-terial subpopulations (B1 and B2) where the administered treatment had killing of both subpopulations but with different potency (B2 were killed more slowly than B1). A rifampicin dose covariate effect was found for the killing of B1 where a 35 vs 10 mg/kg rifampicin dose caused significantly higher kill. The two subpopulations present within the sputum model existed also in the mycobacterial growth model where only B1 were able to grow, however B2 were able to transfer to become B1. The hazard/TTE model described how the growth in the liquid culture was linked to the probability of a positive TTP signalling event. For the hazard model, only B1 bacteria contributed to the probability of positive signalling where the exact contribu-tion of each B1 bacterium was described using a scaling parameter. The scaling parameter was time-dependent where it decreased over time on treatment. The contamination model was different between the sites since a graphical analysis of the data revealed different patterns for the contamina-tion from each site. For Malawi contamination was not determined and for Mozambique, the contamination was moderately high at all time-points. Thus, the contamination-related parameters that were estimated from Tanza-nia data, where contamination was low initially and increased over time, was considered the most relevant contamination model. The contamination mod-el included a linearly increasing probability of contamination. Finally, a sub-model for negative TTP was developed which was described by an Emax rela-tionship between probabilities of negative TTP samples and bacterial load in sputum. Note that handling of negative samples within the TTE approach using right-censoring, which is the standard way of handling negative sam-ples in a survival analysis did not yield a good description of the data.

Figu

re 8

. Sch

emat

ic re

pres

enta

tion

of th

e fin

al c

ombi

ned

mol

ecul

ar b

acte

rial l

oad

(MBL

) and

tim

e-to

-pos

itivi

ty (T

TP) m

odel

. Pa

ram

eter

def

initi

ons a

re sh

own

in T

able

6.

42

Table 6. Parameter estimates from the final molecular bacterial load (MBL)-time-to-positivity (TTP) model

Model, parameter Description Estimate (%RSE)

Sputum model B10,s (CFU/mL) Initial bacterial load of B1 in sputum 0.365×106 (28.8) k1 (week-1) First-order bacterial kill rate of B1 in sputum 1.71 (8.70) B20,s (CFU/mL) Initial bacterial load of B2 in sputum 0.00430×106

(51.4) k2 (week-1) First-order bacterial kill rate of B2 in sputum 0.494 (9.50) Dose35mg Fold increase in bacterial killing of k1 by 35 vs

10 mg/kg rifampicin 1.66 (14.0)

IIV B10,s (%) Inter-individual variability in B10,s 239 (9.18) IIV B20,s (%) Inter-individual variability in B20,s 227 (10.9) Corr B10,s – B20,s (%) Correlation between B10,s and B20,s 45.4 (15.6) ε (%) Additive error on log scale for MBL data 79.7 (4.96) Mycobacterial growth model kG (day-1)a Mycobacterial growth of B1 in liquid culture 0.395 (8.50) k21 (day-1)a Transfer rate from B2 to B1 in liquid culture 0.395 (8.50) Bmax (CFU/mL) Maximal bacterial load in liquid culture 166×106 (24) TTP model ScaleBL Baseline value of scaling parameter accounting

for the contribution of B1 bacteria to the proba-bility of a positive TTP signaling event

6.68×10-9 (31.6)

IIV ScaleBL (%) Inter-individual variability in ScaleBL 80.6 (18.1) ScaleSS Steady state value of scaling parameter 0.601×10-9 (24.3) kS (week-1) First-order rate constant for time-varying change

of the scaling parameter 1.28 (25.1)

Model for negative TTP samples pmax Maximal probability of not having a negative

TTP sample 0.967 (1.50)

B50 Bacterial load of B1+B2 in sputum at which the probability of not having a negative TTP sample is half maximal

49.8 (33.7)

γ Gamma-factor for non-linear Emax relationship for negative TTP samples

0.756 (18.9)

Model for contaminated TTP samples pcon,base

c Baseline probability of TTP contamination 0.0910 (39.0) kp

c (week-1) Linear time-varying increase of probability of a contaminated TTP sample

0.0416 (13.9)

The reported values are the final estimates with relative standard error (%RSE) shown in brackets as the approximate coefficient of variance (%CV) on standard deviation scale ob-tained from the NONMEM covariance step. The IIV (inter-individual variability) and residual error are shown as the approximate %CV on standard deviation scale. ak21 and kG were modelled as a single parameter in the model, bthe parameters for contaminat-ed TTP samples were estimated on data from Tanzania, the other sites included time-constant probabilities of 0 for Malawi (fixed value, since contamination was not measured) and 0.336 (10.0% RSE) for Mozambique CFU; colony forming units

43

Figure 9. Diagnostic plots for the link between time-to-positivity (TTP) and mo-lecular bacterial load (MBL) (a), TTP over time (b) and MBL over time (c). Open circles are observed data and solid lines are median of observed data. Shaded areas are 95% confidence interval of predicted median based on 1000 simulated datasets.

44

The predictions of B1 and B2 in sputum were described by the following equations, respectively: 1 ( ) = 1 , × × × 2 ( ) = 2 , × × where Dose35mg is 0 for 10 mg/kg rifampicin and tt stands for time on treat-ment. For abbreviations of parameters, see Table 6. The individually predict-ed MBL was described by: ( ) = 1 ( ) + 2 ( ) The dynamics within the mycobacterial growth model consisting of B1 and B2 were described by the following differential equations, respectively: = 1 ( ) × × log ( ) ( ) + × 2 ( ) = − × 2 ( )

where tc is time in culture. The initial conditions for each TTP sample were described by: 1 ( = 0) = 1 ( = ) and 2 ( = 0) = 2 ( = ) The hazard within the TTP model was described by the following equation: ℎ( ) = 1 ( ) × ( + ( − ) × (1 − × )) The hazard was used to compute the cumulative hazard as: ( ) = ℎ( ) The cumulative hazard was used to calculate the survival as: ( ) = ( ) The probability of TTP contamination was given by the following: , = , + × Finally, a sub-model was included to describe the probability of a negative TTP sample by: , = 1 − × ( ) ( )( ) ( )

This is the first pharmacometric model to jointly describe MBL and TTP where the link between the biomarkers was established and the model de-scribed the observed data well. The model is semi-mechanistic where chang-es of two bacterial subpopulations in sputum lead to changes in both bi-omarkers. A drawback is that only two mycobacterial subpopulations were included in the model which is an oversimplification since TB is known to exist in at least three different subpopulations.14 During the model develop-ment of the MBL-TTP model, the MTP model which includes three TB sub-populations was explored as an alternative structure for the sputum model but did not give a stable model. The reason for the instability is unknown but

45

in future analyses it should be explored whether more than two subpopula-tions can be described.

An advantage of this model compared to previous semi-mechanistic TTE models for TTP101,102 is that it includes a component for TTP contamination. The model can be used to make clinical trial simulations to predict the ex-pected sample loss due to contaminated TTP samples. Furthermore, the model can be used to predict TTP data from MBL data and vice versa for trials including TTP or MBL only. The model can also be used for power calculations for Phase II trials. It was possible to identify an increased effect of 35 vs 10 mg/kg rifampicin for bacterial killing within the model which indicates that the approach of including MBL and TTP data combined with pharmacometric modelling is a powerful approach for detecting differences between regimens.

Model for culture conversion data (Paper IV) The rifampicin PK model from Paper I was re-estimated based on the PK data in Paper IV. Modifications were made to the PK model including re-moval of the enzyme turn-over model since all patients were assumed to already be fully induced (PK data collected only on day 28). The non-linear increase of bioavailability with dose was replaced by a linear dose-dependent increase. In addition, the model for IIV changed according to Table 7. The PK model adequately described the observed PK data.

A surge function was chosen as the base hazard model for liquid culture TSCC as it gave better fit than the exponential and Weibull models. The model-based rifampicin AUC0-24h (imputed in patients with missing PK ob-servations) was a significant covariate in the model included as a linear rela-tionship where higher rifampicin exposures led to higher probability of early culture conversion. Additional treatment-related covariates that were identi-fied were replacement of ethambutol with moxifloxacin which gave shorter TSCC and replacement of ethambutol with SQ109 which led to longer TSCC. Baseline bacterial load and percentage of unavailable culture results were also included as covariates in the model.

The hazard was described according to the following: ℎ( ) = + 1where SA is the surge amplitude described by: = × 100 × 4.4 × (1 + Θ × − 56.156.1× (1 + Θ × ) × (1 + Θ × ) where pmiss is the individual’s percentage of lost samples, BTTP is the baseline TTP, RIFAUC is the model-based rifampicin AUC0-24h, MX is moxifloxacin

46

instead of ethambutol (1 if yes, otherwise 0) and SQ is SQ109 instead of ethambutol (1 if yes, otherwise 0). For abbreviations of parameters and pa-rameter estimates, see Table 8. The peak time (PT) was described by: = × 4.4 −ΘBTTP × (1 − Θ × − 56.156.1 )× (1 − Θ × ) × (1 − Θ × ) The surge width (SW) was described by: = × 4.4 ΘBTTP × (1 + Θ × ) × (1 + Θ × )The model described the observed data well (Figure 10). A separate model was developed on TSCC using solid culture which gave similar results as the presented model which was based on liquid culture.

Table 7. Re-estimated rifampicin pharmacokinetic parameters from MAMS-TB patients

Parameter Description Estimate (%RSE) IIV (%RSE)

Vmax (mg/h/44.6 kg)

Maximal elimination rate 339 (13.1) -

km (mg/L) Rifampicin concentration at which the elimination is half-maximal 11.7 (18.3) 32.6 (12.0)

V (L/44.6 kg) Volume of distribution 56.5 (3.9) - ka (h-1) Absorption rate constant 1.01 (13.6) 56.7 (19.0) NN Number of transits 4.99 (21.8) 137 (12.3) MTT (h) Mean transit time 1.15 (11.7) 81.9 (10.5) Correlation Vmax-km (%) -70.8 (32.8) -

F450 mg Relative bioavailability for a rifampicin dose of 450 mg 1 FIX 16.1 (15.7)

θF (%/1000mg) Linear increase in bioavailability 13.5 (45.5) - εproportional (%) Proportional residual error 16.2 (4.1) - εadditive (mg/L) Additive residual error 0.0361 (13.7) -%RSE; relative standard error as % coefficient of variation from the NONMEM covariance step

Table 8. Final parameter estimates for model of time to stable culture conversion (TSCC) based on liquid culture

Parameter Description Estimate (%RSE)

SAbase (day-1) Base value, surge amplitude 0.0540 (12) PTbase (day) Base value, peak time 78.3 (4.1) SWbase (day) Base value, surge width 35.4 (7.0) Θpmiss Coefficient for effect of percentage missing samples 2.06 (14) ΘBTTP Coefficient for baseline time-to-positivity 0.211 (17) ΘRIFAUC (%) Coefficient for model-based rifampicin AUC0-24h 3.98 (27) ΘMX (%) Coefficient for replacing ethambutol with moxifloxacin 10.0 (56) ΘSQ (%) Coefficient for replacing ethambutol with SQ109 -13.6 (46)%RSE; relative standard error as % coefficient of variation from the NONMEM covariance step, AUC0-24h; area under the plasma concentration-time curve during 24 hours

47

Figure 10. Kaplan-Meier visual predictive check for the final time-to-event model for culture conversion data. The lines are the observed data and shaded areas are 95% confidence intervals from model simulations. Study arms include the control arm (R10HZE) and the experimental arms as described in Table 2. SCC; sputum culture conversion

In the developed TTE model rifampicin exposure was linked to TSCC which is a common endpoint for TB Phase IIb trials. A 35 mg/kg dose of rifampicin was shown to substantially shorten the TSCC which indicates that higher doses of rifampicin are more effective. The conventional statistical analysis for the underlying study42 consisted of comparisons between the treatment arms within the study which did not allow for assessment of individual pa-tient covariates in contrast to the TTE approach used in this work.

A parametric hazard approach was used which differs from semi-parametric modelling techniques using Cox regression which has been ap-plied to culture conversion data for TB.106 Since Cox regression relies on an assumption of proportionality of hazards between arms it is problematic for exposure-response analyses where drug concentrations and thus the hazard vary over time to a different degree between arms.

The Multistate Tuberculosis Pharmacometric model applied to colony forming unit data (Papers V and VI) The MTP model was applied to clinical CFU data for monotherapy trials of rifampicin (Paper V), clofazimine and pyrazinamide (Paper VI). Statistically significant exposure-response relationships were found between continuous-

48

ly predicted concentrations of each drug and the killing or growth inhibition of at least one subpopulation (Figure 11, Table 9 and Table 10).

Rifampicin was found to fully inhibit growth of fast-multiplying bacteria included as an on/off effect as well as killing of slow- and non-multiplying bacteria described using linear effect models. For rifampicin no PK data existed so the typically predicted PK profiles based on a previous PK mod-el89 were assumed. The model described the observed changes in CFU well for rifampicin-treated and negative control subjects (Figure 12).

For clofazimine a PK model was developed with linear absorption and two-compartment disposition PK with linear elimination. The PK model described the observed PK data well (Figure 13). The individually predicted clofazimine concentrations served as input for the exposure-response analy-sis where clofazimine were found to be able to kill non-multiplying bacteria described by a linear effect model. The observed changes in CFU post clo-fazimine treatment were described well by the model (Figure 12).

For pyrazinamide, the PK observations were described well by a previous PK model90 where a single modification of removing a bi-modal distribution of ka (assuming that the data only included fast absorbers) was made (Figure 12). Pyrazinamide had killing of slow-multiplying, semi-dormant bacteria described by a linear effect model where the observed changes in CFU were described well by the model (Figure 13).

The successful application of the MTP model in three clinical datasets shows a role of the MTP model for analysing clinical data to determine the mechanism of action (i.e. which mycobacterial subpopulations the drug can kill). The MTP model has also been applied to in vitro103 and mouse104 data which suggests that the MTP model has a potential role also for translational predictions across pre-clinical and clinical systems.

The analysis of rifampicin shows that rifampicin has activity against non-multiplying bacteria, i.e. persisters, which explains the known sterilising activity of rifampicin.32

Clofazimine was also found to have killing of non-multiplying bacteria suggesting that clofazimine has sterilising activity which has been shown in substantially longer trials.49,50 The ability to kill non-multiplying bacteria was estimated from short-term monotherapy data here where the CFU in-creased over time which would have been interpreted in a standard analysis as a drug without any killing capacity.51 This shows how the MTP model can be used to interpret data more informatively which allows for appropriate decision-making for TB drug development. Since no previous PK models for clofazimine exist,94 this is the first population PK model for clofazimine.

The analysis showed that pyrazinamide had killing of slow-multiplying, semi-dormant bacteria which can explain why the addition of pyrazinamide to the standard first-line regimen is only beneficial during the first two months of treatment.44

Figu

re 1

1. S

chem

atic

repr

esen

tatio

n of

the

conc

lude

d ex

posu

re-re

spon

se re

latio

nshi

ps b

etw

een

cont

inuo

usly

pre

dict

ed p

lasm

a co

ncen

tratio

ns

of c

lofa

zim

ine

(CCL

O, b

lue)

, rifa

mpi

cin

(CRI

F, re

d) a

nd p

yraz

inam

ide

(CPZ

A, w

hite

) and

the

effe

ct o

n th

e di

ffere

nt b

acte

rial s

tate

s sho

wn

as

dash

ed li

nes i

n bl

ue, r

ed a

nd b

lack

for c

lofa

zim

ine,

rifa

mpi

cin

and

pyra

zina

mid

e, re

spec

tivel

y. F

or re

mai

ning

abb

revi

atio

ns, s

ee T

able

3.

50

Table 9. Pharmacokinetic parameters used for making continuous predictions of plasma concentrations for exposure-response analyses. Drug, para-meter Description Estimate (%RSE) IIV, %CV

(%RSE) IOV, %CV (%RSE)

Rifampicina CL/F (L/h) Apparent clearance 10.0 FIX - - V/F (L) Apparent volume 86.7 FIX - - MTT (h) Mean transit time 0.713 FIX - - NN Number of transits 1.00 FIX - -

Emax Maximal increase in enzyme production rate 1.04 FIX

- -

EC50 (mg/L) Concentration at which half the Emax is reahed 0.0705 FIX

- -

kENZ (h-1) Rate constant for first-order degradation of emzyme 0.00369 FIX

- -

F Bioavailability 1 FIX - -

Ffat,CL/F Contribution of FFM and WT to CL/F 0.311 FIX

- -

Ffat,V/F Contribution of FFM and WT to V/F 0.188 FIX

- -

ε (%) Proportional residual error - - - Clofazimine CL/F (L/h) Apparent clearance 12.5 (145) 74.8 (160) Vc/F (L) Apparent central volume 1138 (18.4) 23.0 (85.9) ka (h-1) Absorption rate constant 0.67 (50.0) 35.3 (95.3) Q/F (L/h) Inter-compartment CL 63.3 (12.7) - Vp/F (L) Peripheral volume 8062 (82.7) - F Bioavailability 1 FIX - 43.8 (26.1)Tlag (h) Absorption lag-time 0.62 (0.75) -ε (%) Proportional residual error 13.9 (0.08) -Pyrazinamideb

CL/F (L/h) Apparent clearence 3.42 FIX 18.7 FIX 15.4 FIX V/F (L) Apparent volume 29.2 FIX 15.8 FIX - ka (h-1) Absorption rate constant 3.56 FIX - 78.9 FIXDur (h) Duration of zero-order input

into dose compartment 0.290 FIX 97.8 FIX -

θWT-CL (kg-1) Slope effect of WT on CL 0.0545 FIX - - θWT-V (kg-1) Slope effect of WT on V 0.433 FIX - - θSEX-V (L) Effect of sex on V 4.55 FIX - - εAdd (mg/L) Additive residual error 1.89 FIX - - εProp (%) Proportional residual error 0.0907 FIX - - aTypical model predictions were made for rifampicin based on a previous model,89 i.e. residu-al error and variability within and between subjects were removed, bparameters for pyra-zinamide were used from a previous model90 assuming the sole existence of fast absorbers in the dataset used in this work FFM; fat-free mass, WT; body weight, IIV; inter-individual variability, IOV; inter-occasion variability; %RSE; relative standard error as % coefficient of variation obtained from the covariance step in NONMEM

Tabl

e 10.

Par

amet

er e

stim

ates

and

pre

cisio

n fo

r exp

osur

e-re

spon

se p

aram

eter

s for

rifa

mpi

cin,

clo

fazi

min

e an

d py

razi

nam

ide

Para

met

er

Des

crip

tion

Rifa

mpi

cin

(%RS

E)

Clof

azim

ine

(%RS

E)

Pyra

zina

mid

e (%

RSE)

B max

(/m

L)a

Syste

m c

arry

ing

capa

city

, det

erm

ines

tota

l bac

teria

l num

-be

r at s

tatio

nary

pha

se

2.61

×109 (3

0.5)

0.

0603

×109 (3

5.2)

0.

0842

×109 (5

4.6)

IIV B

max

(%)

Inte

r-ind

ivid

ual v

aria

bilit

y in

Bm

ax

152

(15.

9)

133

(13.

7)

217

(16.

3)

FGon

/off

Frac

tiona

l inh

ibiti

on o

f gro

wth

of f

ast-m

ultip

lyin

g ba

cter

ia

1 FI

X

- -

SDk (

L×m

g-1×d

ays-1

) Se

cond

-ord

er sl

ow-m

ultip

lyin

g sta

te k

ill

0.20

0 (4

1.6)

-

0.02

14 (3

0.6)

N

Dk

(L×m

g-1×d

ays-1

) Se

cond

-ord

er n

on-m

ultip

lyin

g sta

te k

ill

0.10

6 (1

9.0)

1.

63 (1

1.5)

-

ε (%

) A

dditi

ve re

sidua

l erro

r on

log

scal

e fo

r all

repl

icat

es

110

(12.

0)

128

(7.8

5)

98.5

(6.1

2)

ε repl

(%)

Add

itive

resid

ual e

rror o

n lo

g sc

ale

betw

een

repl

icat

es

23.1

(10.

2)

49 (1

7.4)

39

(11.

6)

a The

othe

r Mul

tista

te T

uber

culo

sis P

harm

acom

etric

(MTP

) par

amet

ers i

nclu

ding

tran

sfer

rate

s bet

wee

n sta

tes w

ere

fixed

from

103 a

nd th

e ex

act v

alue

s use

d ca

n be

foun

d in

Tab

le 3

Th

e m

odel

s wer

e de

fined

by

the

follo

win

g eq

uatio

ns:

=×++

×1−EFF

×+×−

× −×

=×+×

−×−×

−×

=×+

×−×−

× w

here

kFS

is d

escr

ibed

by

k FS,

lin×t

. The

dru

g ef

fect

s for

the

effe

ct si

tes w

ere

the

follo

win

g:

Rifa

mpi

cin:

EFF

FG=F

Gon

/off,

EFF

SD=S

Dk,

RIF

×CR

IF a

nd E

FFN

D=N

Dk,

RIF

×CR

IF

Clof

azm

inin

e: E

FFFG

=0 (i

.e. n

o ef

fect

), EF

F SD=0

(i.e

. no

effe

ct) a

nd E

FFN

D=N

Dk,

CLO

×CC

LO

Pyra

zina

mid

e: E

FFFG

=0 (i

.e. n

o ef

fect

), EF

F SD=S

Dk,

PYR×

C PY

R an

d EF

F ND=0

(i.e

. no

effe

ct)

whe

re E

FFFG

, EFF

SD a

nd E

FFN

D a

re p

lace

hold

ers

for d

rug

effe

ct in

clus

ions

as

inhi

bitio

n of

fast

mul

tiply

ing

grow

th, k

illin

g of

slo

w-m

ultip

lyin

g ba

cter

ia a

nd

killi

ng o

f non

-mul

tiply

ing

bact

eria

, res

pect

ivel

y an

d C R

IF, C

CLO

and

CPY

R sta

nds

for p

lasm

a co

ncen

tratio

ns o

f rifa

mpi

cin,

clo

fazi

min

e an

d py

razi

nam

ide,

re-

spec

tivel

y. O

ther

par

amet

er a

bbre

viat

ions

can

be

foun

d in

Tab

le 3

%

RSE;

rela

tive

stand

ard

erro

r as %

coe

ffici

ent o

f var

iatio

n ob

tain

ed fr

om th

e co

varia

nce

step

in N

ON

MEM

52

Figure 12. Visual predictive checks (VPCs) for the final models for negative con-trol, rifampicin, clofazimine and pyrazinamide. Open circles are observations, black lines are median of observed and dashed lines are 5th and 95th percentiles of ob-served data. Red shaded areas are 95% confidence interval (CI) of simulated median and blue shaded areas are 95% CI of the 5th and 95th percentiles, all based on 1000 simulated datasets. For rifampicin, a prediction-corrected VPC118 was performed which means that data from all dose groups were included in a single plot.

Figure 13. Visual predictive checks (VPCs) for plasma concentrations data (day 14) for clofazimine and pyrazinamide. Observations are shown as open circles with black lines showing the median of observed and dashed lines are 5th and 95th percen-tiles of observed data. Red shaded areas are 95% confidence interval (CI) of simu-lated median and blue shaded areas are 95% CI of the 5th and 95th percentiles, all based on 1000 simulated datasets.

53

Sample size requirements for Phase IIa tuberculosis trials (Paper VII) The power to detect a statistically significant drug effect vs sample size for each tested method including the MTP model, mono- and bi-exponential regression, t-test and ANOVA are shown in Figure 14. The required sample size to attain 90% power was lowest for the PKPD-based analysis using the MTP model for all drugs where sample size could be lowered at least two-fold. The PKPD-based analysis was followed by t-test or mono-exponential analysis apart from for Drug C. For Drug C only the PKPD-based approach and ANOVA reached power above 0 (why this occurred is described below). Overall, the ANOVA resulted in highest sample size.

The lowest sample sizes were required for Drug A (inhibition of growth of F and killing of S and N, similar to rifampicin in Paper V) followed by Drug B (same mechanism as Drug A but 50% as potent). Drug B was fol-lowed by Drug D (killing only of S). Finally, Drug C required the highest sample sizes to reach 90% power where no other method than PKPD and ANOVA reached power above 0. The reason for this was that the t-test, mono-exponential and bi-exponential models required a trend of lowering of CFU to be considered statistically significant within this work and as can be seen for the typical CFU pattern for Drug C (Figure 3), the CFU is increas-ing (discussed in greater detail below).

The results from Paper VII confirms the known difficulty in finding drug effects and differences between doses of the same drug for Phase IIa at sam-ple sizes of 10-15 patients per group (corresponding to a total sample size of 50-75 patients in this work which assumed five arms and a balanced design).The work shows that if a PKPD-based approach is used when designing andanalysing Phase IIa TB trials the sample size can be reduced at least two-foldwhich contributes to cheaper and more rapid TB drug development whichcan help to reduce the time until drugs become available for patients.

Drug C was only able to kill non-multiplying bacteria which caused an increase in CFU at day 14 for the highest dose (Figure 3). The reason for this pattern was due to a regrowth phenomenon occurring for the MTP model, which was used to simulate data. Specifically, as non-multiplying bacteria die it creates space for fast-multiplying bacteria to grow which is governed by the growth function × log ( ). It was assumed that the infectionwas in a stationary phase at start of treatment (F+S+N=Bmax) where no growth occurs. As bacteria die the Bmax/(F+S+N)-ratio becomes high and bacterial growth takes place. Drug C which actually has killing of non-multiplying bacteria would have been deemed ineffective according to the commonly used analysis methods. The same behaviour was seen for clo-fazimine which was successfully described using the MTP model in Paper VI and a similar observation has been seen for SQ109.119

54

Figure 14. Predicted power (5% significance level) vs total sample size for four hypothetical drugs A-D labelled a-d, respectively. Power to detect a drug effect is shown as filled squares for the pharmacokinetic-pharmacodynamic (PKPD) based approach, filled circles for mono-exponential regression, filled triangles for t-test, filled diamonds for ANOVA and crosses for bi-exponential regression. The dashed lines indicate 90% power.

Model for treatment outcome in mice (Paper VIII) The final logistic model for treatment outcome data in mice included a non-linear, sigmoidal Emax relationship between treatment time and probability of cure. The baseline failure rate (pbase) which is the probability of treatment failure without treatment was 1 (i.e. 100%) and the maximal achievable

55

probability of cure (Emax) was also 1 (Table 11). The time at which half the Emax was achieved (T50) was different between regimens as it was ~50% higher for RZMH than RpZHE and RZME which indicates lower efficacy for RZMH. The final model described the observed data well (Figure 15).

Figure 15. Visual predictive check of the final model for A) rifapentine, pyra-zinamide (Z), isoniazid (H) and ethambutol (E, RpZHE), B) rifampicin (R), Z, moxi-floxacin (M) and E (RZME) and C) R, Z, M and H (RZMH). Open circles are the observed proportion of cured animals and shaded areas are 95% confidence interval of the predicted cure based on 1000 simulated datasets.

56

Table 11. Final parameter estimates of the model for treatment outcome in mice

Parameter Description Parameter estimate (%RSE)

pbase Baseline probability of treatment failure 1 FIX Emax Maximal probability of cure 1 FIX

T50RpZHE,RZME (months) The treatment length where half the Emax isachieved for RpZHE and RZME 2.87 (5.4)

T50RZMH (months) The treatment length where half the Emax is achieved for RZMH 4.35 (6.0)

γ Shape factor 9.82 (23.0) %RSE; relative standard error as % coefficient of variation from the covariance step in NONMEM, Rp; rifapentine, Z; pyrazinamide, R; rifampicin, M; moxifloxacin, H; isoniazid, E; ethambutol The final model was described by the following equation: = 1 − = × (1 − ×+ )

where t is treatment length and T50 differed depending on the regimen according to the table.

The final model for treatment outcome assessment shows how an improved, more efficient design of mouse experiments in combination with mathemati-cal modelling can improve the information yield in comparison to conven-tional design and analysis of TB mouse experiments. Conventionally, few treatment lengths are studied with a high number of animals per treatment length whereas in Paper VIII the design included many treatment lengths with few mice per time-point. This update of the design, combined with mathematical modelling, led to a better characterisation of the relationship between treatment length and treatment outcome which would not have been possible with a conventional design. Since a difference in efficacy was de-tected between regimens it shows that the suggested approach is powerful for detecting differences between regimens when using relatively few mice (n=3 per treatment length). Furthermore, a conventional treatment outcome design includes an additional, earlier part of the experiment where the drug efficacy in the early part of treatments is studied. This earlier part of the experiment was not included in our study which means that the suggested design limits the use of animals. It is unclear what the added value is of the earlier part of the conventional design for the resulting assessment of treat-ment outcome.86,87

Overview of developed models Table 12 shows an overview of all pharmacometric models developed in this thesis based on estimations from observed data.

Tabl

e 12.

Ove

rvie

w o

f pha

rmac

omet

ric m

odel

s dev

elop

ed w

ithin

this

thes

is

Pape

r PK

, PD

or

PK

PD

Clin

ical

or

pre

-cl

inic

al

Dep

ende

nt v

aria

ble

(type

of d

ata)

D

rug(

s)

Stud

y siz

e St

udy

dura

tion

Run-

time

Estim

at-

ion

met

hod

Com

men

t

I PK

Cl

inic

al

Plas

ma

conc

entra

t-io

ns (c

ontin

uous

) Ri

fam

pici

n 83

2

wee

ks

27 h

18

min

La

plac

e Th

e m

odel

was

use

d as

inpu

t for

PK

PD m

odel

-lin

g in

Pap

ers I

I and

IV

II PK

PD

Clin

ical

TT

P (ti

me-

to-

even

t) Ri

fam

pici

n 83

2

wee

ks

28 s

Lapl

ace

Sign

ifica

nt sh

ort-t

erm

exp

osur

e-re

spon

se o

f rif

ampi

cin

was

foun

d. M

odel

was

use

d to

sim

ulat

e an

une

xplo

red,

50

mg/

kg d

ose

III

PD

Clin

ical

TT

P (ti

me-

to-

even

t) an

d M

BL

(con

tinuo

us)

Rifa

mpi

cin,

iso

niaz

id,

pyra

zina

-m

ide,

eth

am-

buto

l

105

12 w

eeks

5

h 10

m

in

IMP

Join

t sem

i-mec

hani

stic

mod

el d

escr

ibin

g th

e re

latio

nshi

p be

twee

n M

BL a

nd T

TP

IV

PKPD

Cl

inic

al

Cultu

re c

onve

rsio

n(ti

me-

to-e

vent

) Se

e Ta

ble

2 33

6 26

wee

ks

8 s

Lapl

ace

Sign

ifica

nt lo

ng-te

rm e

xpos

ure-

resp

onse

of

rifam

pici

n w

as fo

und

V

PKPD

Cl

inic

al

CFU

(con

tinuo

us)

Rifa

mpi

cin

23

2 w

eeks

6

min

FO

CE

The

mod

el id

entif

ied

a ki

lling

effe

ct o

n pe

r-sis

ters

usin

g th

e M

TP m

odel

VIa

PK

Cl

inic

al

Plas

ma

conc

entra

t-io

ns (c

ontin

uous

) Cl

ofaz

imin

e14

2

wee

ks

5 m

in

22 s

FOCE

Th

e m

odel

was

use

d as

inpu

t for

PK

PD m

odel

-lin

g fo

r mod

el la

belle

d as

VIb

VIb

PK

PD

Clin

ical

CF

U (c

ontin

uous

) Cl

ofaz

imin

e 14

2

wee

ks

3 m

in

47 s

FOCE

Th

e m

odel

iden

tifie

d a

killi

ng e

ffect

on

per-

siste

rs u

sing

the

MTP

mod

el

VIc

PK

PD

Clin

ical

CF

U (c

ontin

uous

) Py

razi

nam

ide

15

2 w

eeks

4

min

FO

CE

The

mod

el id

entif

ied

a ki

lling

effe

ct o

n se

mi-

dorm

ant T

B ce

lls u

sing

the

MTP

mod

el

VIII

PD

Pr

e-cl

inic

al

Trea

tmen

t out

com

e (b

inar

y)

See

Figu

re 1

5 30

9

mon

ths

1 s

FO

Impr

oved

des

ign

of p

re-c

linic

al e

xper

imen

ts

Abb

revi

atio

ns: P

K; p

harm

acok

inet

ics,

PD; p

harm

acod

ynam

ics,

TTP;

tim

e-to

-pos

itivi

ty, C

FU; c

olon

y fo

rmin

g un

it, IM

P; im

porta

nce

sam

plin

g; F

OCE

; firs

t-or

der c

ondi

tiona

l esti

mat

ion,

FO

; firs

t-ord

er m

etho

d, M

TP; M

ultis

tate

Tub

ercu

losis

Pha

rmac

omet

ric

58

Framework for model-based therapeutic drug monitoring for tuberculosis (Paper IX) The proposed Bayesian TDM targets at steady state were 181-214 h×mg/L for AUC0-24h and 33-38 mg/L for Cmax. The targets including MIC were 1448-1712 and 264-304 for AUC0-24h and Cmax, respectively. The MIC-based targets were derived based on an assumed literature MIC of 0.125 mg/L. All proposed targets are reflective of steady state without any influence of IOV.

The individually predicted doses according to the developed Bayesian TDM targets in the patient dataset are shown in Figure 16. The predicted doses were overall similar for dosing based on AUC0-24h and Cmax, but as indicated by the dashed lines in Figure 16a, the doses were slightly lower for Cmax in some individuals. Dosing according to the MIC-based targets led to substantially lower doses than the corresponding PK only targets (Figure 16b-c).

Of the developed targets, the AUC0-24h steady state target of 181-214 h×mg/L is recommended to be tested prospectively. For rifampicin, AUC0-24h has better correlation with treatment outcome than Cmax

120 which is why AUC0-24h is proposed rather than Cmax. The MIC-based targets are not rec-ommended as proposed targets since determination of individual MICs is associated with high uncertainty/variability.121 The high variability combined with the fact that MIC is a crude measurement (since it is always based on two-fold dilutions) can result in unacceptably large differences in the pre-dicted dose.

The median predicted dose for the suggested AUC0-24h-based target is 1800 mg (Figure 16) which is substantially higher than the currently recom-mended dose of 10 mg/kg which corresponds to 600 mg. The predicted dos-es ranged between 1200 and 3000 mg which suggests that patients will actu-ally get different doses based on the suggested approach.

Within the patient dataset used in this work the dose was not updated based on the measured concentrations. This means that the proposed target must be validated in a prospective trial. However, the PK sampling design in the patient dataset included sparse sampling of plasma at three different time-points which is well-suited for programmatic settings. This shows that data likely to be collected in a clinical setting can be used to predict the dose using the suggested approach. An overview of how the approach can be im-plemented is shown in Figure 17. It is advisable to include PK sampling on at least two separate occasions due to IOV of rifampicin. Predicting the fu-ture dose using the approach is quick (minutes) and do not require any model development. The lower panel in Figure 17 shows how the relative precision in the dose is expected to change as more data is collected and the dose pre-diction is updated.

59

Figure 16. Distribution of predicted rifampicin doses according to the developed Bayesian therapeutic drug monitoring (TDM) targets for (a) AUC0-24h and Cmax, (b) AUC0-24h and AUC0-24h/MIC and (c) Cmax and Cmax/MIC. Doses are shown as open circles where difference in individual dose can be seen by dashed lines. AUC0-24h; area under the plasma concentration-time curve during 24 hours, Cmax; highest plas-ma concentration during 24 hours, MIC; minimal inhibitory concentration

Figu

re 1

7. S

ugge

stion

for i

mpl

emen

tatio

n of

the

ther

apeu

tic d

rug

mon

itorin

g (T

DM

) app

roac

h co

uple

d w

ith B

ayes

ian

fore

casti

ng. T

op p

anel

su

gges

ts ph

arm

acok

inet

ic a

nd p

oten

tial m

inim

um in

hibi

tory

con

cent

ratio

n (M

IC) s

ampl

ing

whe

re …

indi

cate

s wai

ting

time

for M

IC re

adou

t. M

iddl

e pa

nel s

how

s the

fore

casti

ng a

nd d

ose

pred

ictio

n ste

p w

hich

lead

s to

a do

sing

deci

sion.

The

low

er p

anel

show

s the

exp

ecte

d re

lativ

e in

crea

se in

pre

cisio

n as

mor

e da

ta b

ecom

es a

vaila

ble.

61

Conclusions and perspectives

Tuberculosis has a major impact on the well-being in the world as 10 million people get infected each year. Most patients have DS-TB and can be treated with a standard six month regimen to attain stable cure. However, 500 000 patients each year get MDR-TB which requires sufficiently longer treatment (18-24 months) and about 50% of these patients get treatment failure. Multi-drug resistant TB has been declared a global health crisis5 where new and improved treatments are urgently needed to combat MDR-TB. However, new treatments will not reach patients in time given the status of the present drug pipeline and the inefficiency of the current TB drug development pro-gramme. This thesis presents pharmacometric tools that can speed up TB drug development and also includes suggestions of how to improve current treatment. If the suggested approaches are implemented they can help to reduce the impact of the global burden of MDR-TB.

The different projects of this thesis aimed to improve the development and treatment of drugs against TB. Papers I-VI exemplify how pharmaco-metric models can be used to allow for better decision-making in clinical drug development of anti-TB drugs. Papers VII and VIII give design rec-ommendations for more efficient pre-clinical and clinical drug development. Paper IX sets up a framework for personalised medicine which can lead to better treatment of TB. An overview of the developed models is included in Table 12.

Papers I and II describe the PK and short-term PKPD of high-dose rifam-picin (up to 40 mg/kg). Using a semi-mechanistic modelling approach a sta-tistically significant exposure-response relationship was found between ri-fampicin exposure and bactericidal activity. This finding contrasts the con-ventional analysis of the same trial where no exposure-response relationship could be detected.38 Based on the identified PKPD relationship, the EBA for an even higher, 50 mg/kg dose was predicted which can aid in deciding whether to study 50 mg/kg. The model-based approach used here which allowed an otherwise undetected exposure-response relationship and clinical trial simulations of an unexplored dose exemplifies how pharmacometrics can be used to make decision-making more efficient. Paper IV also de-scribed the clinical rifampicin exposure-response relationship but for long-term high-dose rifampicin data (up to 35 mg/kg) and was based on culture conversion data. The model developed in Paper I was used to describe the PK in the PKPD link in Paper IV. A statistically significant exposure-

62

response relationship of high-dose rifampicin was identified. The conven-tional statistical analysis for the data used for Paper IV detected a statistical-ly significant improvement in culture conversion for high-dose rifampicin.42 However, the conventional analysis did not include any link between PK and PD and therefore the original analysis cannot be used for making clinical trial simulations which is valuable for decision-making. The gained knowledge of the rifampicin exposure-response from Papers I, II and IV can contribute to an optimised rifampicin dose to improve treatment of DS-TB patients. Optimising DS-TB treatment can lead to fewer treatment failures (currently ~20% of DS-TB patients get treatment failure under programmatic settings)1 which means that fewer patients are put at unnecessarily high risk of developing MDR-TB.

The model for TTP developed in Paper II was used and expanded to de-scribe the relationship between TTP and MBL in Paper III. The MBL assay is a new biomarker which is quick and contamination-free. It has already been shown that MBL is correlated to TTP with correlation coefficients of -0.525 to -0.8.28 The correlation coefficients, however, do not give relevant information on how MBL and TTP are related. The model-based relationship established in Paper III reveals that the two biomarkers can be described by the existence of two distinct bacterial subpopulations within the sputum model including a rapidly killed TB subpopulation alongside a more tolerant TB subpopulation. The sputum model was linked to a liquid culture growth model where only the rapidly killed population was able to grow and could readily contribute to a short TTP whereas the tolerant subpopulation had no growth but could transfer into a growing state. These new insights increase the understanding of MBL and put it in context of the established TTP bi-omarker. This valuable information can pave the way for a more informed development and implementation of the MBL biomarker. Furthermore, a statistically significant increased bacterial killing by rifampicin 35 vs 10 mg/kg was identified in Paper III which shows that the joint collection of MBL and TTP data used together with the developed model can lead to im-proved regimen selection in Phase II trials.

Papers V and VI demonstrates a novel way of analysing clinical short-term CFU data using the in vitro-derived semi-mechanistic MTP model103 which allows for drug effect evaluations on a defined non-multiplying, per-sister subpopulation. Whilst applying this methodology, statistically signifi-cant exposure-response relationships for killing of persisters were found for rifampicin and clofazimine. This information is valuable at the early stages of developing anti-TB drugs since persisters are the probable cause for pa-tient relapse and thus drugs able to kill persisters are essential to avoid re-lapse. The current way of studying how well a drug prevents relapse is by studying patients for a complete treatment duration including an additional ≥6 months of follow-up.71 With this novel approach it was possible to detect drug effects on persisters based on two-week monotherapy data which can

63

be a valuable approach to decide at an early stage what compounds to bring forward in clinical drug development. Furthermore, using the MTP model for analysing clinical data formed the basis for the design recommendations given in Paper VII. The MTP model had better power than conventional statistical methods for finding drug effects in Phase IIa TB trials. The in-creased power shows that if the MTP model is used to design and analyse Phase IIa trials the sample size can be reduced and thus, less time has to be spent on patient recruitment. This saves both time and money when develop-ing new drugs against TB and the likelihood of new drugs reaching the pa-tients in time increases.

Paper VIII also gives design recommendations, but for pre-clinical treat-ment outcome assessments in mouse studies with the aim of developing a more informative approach for studying treatment outcome in mice com-pared to a conventional design. The new design included more treatment lengths than the conventional design and when combined with mathematical modelling, a more informative relationship was established between treat-ment length and cure than the conventional design. At the same time, the total number of mice was kept low since fewer mice per studied treatment length were included than for the conventional design.

Paper IX proposed a TDM framework for TB, exemplified for rifampicin. New Bayesian TDM targets were developed based on the PK model devel-oped in Paper I together with information on bacterial killing for different rifampicin doses from Papers II and IV. For the available first-line drugs it is most relevant to perform TDM for rifampicin57 since it has high degree of variability in PK as shown in Paper I. Apart from improving rifampicin treatment for DS-TB patients, the framework can be extended for drugs used to treat MDR-TB patients where TDM may be of even more value than for the general DS-TB patient. A further extension of the approach would be to include biomarker data. But inclusion of biomarker data in dosing decisions for TB is problematic due to the long waiting times for the existing culture-based biomarkers. However, the MBL biomarker studied in Paper III is much quicker (hours) than culture-based methods (days to weeks) and could potentially replace TTP or CFU to allow for more rapid dosing decisions.

In conclusion, this thesis presents the development of pharmacometric models which will streamline the development and use of drugs against TB. A set of pharmacometric tools were developed as applied examples to facili-tate decisions of drugs to bring forward in development, dose selection and what biomarkers to include in a trial. Recommendations were also given for how to best design and analyse pre-clinical and clinical experiments to max-imise information yield whilst keeping the sample size at a minimum. Final-ly, a TDM coupled with Bayesian forecasting approach towards individual-ised TB treatment was proposed and applied to rifampicin but with a frame-work suitable also for other anti-TB drugs including drugs against MDR-TB.

64

Populärvetenskaplig sammanfattning

Årligen världen över smittas 10 miljoner människor av tuberkulos varav de flesta är av så kallat känsligt slag och kan behandlas med en standardkombi-nation bestående av fyra olika läkemedel som ges över en period av sex månader. Behandlingen är effektiv och under kontrollerade former kan 95% botas framgångsrikt. I klinisk vardag är situationen annorlunda där ca 20% av patienterna får behandlingssvikt. Utöver känsliga infektioner förekommer multiresistenta infektioner vilket årligen drabbar en halv miljon människor. Behandling av multiresistent tuberkulos är markant längre (normalt 18 till 24 månader), involverar ännu fler läkemedel (minst fem st) och andelen patien-ter som får behandlingssvikt är betydligt högre (50%) än för en känslig in-fektion. Att endast hälften kan botas visar på att nya läkemedel för att kunna behandla multiresistent tuberkulos mer effektivt är ett akut behov. Dock är det osannolikt att tillräckligt många nya läkemedel når patienterna innan det är försent eftersom den nuvarande utvecklingsprocessen för läkemedel mot tuberkulos är för långsam. Utöver att förbättra behandlingen av resistent tuberkulos finns det värde i att optimera behandlingen av känslig tuberkulos. I klinisk vardag är det trots allt 20% av känsliga patienter som får behan-dlingssvikt och dessa 20% är under stor risk för att utveckla resistens. En bättre behandling av känslig tuberkulos kan alltså minska uppkomsten av resistent tuberkulos. Denna avhandling ger förslag på hur farmakometriska modeller kan användas för att effektivisera utveckling av nya läkemedel mot tuberkulos och optimera behandling av känslig tuberkulos.

Farmakometri är utvecklandet och användandet av matematiska modeller som beskriver läkemedels upptag, fördelning och rening från kroppen, även kallat farmakokinetik, och läkemedlets effekt på kroppen, även kallat farma-kodynamik. Sambandet mellan farmakokinetik och farmakodynamik, det farmakonetiska-farmakodynamiska sambandet, beskriver hur exponering av ett läkemedel (såsom läkemedelskoncentrationen i blodet) ger upphov till en effekt, ofta i form av förändring av en biomarkör. En biomarkör är en mätbar indikator av ett biologiskt tillstånd och inom tuberkulos innebär detta främst bakterieodlingar. Ett väldefinierat farmakokinetiskt-farmakodynamiskt sam-band har en central roll i modern läkemedelsutveckling men är alltför ovan-ligt vid utveckling av läkemedel mot tuberkulos.

Målet med avhandlingen var att utveckla farmakometriska modeller för att optimera läkemedelsutveckling och behandling för läkemedel mot tu-berkulos.

65

Artiklarna I-VI exemplifierar farmakometriska modeller som möjliggör bättre beslutsfattning vid utvecklandet av läkemedel mot tuberkulos. I Artikel I utvecklades en farmakokinetisk modell för rifampicin, ett första-handsmedel vid tuberkulos. Baserat på Artikel I utvecklades en farmakoki-netisk-farmakodynamisk rifampicinmodell för korttidsdata i Artikel II. Mod-ellen bevisade att rifampicindoser högre än den just nu rekommenderade dosen på 600 mg ger betydande ökning av effekten baserat på biomarkören time-to-positivity. Detta visar att högre rifampicindoser kan optimera tu-berkulosbehandlingen, en slutsats som kunde dras tack vare en farmakome-trisk modell. Artikel III var en utökning av Artikel II där förhållandet beskrevs mellan time-to-positivity och en ny biomarkör kallad ‘molecular bacterial load’. Till skillnad från time-to-positivity är den nya biomarkören inte en odlingsbaserad metod och är därför snabbare och okänslig för konta-minering. En modell utvecklades som gav värdefull information om hur dessa två biomarkörer är relaterade. Informationen kan vara till hjälp vid val av biomarkörer inför framtida studier. I Artikel IV utvecklades en modell likt den i Artikel II, fast för långtidsdata. Modellen var baserad på den farmakokinetiska modellen från Artikel I och visade att högre rifampic-indoser gav högre effekt, i enlighet med Artikel II.

I Artiklarna V-VI applicerades en tidigare utvecklad modell från en studie med bakteriekulturer i labbmiljö (in vitro) på kliniska korttidsdata. Modellen heter ‘the Multistate Tuberculosis Pharmacometric model’ och beskriver olika subpopulationer av tuberkulos bestående av snabbt och långsamt växande samt metaboliskt inaktiva subpopulationer. Data fanns tillgängligt för rifampicin och klofazimin (ett andrahandsmedel vid tuberkulos). Läke-medlens avdödande förmåga på dem olika subpopulationerna utvärderades och både rifampicin och klofazimin visade sig ha bakterieavdödande effekter av metaboliskt inaktiva bakterier. Metaboliskt inaktiva bakterier är generellt svårdödade men samtidigt är avdödandet nödvändigt för lyckad behandling. Utan en farmakometrisk modell hade det varit omöjligt att få ut samma in-formation med givna data. Utöver detta demonstrerades det i Artikel VII att med tillvägagångssättet i Artikel V och VI gick det att identifiera statistiskt signifikanta läkemedelseffekter med färre antal patienter jämfört med en konventionell analys. Detta innebär att kliniska studier som designas med denna modell i åtanke leder till studier med färre patienter vilket betyder snabbare och billigare läkemedelsutveckling.

I Artikel VIII föreslogs en ny metod för långtidsstudier i möss. Konven-tionellt studeras få behandlingslängder med många möss per behandlings-längd medans i Artikel VIII innehöll designen många behandlingslängder med få möss per behandlingslängd. Den nya designen kombinerat med en farmakometrisk analys gav mer information om sambandet mellan behan-dlingens längd och utfall än en konventionell design.

Artikel IX föreslår en modellbaserad metod för individuell dosanpassning för rifampicin utefter uppmätta läkemedelskoncentrationer. Baserat på mod-

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ellerna från Artiklarna I, II och IV togs ett komplett doseringsverktyg fram som tillåter specifika dosprediktioner redan från dag ett baserat på nya målvärden som är i linje med den senaste datan om rifampicin.

Sammanfattningsvis presenterar den här avhandlingen farmakometriska modeller som bidrar till effektivare läkemedelsutveckling och behandling för läkemedel mot tuberkulos. Effektivare läkemedelsutveckling betyder att fler nya läkemedel kan nå patienterna i tid. Optimerad behandling för patienter med känsliga infektioner leder på sikt till minskad risk för att patienter ut-vecklar resistenta infektioner.

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Acknowledgements

The research presented in this thesis was conducted at the Department of Pharmaceutical Biosciences at Uppsala University. The work was funded through the Swedish Research Council (grant number 521-2011-3442) and the Innovative Medicines Initiative Joint Undertaking (grant agreement number 115337) for the PreDiCT-TB consortium, resources of which are composed of financial contributions from the European Union’s Seventh Framework Programme (FP7/2007-2013) and EFPIA companies’ in kind contribution. Generous travel grants from Anna-Maria Lundin’s Fund at Smålands Nation and Apotekarsocieteten allowed me to attend valuable courses and present results at international conferences. I am grateful to the Swedish Foundation for International Cooperation in Research and Higher Education (STINT, grant number SA2015-6259) jointly with the South African National Research Foundation (NRF, grant number 101575) which facilitated an exchange to University of Cape Town, South Africa for knowledge sharing.

A very important part of this thesis was the use of clinical data. I would like to express gratitude towards the patients and local staff that made it possible to generate the results of this thesis.

There is a long list of people that contributed directly or indirectly to this work. I would especially like to thank the following people:

My main supervisor Ulrika for giving me the opportunity by taking me on as your student. I have learned so much from you about several parts of pharmacometrics both inside and outside the NONMEM control stream. You really made me enjoy this journey with your endless support, especially when I needed that extra boost!

My co-supervisor Mats. It has been an honour to be a part of your research group. I am so thankful for the knowledge and advice you have shared dur-ing my studies. You are a true inspiration!

I am thankful to all my co-authors. From University of St Andrews I’d like to thank Stephen (for sharing your knowledge of TB and for hosting us sev-eral times in St Andrews) and Wilber. Thank you to all PanACEA collabo-

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rators, especially: Rob, for hosting the best TB workshop in the world and for helping us understand the PK of high-dose rifampicin. Martin, for in-creasing the dose of rifampicin . Andreas and Rodney for the very good data. Additional thanks to Jurriaan and Bas from Erasmus MC and my Swedish collaborators Thomas, Erik, Judith, Lina, Katarina and Jakob.

Thank you to Paolo for all the nice encounters with you on conferences around the world and for allowing me to visit your lab at Division of Clinical Pharmacology at University of Cape Town.

I would like to thank all colleagues during my time at Pharmetheus, espe-cially Marie for giving me the opportunity to work at Pharmetheus and Jakob for everything you taught me.

I am thankful to all colleagues in the PM research group and the tPKPD research group at Uppsala University. You all made our BMC corridor an excellent work place. Extra big thanks to the following people:

Past and present TB group members for all the nice trips and for always be-ing supportive: Oskar (my no 1 travelling partner, cheers!), Chunli, Elin (probably the best Svensson-Svensson high-dose rifampicin collaboration in the world?), Sebastian, Lénaïg, Alan, Rami, Budi and Lina.

Margareta, Lena, Andy, Mia, Elisabet, Elodie, Joakim, Sebastian and Irena for creating a healthy research environment and for being role models and big sources of inspiration!

I am very grateful to Siv, my master student project supervisor, for always being so happy and kind and for teaching me pharmacometrics. Also thanks to Emma and Jacob who also supervised me when I was a master student.

All post docs of the group, past and present. Especially Yasunori, Elke, Thomas (for our conversations about and drinking of home brewed beer), Chayan, Eva, Xiaomei, Tomás, Iris, Carolina, Jill, Philipe, Margreke and Rory (for inventing inne-Brandy).

All amazing PhD students that I have gotten to know at our department: Erik, for all football memories both in Solna and sports bars and for all in-teresting conversations in general. Anders T, for raising the bar of awkward conversations and for being a nice travelling partner (and that you talked me out of buying the “hand grenade” drink in New Orleans). Henrik, you are my bucket list! Siti, for being a very kind and extremely tidy office mate. João, for all the support during difficult times and memories shared as my office mate and for that special night club experience in Zürich. Gustaf, for

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being a good travel mate and actor, and for lending me your club blazer. Gunnar, for always being helpful and good mediator for entertaining dis-cussions during fika and lunch. Benjamin, for all rif discussions. Anders K, for always being helpful and brewing very good beer. Ari, for just being a rad and awesome person. Also big thanks goes to Emilie, Anne-Gaëlle, Ana, Steve, Marina, Camille, Brendan, Ida, Viktor, Nebojsa, Maria, Yang, Sreenath, Estelle, Moustafa, Salim, Shijun and Chenyan!

Kajsa, Rikard and Svetlana for all work and support with PsN and system development, I can’t imagine what we would do without you!

Thank you to all teachers in pharmacokinetics and pharmacotherapy, especially Jörgen, for supporting my teaching and being a role model as a teacher and of course for introducing me to the gym.

All administrative and IT staff at our department, especially: Marina, Ka-rin, Agneta, Ulrica, Magnus, Jerker and Tobias.

Tack till alla vänner jag träffade under studietiden som gjorde Apotekarpro-grammet oförglömligt! Speciellt tack till Emil och Jesper för att ni är un-derbara energiknippen till vänner som alltid ställer upp och för att ni hjälper till med festen. Tack till Tim, Patrik, Nick (“Mr Two-ways”), Oscar, Lasse (“1080p-mannen”) och Gunnar! Dessutom SIK-gänget Oliver, Leo, Sascha, Jakob (“Ox in the box”), Pettsson och Victor… SKÅL! Tack till Sebastian och alla underbara resor till Cambridge (enda klagomålet är half pints)!

Mina barndomsvänner Mikael och Robin, ser er alltför sällan men ni är fortfarande några av mina bästa vänner och det är alltid lika roligt att ses!

Största möjliga tack till mina föräldrar Carina och Per-Inge, ni har varit ett fantastiskt stöd längs hela denna resa. Ni är alltid så hjälpsamma med allting och alltid lika kul när ni kommer och hälsar på! Tack till min bror Linus, du valde att bo i studentstad nummer 2 så vi ses inte lika ofta som jag önskar. Vi får se till att ändra på det i framtiden!

Sist men inte minst vill jag tacka Emmi för allt stöd du bidragit med på den här resan. Du är en fantastisk person och finns alltid där och ger mig styrka när jag är nere. Jag älskar dig!

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Acta Universitatis UpsaliensisDigital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Pharmacy 267

Editor: The Dean of the Faculty of Pharmacy

A doctoral dissertation from the Faculty of Pharmacy, UppsalaUniversity, is usually a summary of a number of papers. A fewcopies of the complete dissertation are kept at major Swedishresearch libraries, while the summary alone is distributedinternationally through the series Digital ComprehensiveSummaries of Uppsala Dissertations from the Faculty ofPharmacy. (Prior to January, 2005, the series was publishedunder the title “Comprehensive Summaries of UppsalaDissertations from the Faculty of Pharmacy”.)

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