## ABSTRACT

Pretomanid is a nitroimidazole antibiotic in late-phase clinical testing as a component of several novel antituberculosis (anti-TB) regimens. A population pharmacokinetic model for pretomanid was constructed using a Bayesian analysis of data from two phase 2 studies, PA-824-CL-007 and PA-824-CL-010, conducted with adult (median age, 27 years) patients in Cape Town, South Africa, with newly diagnosed pulmonary TB. Combined, these studies included 63 males and 59 females administered once-daily oral pretomanid doses of 50, 100, 150, 200, 600, 1,000, or 1,200 mg for 14 days. The observed pretomanid plasma concentration-time profiles for all tested doses were described by a one-compartment model with first-order absorption and elimination and a sigmoidal bioavailability dependent on dose, time, and the predose fed state. Allometric scaling with body weight (normalized to 70 kg) was used for volume of distribution and clearance, with the scaling exponents equal to 1 and 3/4, respectively. The posterior population geometric means for the clearance and volume of distribution allometric constants were 4.8 ± 0.2 liters/h and 130 ± 5 liters, respectively, and the posterior population geometric mean for the half-maximum-effect dose for the reduction of bioavailability was 450 ± 50 mg. Interindividual variability, described by the percent coefficient of variation, was 32% ± 3% for clearance, 17% ± 4% for the volume of distribution, and 74% ± 9% for the half-maximum-effect dose. This model provides a dose-exposure relationship for pretomanid in adult TB patients with potential applications to dose selection in individuals and to further clinical testing of novel pretomanid-containing anti-TB regimens.

## INTRODUCTION

Pretomanid (PA-824) is a nitroimidazole antibiotic discovered by optimization of a bicyclic nitroimidazofuran radiosensitizer and introduced by Stover et al. (1) as a novel small-molecule candidate for the treatment of tuberculosis (TB). Pretomanid is a prodrug, bioactivated by Mycobacterium tuberculosis deazaflavin-dependent nitroreductase (Ddn), with activity against replicating and nonreplicating hypoxia-adapted bacilli (1, 2). With the exception of delamanid (3), also an anti-TB nitroimidazole, there is no indication of cross-resistance between pretomanid and other currently employed anti-TB drugs (1, 4). The activity of pretomanid was described as time dependent in a mouse model of TB (5), consistent with the dose-response relation observed in phase 2 early-bactericidal-activity (EBA) studies (6, 7). Currently, pretomanid is in phase 3 clinical testing as a component of several novel anti-TB regimens at a once-daily oral dose of 100 or 200 mg (8).

The requirement of combination chemotherapy for active TB (9) and a recent emphasis on an entire regimen as the unit of development (10) open the possibility of further dose optimization for each component drug to improve the safety and efficacy of the regimen as a whole. However, the ability to identify such optimized dosage regimens through clinical evaluation alone is limited by the large number of dose combinations that would require testing. This increases the importance of pharmacometric methods (11) that may better direct investigative resources to those regimens that most closely meet the therapeutic objectives. A fundamental task in such an approach is to establish a quantitative relationship between the administered dose, the drug concentrations in plasma or serum as a surrogate for those at target sites throughout the body, and the therapeutic and toxic responses. Such dose-exposure-response relationships are commonly determined in parts, as dose-exposure or pharmacokinetic (PK) and exposure-response or pharmacodynamic (PD), that can then be linked (12). While always a simplified and approximate description of complex physiological and biochemical processes, predictive mathematical models of PK/PD relationships provide for the simulation and analysis of new study designs prior to their implementation in each successive stage of development. These considerations motivate here the construction of a PK model for pretomanid as a quantitative tool to facilitate further clinical testing of this drug.

Clinical data for pretomanid that could support PK model development have been described in published phase 1 studies that evaluated (i) the safety, tolerability, and PK of pretomanid with escalating doses (13), (ii) the effects of pretomanid on renal function (14), (iii) the effect of food on pretomanid bioavailability, PK, and safety (15), and (iv) drug-drug interactions of pretomanid with efavirenz, ritonavir-boosted lopinavir, or rifampin (16) and pretomanid with midazolam (17). Additional PK data have been collected in phase 2 EBA studies with pulmonary TB patients for pretomanid as a single drug (6, 7) and in various combinations with bedaquiline, pyrazinamide, and clofazimine (18). While several of these studies included intensive sampling of plasma drug concentrations, the types of quantitative PK analyses of those measurements were limited to noncompartmental analysis (NCA) and graphical summaries of concentration-time profiles.

In the present study, a population PK model of pretomanid in TB patients was developed using mass-balance compartmental methods (19) and Bayesian hierarchical modeling (20). The completed analyses of pretomanid phase 1 data reported by Ginsberg et al. (13, 14), Winter et al. (15), and Dooley et al. (16) were used to construct the model equations and to inform prior probability distributions for the unmeasured model parameters. The prior distributions were updated, using Bayes' rule, to a posterior distribution conditioned on pretomanid plasma concentration-time measurements from adult patients with newly diagnosed pulmonary TB in two single-drug phase 2 studies, PA-824-CL-007 (CL-007) (6) and PA-824-CL-010 (CL-010) (7), conducted in Cape Town, South Africa. The two studies included 63 males and 59 females (median age, 27 years; age range, 18 to 56 years) administered once-daily oral pretomanid at doses of 50, 100, 150, 200, 600, 1,000, or 1,200 mg for 14 days with PK sampling throughout. The model equations and individual patient data were organized in a statistical model with population- and individual-level parameters, and the posterior distribution was sampled using Markov chain Monte Carlo (MCMC) simulation (21). Model simulations using the posterior distribution were conducted to assess the model fit and to estimate the probability of attaining effective pretomanid concentrations in TB patients with the dosages under current clinical testing.

## RESULTS

Structural model.The structural model equations were developed to account for the PK features that were most evident in the shapes and numerical patterns of the graphical summaries and tabulated NCA parameters reported in published phase 1 studies (Table 1) of orally administered pretomanid in healthy adults. These features consisted of (i) moderately rapid absorption and monoexponential elimination profiles, including values for time to peak (maximum) concentration (*T*_{max}) and elimination half-life (*t*_{1/2}), that were approximately conserved across doses, for the fasted or fed state, and for single or multiple dosing (13–16) and (ii) a dose-dependent plateau of peak and cumulative plasma drug concentrations observed in fasted subjects in the single-dose studies and on day 1 in the multiple-dose studies (13–15). This plateau was not apparent with a high-fat high-calorie meal prior to dosing, which resulted instead in an approximate dose-proportional exposure (15). A trend toward dose-proportional exposure with increasing time was also apparent with multiple daily doses (13, 14).

The PK features identified in the phase 1 study results were summarized as structural elements, without specification of the values for the model parameters, in a minimal set of mass-balance ordinary differential equations. The equations described a central compartment drug concentration (*C*) and an absorption compartment drug mass (*q*) as functions of time (*t*) that satisfied the following:
*q*(*t*=0) = 0 and *C*(*t*=0) = 0, where *t* ≥ 0 is the time since start of treatment. Each dosage regimen was specified by the number (*N _{D}*) of oral doses (

*D*) administered at times

*t*,

_{n}*n*= 1, . . . ,

*N*, with pulsed input to the absorption compartment described by the Dirac delta function, δ(

_{D}*t*−

*t*

_{n}). Drug absorption was described as a first-order process with an oral absorption rate constant

*k*. The volume of distribution (

_{a}*V*) and clearance (CL) were allometrically scaled as

*V*=

*V*⋅ BW and CL = CL

_{C}_{C}⋅ BW

^{0.75}, where

*V*and CL

_{C}_{C}are allometric constants and where the scaled body weight (BW) = [total body weight (kg)]/[standard body weight (kg)], with standard body weight = 70 kg (22). An inhibitory sigmoidal function with multiplicative terms that modulated the magnitude of the dose-dependent effect was used to describe a saturable bioavailability that decreased with increasing dose and increased with increasing time and predose fed state. In addition to the maximum bioavailability (

*F*

_{max}), the time, dose, and fed-state dependencies of the bioavailability were characterized by a time constant (

*τ*), an oral dose at half-maximum effect (ED

_{F}_{50}), and a fed-state coefficient (β

_{F}). The model parameters are summarized in Table 2.

Prior distributions.The pretomanid phase 1 study data used to develop the structural model equations were also used to inform prior probability distributions for the statistical model parameters. For a maximal fed state, the structural model equations reduced to a standard one-compartment model, and point values for the absorption, volume, and clearance parameters were set from the fed-state NCA parameter values reported by Winter et al. (15). The NCA results reported in the dose-escalation study of Ginsberg et al. (14) showed a clear pattern of saturable exposure from which an estimate of the bioavailability oral dose at half-maximum effect was determined by inspection. However, the multidose results (13, 14) were considered informative only for a lower bound on the bioavailability time constant. The resulting values for ED_{50}, τ_{F}, *k _{a}*,

*V*, and CL

_{C}_{C}were used to specify the geometric means (GMs) of the lognormal distributions for the population GM of each PK model parameter. The uncertainties in these central values were specified by geometric standard deviations (GSDs) based on interstudy differences between the values of the corresponding NCA parameters. The distributions for population variances accounting for interindividual variability were specified with half-normal distributions informed by the variances of the NCA parameter values for each tested dose group in the work of Ginsberg et al. (13, 14). These prior distributions for the population GM and variance of each PK model parameter are given in Table 3. A prior for the population residual error (

*e*

^{σ}) was assigned a log-uniform distribution (LU), e

^{σ}~ LU(1.05, 10), with a lower bound corresponding to the bioanalytic assay precision of 5% coefficient of variation (CV) (13).

CL-007 and CL-010 patient data.As the physical characteristics and vital signs of the patients from CL-007 and CL-010 on day 1 were statistically similar (Table 4), the PK data from both studies were combined into a single data set with 122 patients in the pretomanid-containing dose groups (61 in CL-007 and 61 in CL-010). Individual data records were constructed for each patient and consisted of the dose and schedule of administration, the daily total body weight, the serially measured pretomanid concentrations in plasma, and the corresponding sampling time points for those concentrations throughout the 14 days of testing. There were a total of 5,185 plasma concentration-time measurements, including 111 missing values, 104 of which were from five early-withdrawal patients. There were 133 below-the-level-of-quantitation (BLQ) measurements (<10.0 ng/ml), with 118 of these occurring pretreatment (predose on study day 1). Three patients from CL-010 and one from CL-007 had pretreatment plasma concentrations that ranged from 3 to 100 times the lower limit of quantitation (LLOQ) and were excluded from further analysis. The 15 posttreatment BLQ values occurred in 11 patients, with only 1 corresponding to a trough concentration. There were 1,708 daily body weight measurements, including 35 missing values from eight individuals; all but 3 of these missing values corresponded to missing drug concentration measurements. The latter three missing body weights were one each from separate individuals on the last day (day 14) of testing and were imputed with the last observation carried forward. The characteristics of the 118 patients that were included in the statistical model for parameter estimation are summarized in Table 5. The final numbers of patients and the numbers of plasma drug concentration, BLQ, and missing concentration measurements for each dose group are summarized in Table 6.

Posterior distribution.The unmeasured population- and individual-level PK model parameters were estimated as a joint posterior probability distribution conditioned on the individual patient data from CL-007 and CL-010 as the product of the likelihood and prior distributions. As all tested doses were orally administered when each patient was in a fasted state, the maximum bioavailability (*F*_{max}) was set equal to 1 as a relative value, and the fed-state coefficient (β_{F}) was set to zero for a minimum food effect on bioavailability. The posterior distribution was obtained from 10 independent MCMC simulations, each consisting of 70,000 iterations, with the retention of every 20th iteration of the last 20,000. The retained 1,000 samples from each of the 10 chains were concatenated to form a final 10,000 samples from the posterior distribution. Adequate convergence of the sampling chains was found, with the Gelman-Rubin diagnostic (*R̂*) < 1.05 for all sampled parameters, leaving an approximately 5% maximum further scale reduction with additional sampling. The precision for posterior inferences was determined as an effective sample size (*n*_{eff}) > 400 for all sampled parameters, corresponding to a standard error of the posterior means of less than 5% of the corresponding posterior SDs. Summaries of the marginal distributions for the population parameters are shown in Fig. 1 and Table 7, where ^{2} is the population variance. The experimental data were sufficiently informative to modify the prior distributions, with the population mean distributions being shifted from their prior central values and with reduced SDs indicating decreased uncertainty in those values. The posterior population distributions remained unimodal and within the prior truncation bounds, and the corresponding trace plots shown in Fig. 2 indicated stable and uniform mixing within well-defined ranges. *e*^{σ} was sharply peaked with a mean equal to 1.37 (SD, 0.14), corresponding to a CV of approximately 32%, consistent with the magnitude of residual errors in the likelihood for BLQ measurements discussed by Beal (23).

The marginal distributions for the PK model parameters for each individual patient were summarized with an arithmetic mean and SD and are shown plotted with their corresponding dose group in Fig. 3. The individual mean values for ED_{50} and τ_{F} tended to shrink toward the total mean with decreasing dose, with a loss of identifiability occurring below the 150-mg dose group. The absorption rate constant showed high interindividual variability throughout the range of tested doses, while the interindividual variability for clearance was higher at the lower doses and showed a small downward trend in the mean values with increasing dose, and the volume of distribution exhibited little interindividual variability and was nearly constant across the dose groups. The distributions of the mean values for these individual parameter sets are summarized in Table 8, which includes a comparison between males and females. These results show a statistically significant (*P* < 0.05) difference in the volume of distribution between males and females and a lesser but still significant difference in clearance between males and females. Correlations between PK model parameters were calculated as the average of the correlations across the 118 individual patients for each of the 10,000 joint posterior samples. The results shown in Table 9, with a maximum absolute value of less than 0.3, show no significant induced correlations with conditioning on the data, consistent with the prior assumption of independence between the population PK model parameters.

Model simulations.Monte Carlo (MC) simulations of pretomanid plasma concentration-time profiles in a randomly generated patient population for each dose group on treatment days 1 and 14, together with the corresponding observed values, are shown in Fig. 4. Descriptive statistics for peak, trough, and cumulative exposure parameters for these plots are given in Tables 10 and 11. The best agreement between observed and predicted percentiles is seen for the 50-mg to 600-mg dose groups, with a definite underprediction of the central tendency being seen in the 1,000-mg and 1,200-mg dose groups. Values obtained from simulations of concentration-time profiles performed using individual marginal posterior mean values for the PK model parameters were compared to the corresponding observed patient data, with examples being shown in Fig. 5 for the first five individuals from each of the CL-010 100-, 150-, and 200-mg dose groups and in Fig. 6 for the 15 complete profiles from the CL-007 1,000-mg dose group. The large interindividual variability of the concentration-time profiles is evident in the 1,000-mg dose group illustrated in Fig. 6. With the exception of the day 1 concentration for a single patient in the 1,000-mg dose group, model simulations of these individual profiles accurately describe the differing peak-trough ranges and patterns of drug accumulation.

Additional comparisons between the observed pretomanid plasma concentrations and the corresponding model-predicted values for each individual patient and for the mean for the population-predicted distributions from the MC simulations are given in the goodness-of-fit plots in Fig. 7. The scatter plots of observed versus predicted values show a bias toward underprediction at higher concentrations for the population mean predictions but a reasonably good fit for the individual predicted values, with a symmetric and uniform pattern about the line of perfect fit. The weighted residual plots show that the bias in the population mean predicted values is primarily in the high concentrations but similar to the individual residuals over time. For both the individual and population residuals, 98% of the points fall within weighted residual values of ±3, indicating a reasonably good fit (11).

Probabilities for standard PK/PD indices to attain a range of values were calculated using MC simulations of an effective concentration (*C*_{eff}) = *f _{u} C/*MIC, for the currently employed 100- and 200-mg/day dosages, where

*f*is a distribution for the unbound drug fraction, MIC is the distribution of MICs, and

_{u}*C*is the model-predicted distribution of pretomanid concentrations, including a distribution of fed states (β

_{F}) to account for a possible food effect on bioavailability. The percentage of the time that the free drug concentration remained above the MIC (%

*fT*

_{>MIC}), the free drug 24-h cumulative concentration (the free drug 24-h area under the concentration-time curve [

*f*AUC

_{24}]) divided by the MIC (

*f*AUC

_{24}/MIC), and the free drug peak (maximum) concentration (

*C*

_{max}) divided by the MIC (

*fC*

_{max}/MIC) were calculated for each of 10,000 simulated

*C*

_{eff}profiles for day 14 of dosing. The probabilities that each PK/PD index would have a value greater than or equal to various specified values were calculated from their corresponding MC distributions as the complementary cumulative distribution functions shown in Fig. 8.

## DISCUSSION

The late-phase clinical development of pretomanid is regimen based (10), with promising anti-TB drug combinations including pretomanid with bedaquiline and linezolid (24) and pretomanid with bedaquiline, moxifloxacin, and pyrazinamide (25). While these novel regimens provide shorter, simpler, and possibly more effective treatments than those currently available for patients with multidrug-resistant TB (MDR-TB) and extensively drug-resistant TB (XDR-TB) (26, 27), they require careful monitoring for serious adverse events, especially for linezolid, which often requires dose adjustment or interruption (28). Together with existing population PK models for bedaquiline (29, 30), linezolid (31, 32), moxifloxacin (33, 34), and pyrazinamide (35, 36) that were developed with TB patient data, the PK model for pretomanid developed here provides a starting point for a mathematical model-based approach to optimizing regimens containing these drugs.

The development of the PK model equations and the specification of prior distributions for the model parameters were conducted as an exploratory data analysis (EDA) (37) of an extensive set of statistical and graphical data from the combined results of several phase 1 studies (13–16). The model equations were a summary of the most evident structural features of drug absorption, distribution, and elimination that could be considered common to all individuals in the phase 1 study populations, and the prior parameter distributions were informed by the descriptive statistics of the corresponding NCA parameters. The approach, in this case, provided an *a priori* incorporation of phase 1 study results with multiple experimental conditions into the phase 2 study modeling. With the further aim of parameter estimation using phase 2 study data, there was an implicit assumption that those structural features identified in healthy adults would also be present in TB patients.

Pretomanid PK profiles were described by one-compartment kinetics with first-order absorption and elimination and with a saturable bioavailability described with a sigmoidal function of dose, time, and predose fed state. The observed dose-dependent plateau of pretomanid plasma exposure was explained in terms of bioavailability by Winter et al. (15), with the saturability of absorption being related to drug solubility or tablet dissolution, or both. A similar dose-dependent absorption plateau observed with rifapentine was modeled using a linear function with parameters for relative bioavailability and slope (38). While the use of a sigmoidal function to characterize the plateau was noted, the available data in that study did not support parameter estimation beyond the linear case. For pretomanid, the phase 1 study data (13, 14) provided a clear pattern of saturability and enough detail to specify an informative prior value for a half-maximum effect in the sigmoidal function used here. The tendency toward dose-proportional exposure with multiple dosing was described with a time-dependent exponential decay term, similar to the exponential decay with an estimated time constant used in a model of autoinduction for rifampin (39). For pretomanid, no additional data or discussion, beyond noting the presence of this time-dependent exposure, was provided in the phase 1 study reports (13, 14), and further study may be required to determine a mechanistic explanation. An example of increasing bioavailability with multiple dosing that may or may not be relevant to pretomanid is seen with the benzimidazole proton pump inhibitor omeprazole, with explanations including a time-dependent decrease in first-pass elimination and decreased drug degradation with increasing stomach pH (40, 41). For pretomanid, drug stability measurements could inform the latter, while a time-dependent inhibitor for clearance, not included in the model presented here, could be used to investigate the former. The exponential factor for the food effect was included as a continuous parameter, with the coefficient range corresponding to minimal or near maximal food effects. The food effect coefficient could be used as a categorical variable with minimum (zero) and maximum (>6) values corresponding to the fasted state and a high-fat high-calorie meal fed state, respectively, or as a continuous value that could be estimated from data from individuals and subpopulations with variable fed state conditions. These equations were considered here as a minimal model, or first-order approximation, of pretomanid PK with the understanding that additional structure, such as absorption delays and peripheral compartments, may be more or less evident in individual profiles. Structural elements that could be included for additional detail include transit compartments (42) for a more flexible description of absorption profiles, Michaelis-Menten kinetics for clearance to better describe enzymatic elimination (19), and fat-free mass (FFM) (43) instead of body weight to account for male and female differences in body composition.

The Bayesian analysis including the hierarchical statistical model with prior lognormal and half-normal distributions is standard for the type of structural model and data used in this study (11, 44, 45). Central tendencies for the prior distributions were based on relationships between mean values for the NCA parameters and compartmental PK model parameters often used to identify starting values in conventional likelihood-based parameter estimation (19), and dispersions were based directly on the variances of the observed exposure parameters. While these prior distributions were considered informative, their purpose was only temporary and they were updated in the calculation of the posterior distribution conditioned on individual patient data from the combined CL-007 and CL-010 phase 2 studies (6, 7). The large range of tested doses and the resulting rich set of pretomanid concentration-time measurements from these two studies, summarized in Table 6, arose from the first of these studies, CL-007, showing a flat dose-response and suspected time-dependent activity (6), which then led to the subsequent CL-010 study with lower doses (7). The two studies were similarly designed and had statistically similar patient populations, as shown in Table 4. There were a small number of missing concentration measurements, less than 3% of the total, which were treated without imputation and were ignored in all calculations. While the BLQ measurements were also relatively few, making up less than 3% of the total, and while it is often acceptable in such a case to set these values to constants, such as zero or one-half the lower level of quantitation (LLOQ/2), the choice in this study was to include the measurement and model uncertainty uniformly for all BLQ measurements in terms of their likelihood (23), including the pretreatment measurements corresponding to the initial conditions.

The posterior population distributions were generally within the range of the prior distributions, but with reduced uncertainties from the additional information in the phase 2 study data. This suggests that possible differences in the volume of distribution and clearance between healthy adults and TB patients are primarily due to differences in body weight, as it is the corresponding allometric constants that are similar between these two subpopulations. The GM for ED_{50} is more than twice the current maximum 200-mg/day dosing, indicating a relatively small effect on bioavailability for the current dosing. Also, considering a time to steady state of approximately four half-lives, the 1,200-h bioavailability time constant implies a slowly increasing bioavailability over a 20-week duration for a fasted patient. The CVs in Table 7 accounted for interindividual variability and were the highest for the absorption parameters at approximately 66% for the absorption rate constant, 74% for the half-maximum effective dose, and 78% for the bioavailability time constant, while the variability for clearance was approximately 32% and that for the volume of distribution was 17%. This range of variability for the PK model parameters is consistent with the complexity and response time scales of the associated processes, with absorption depending on highly variable molecular and physiological processes, and volume of distribution depending primarily on a more stable tissue composition. At the individual level, the parameter values associated with male and female patients in Tables 8 and 5 showed a larger volume of distribution and a lower clearance for females than males, consistent with the observation of larger values for the area under the concentration-time curve (AUC) and *t*_{1/2} in females than males noted by Diacon et al. (7) and in the phase 1 study of Ginsberg et al. (14). The allometric scaling of CL and *V* separates body weight from factors that might account for these differences, such as body tissue composition and drug metabolism. Here, the larger *V _{C}* for females than males is consistent with the high lipophilicity of pretomanid (octanol/water partition coefficient [logP], equal to 2.75 [46]), resulting in a greater distribution into tissues with a generally higher fat content in females than males (47). The difference in the values for CL

_{C}between males and females is only slightly statistically significant and is consistent with a higher basal metabolic rate in males than females (47).

The aim of the PK model was to establish an accurate quantitative relationship between an administered oral dose of pretomanid and the resulting plasma concentration as a function of time, both for an individual and for the central tendency and variability of a subpopulation in a specified dose group. For an individual, the model was able to describe the range of concentration-time profiles with individual parameter sets that may vary considerably from patient to patient, illustrated by Fig. 3, 5, and 6. The simulated exposure for dose group subpopulations with MC sampling from parameter distributions that were determined from the entire set of data spanning 50-mg/day to 1,200-mg/day dosing is reasonably accurate for both the central tendency and variability for the range of 50 to 600 mg/day, indicated by the comparison of observed and predicted percentiles shown in Fig. 4 and the descriptive statistics presented in Tables 10 and 11. The tendency toward underprediction of central tendencies in the population simulations for doses above 600 mg is consistent with saturable clearance at very high doses, which was not included in the structural model but which is seen with a decreasing trend in the values for individual clearance parameters with increasing dose shown in Fig. 3. However, the current phase 3 testing of 100 mg/day and 200 mg/day dosages, which were determined empirically through extensive phase 2 testing, is well within the range of accuracy of the model and parameter distributions determined here. While the food effect coefficient was not included for parameter estimation, as the CL-007 and CL-010 patients were fasted, and while the bioavailability time constant has a relatively small effect over the 2-week duration of these phase 2 studies, the effects of both of these constants are expected to be larger in phase 3 studies as a result of the variable fed states and longer treatment durations in those studies (24, 25).

The MC simulations of effective concentrations and the resulting probabilities for attaining specified values for the standard PK/PD indices shown in Fig. 8 can be compared to the efficacy breakpoints established in a dose fractionation study with mice performed by Ahmad et al. (5). The day 14 probabilities of attaining a %*fT*_{>MIC} of 48%, associated with bactericidal activity in mice, were approximately 0.48 for 100 mg/day and 0.72 for 200 mg/day. These probabilities show a significant difference between the 100- and 200-mg/day dosages and indicate an importance to avoiding monotherapy at target sites for pretomanid-containing regimens, as 30% of patients may have exposures that are less than bactericidal at the 200-mg/day dosage. The results of the study with mice also indicated that the greatest reduction in the number of log_{10} CFU was associated with free drug area under the concentration-time curve from 0 to 24 h (*f*AUC_{0–24})/MIC values greater than 167, which were attained with probabilities of 0.66 for 100 mg/day and 0.85 for 200 mg/day. While *fC*_{max}/MIC values were not indicated to be correlates of efficacy, the probabilities of attaining an *fC*_{max}/MIC > 1 were 0.56 for 100 mg/day and 0.79 for 200 mg/day, intermediate between the latter two indices, *f*AUC/MIC and %*fT*_{>MIC}. As there are considerable differences in the pathology of TB between mice and humans (48, 49), the expression for an effective drug concentration may be improved by including some measure of human target site exposure (50) and MIC with, for example, a target site/plasma partition coefficient (*P _{T/P}*) and MICs for bacteria at the target site (MIC

_{T}), with

*C*

_{eff}

*=*(

*f*)/MIC

_{u}C P_{T/P}_{T}, where the target sites may include multiple different regions of a TB lesion.

The model-predicted pretomanid plasma exposures, together with an accounting for variable predose fed states, reported protein binding measurements (14, 46, 51), and a wide range of MIC values from drug-susceptible and drug-resistant clinical samples (1, 4), support 200-mg/day dosing to be significantly more effective than 100-mg/day dosing. However, this result should be interpreted with caution, as the breakpoints on which this conclusion is based were determined in mice (5) and the dependence of the effective exposures on protein binding and MICs remain to be validated by comparison with human efficacy data, which was not performed in this study. Such a comparison would provide a measure of mouse-to-human translation for pretomanid PK/PD parameters. Applications of this model to further clinical development of pretomanid could include (i) linking of the PK model to the individual observed bacterial load and the frequencies of adverse events (6, 7) to establish a pretomanid population PK/PD model for therapeutic and toxic responses and (ii) incorporation of drug-drug interaction terms in the PK model to quantify the effects on pretomanid exposure of the other pretomanid-containing regimen components currently in phase 3 testing (24, 25).

## MATERIALS AND METHODS

Structural model.The structural model equations describing the time course of orally administered pretomanid in plasma were informed by results presented in the phase 1 studies listed in Table 1. These studies included intensive PK sampling and analysis of pretomanid concentrations in plasma following administration of single or multiple oral doses ranging from 50 to 1,500 mg to approximately 200 healthy adult males and females and included predose fed or fasted conditions. For each tested dose, the NCA results included tabulated summary statistics of the peak (maximum) concentration (*C*_{max}), the time to the peak (maximum) concentration (*T*_{max}), the elimination half-life (*t*_{1/2}), and the area under the concentration-time curve (AUC) from time zero to a specified time point *t* (AUC_{0–t}) or the AUC from time zero extrapolated to infinity (AUC_{0–∞}). The line charts consisted of the mean or median concentration-time profiles for each sampling time point over the study duration. While pretomanid has been described to be extensively metabolized (16), the kinetic data in these studies were limited to the parent drug. The PK model equations were constructed as a minimal set of compartmental PK mass-balance differential equations (19) that summarized the general characteristics of pretomanid exposure across all of the tested experimental conditions. Standard allometric scaling was included for volume and clearance parameters on the basis of general physiological considerations (52).

Statistical model.The unmeasured PK model parameters were estimated using Bayesian analysis of individual patient data in a hierarchical statistical model, with individual and population levels (44, 53–55) specified as follows:
*y _{ij}* denotes the

*j*th observation of the drug concentration for the

*i*th individual at time

*t*,

_{ij}*D*is the administered dose, ϕ

_{i}_{ij}is a vector of measured covariates, and θ

_{i}is a vector of unmeasured PK model parameters, where

*i*= 1, …,

*I*and

*j*= 1, …,

*J*, with

*I*being the number of individuals and

*J*being the number of measurements. The

*y*were assumed to be independent and lognormally (LN) distributed with GM

_{ij}*e*and GSD

^{f}*e*

^{σ}, where

*f*= log

*C*, with

*C*=

*C*(

*t*,

_{ij}*D*, θ

_{i}_{i}, ϕ

_{ij}), the model-predicted drug concentration. The notation used here for

*Y*lognormally distributed with GM

*e*

^{μ}and GSD

*e*

^{σ}is

*Y*∼ LN(μ, σ) ⇔ log

*Y*∼

*N*(μ, σ), with log denoting the natural logarithm and

*N*(μ, σ) denoting the normal distribution with mean μ and SD σ or variance σ

^{2}and with the coefficient of variation

*E*(

*Y*) = exp(μ + σ

^{2}/2). Lower and upper truncation bounds to limit MCMC sampling of implausible values, and variability parameters based on observed ranges for MC simulations, were specified using exp(μ ±

*n*σ) = GM ×/ GSD

^{n}, where ×/ denotes multiplied or divided by, and with the choices

*n*= 2 or

*n*= 3 including approximately 95.5% or 99.7% of the distribution, respectively. The individual parameter vectors (θ

_{i}) were lognormally distributed with population GM

*e*

^{μ}with the prior distributions for each component of μ, corresponding to each unmeasured PK model parameter normally distributed with mean

*M*

_{μ}and SD

*S*

_{μ}. Interindividual variability was specified by the variance-covariance matrix (Ω), with diagonal elements denoted by the variances ω

^{2}and the corresponding SDs by ω. The PK model parameters were assumed to be uncorrelated, and prior distributions for ω

^{2}were assigned half-normal (HN) distributions, parameterized by an SD, denoted here by

*S*

_{ω}, with the mean of HN(

*S*

_{ω}) equal to

*U*) prior distribution with lower bound

*a*and upper bound

*b*(45).

Prior distributions.For θ = (ED_{50}, τ_{F}, *k _{a}*,

*V*, CL

_{C}_{C}), informative prior distributions for the population GMs (

*e*

^{μ}) and variances (ω

^{2}) were determined using the tabulated NCA results from the food effect study by Winter et al. (15) and the ascending dose study by Ginsberg et al. (13). As the high-fat high-calorie meal prior to dosing was assumed to correspond most closely to maximum bioavailability, with exp(−β

_{F}) ≈ 0, and as the lowest administered dose would also correspond most closely with maximum bioavailability, the 50-mg fed state parameters

*T*

_{max}= 4.00 h,

*t*

_{1/2}= 19.2 h, and AUC

_{0–∞}= 14,661 ng · h/ml from Winter et al. (15) were used to calculate point estimates of the minimum oral clearance [min(CL/

*F*) ≈ CL/

*F*

_{max}= dose/AUC

_{0–∞}], the minimum oral volume of distribution [min(

*V/F*) ≈

*V/F*

_{max}

*= t*

_{1/2}· CL

*/F*

_{max}/log(2)], and the absorption rate constant by numerical solution of

*k*·

_{a}*T*

_{max}= log[

*k*

_{a}t_{1/2}/log(2)] + log(2) ·

*T*

_{max}/

*t*

_{1/2}for

*k*> log(2)/

_{a}*t*

_{1/2}. With the standard body weight, CL and

*V*were equal to their corresponding allometric constants. A prior point estimate for ED

_{50}was set as the administered dose most closely corresponding to a half-maximum effect in the day 1 values for

*C*

_{max}tabulated by Ginsberg et al. (13). Uncertainties in these values were set with a GSD of 1.2, corresponding to 20% CV, providing for the interstudy differences in the 200-mg mean peak concentration and mean oral clearance values (13, 15). A prior estimate for τ

_{F}was set as a lower bound, with the constraint that it had a negligible (<5%) effect on day 1 of exposure. Uncertainty in this value was set with a GSD of 1.6, corresponding to 50% CV, representing a degree of uncertainty higher than that for the other parameters with more informative measurements. The half-normal distributions were set with

*S*equal to 0.2, corresponding to an interindividual variability of 40% CV. This was a conservative estimate, based on the approximate 20% average CV for the NCA parameters in both studies (13, 15), and represents an otherwise possibly high level of interindividual variability (56). Truncation bounds on the lognormal distributions were set to GM ×/ GSD

_{ω}^{3}, where GSD was calculated to include both interindividual variability and uncertainty in the mean values. The prior population residual error was specified by its geometric mean (

*e*

^{σ}) and assigned a noninformative log-uniform distribution with a lower bound corresponding to the bioanalytic assay precision.

CL-007 and CL-010 patient data.Individual patient data collected in the CL-007 (6) and CL-010 (7) phase 2 studies provided the basis for PK model parameter estimation. Both studies were designed to assess the EBA, safety, and PK of pretomanid as a single drug administered daily for 14 days in patients with newly diagnosed pulmonary TB, and both were conducted by the same clinical investigators at the same study sites in Cape Town, South Africa. The individual patient data from CL-007 and CL-010 were provided for the present PK model-based analysis by the Global Alliance for TB Drug Development (TB Alliance) (57). The data files were anonymized and were organized and formatted consistent with the Clinical Data Interchange Standards Consortium (CDISC) study data tabulation model (SDTM) (58).

Detailed descriptions of patient characteristics and study design for CL-007 (6) and CL-010 (7) can be found in their respective publications. Briefly, CL-007 tested pretomanid daily oral doses of 200, 600, 1,000, and 1,200 mg, and CL-010 tested daily oral doses of 50, 100, 150, and 200 mg. The planned blood sampling times for CL-010 were predose on days 1 to 14, with intensive sampling at 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 12, and 16 h postdose on day 1 and day 14 and with day 14 including the collection of additional samples at 24 and 30 h postdose. The planned blood sampling times for CL-007 were predose on days 1 to 14, with intensive sampling at 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 12, and 16 h postdose on days 1, 8, and 14. All doses were administered following an overnight fast, and total body weights and vital signs were recorded daily. Bioanalytical measurements of pretomanid concentrations in plasma were made using liquid chromatography-tandem mass spectrometry, with the LLOQ equal to 10 ng/ml.

Posterior distribution.The population- and individual-level statistical model parameters were estimated as a joint posterior probability distribution, *P*(μ, Ω, θ, σ∣*y*), conditioned on the individual pretomanid concentration-time measurements (*y*). This posterior distribution was determined using Bayes' rule (20),
*P*(*y*∣μ, Ω, θ, σ) is the likelihood of *y*, and *P*(BLQ∣*f*) is the likelihood of a BLQ observation. *P*(μ), *P*(Ω), and *P*(σ) are the population-level prior distributions specified by the parameters (*M*_{μ,} *S*_{μ}), *S*_{ω}, and (*a*, *b*), respectively. The BLQ measurements were included as censored observations using method M3 of Beal (23), with *P*(BLQ∣*f*) *=* Φ{[log(LLOQ) − *f*]/σ}, where Φ is the normal cumulative distribution function.

The joint posterior distribution was evaluated by MCMC simulation (21). Multiple sampling chains were run in parallel, with each chain starting from a different set of randomly sampled parameter values. All but the tail ends of each chain were discarded, and the chains were additionally thinned to decrease autocorrelation. Convergence of the multiple chains to a common stationary distribution was assessed by visual inspection of trace plots of the sampled parameter value at each iteration and by comparison of inter- and intrachain variance using the Gelman-Rubin scale reduction factor (*R̂*) (20). The effective number of independent samples from the posterior distribution, adjusted for autocorrelation, was determined by the effective sample size (*n*_{eff}) (20, 59). All summaries and inferences regarding the posterior distribution were obtained from the aggregate of retained samples from each chain.

Model simulations.Posterior predictive simulations of population concentration-time profiles were performed by MC simulation of each dosage regimen. Each MC simulation consisted of 10,000 iterations, with each iteration performed by evaluating the pretomanid plasma concentration-time profile for a specified dosage in a randomly generated individual defined by a total body weight and PK model parameter set. The total body weight was generated as a random sample (with replacement) from the complete set of observed daily body weights from the combined CL-007 and CL-010 data sets. The PK model parameter set was generated from the individual parameter vector θ ∼ LN(μ, Ω), where μ and Ω were sampled from the joint posterior population parameters. NCA of the model output and observed data included the peak (maximum) concentration (*C*_{max}), the minimum concentrations (*C*_{min}), and the area under the concentration-time curve during the 24-h dosing interval (AUC_{24}), with AUC_{24} calculated using the linear trapezoidal rule (19). The observed BLQ measurements were ignored in these NCA calculations. Simulations of pretomanid concentration-time profiles for each individual patient were performed using the corresponding dosage regimen, individual body weights, and mean values for the posterior individual PK model parameter distributions.

Graphical comparisons, as goodness-of-fit plots, between the observed pretomanid plasma concentrations and the corresponding individual predicted values and the means for the population predicted distributions from the MC simulations were made with linear regression and analysis of residuals. Linear least-squares regression of the observed versus predicted values was performed, with weighted residuals calculated as standardized (or Studentized) residuals (60) and plotted versus the predicted concentrations and versus time.

Probability distributions for the unbound drug fraction (*fu*), the MIC, and the model-predicted total plasma concentration (*C*) were combined as an effective concentration (*C*_{eff}) = *f _{u} C/*MIC, and evaluated by MC simulation for selected dosage regimens. The simulation for

*C*included a distribution for the food effect coefficient as β

_{F}∼ LN(−0.367, 1.08), which described a 50% fed state [exp(−median β

_{F}) ≈ 0.5] with a GM ×/ GSD

^{2}range of 0 < β

_{F}< 6, containing approximate minimal and maximal fed states. The distributions for

*f*and MIC were specified on the basis of literature values, as

_{u}*f*∼ LN(−2.3, 0.2) with a GM of 0.1 and CV = 20% and MIC ∼ LN(−2.3, 0.83) with GM = 0.1 μg/ml and CV = 100%. The parameters for

_{u}*f*were based on 90% protein binding, with GSD set to include an approximate 85% to 95% GM ×/ GSD

_{u}^{2}range, used in a similar calculation by Ahmad et al. (5), and including reported values of 90% in mice (46) and 95% (14) and 88.9% (51)

*in vitro*. For the distribution of MICs, the central value of 0.1 μg/ml was used by Diacon et al. (61) as a point estimate for %

*fT*

_{>MIC}calculations. The GSD was chosen to include a GM ×/ GSD

^{2}range of 0.02 < MIC < 0.53 μg/ml observed in clinical isolates (1, 4).

*C*

_{eff}was used to calculate the PK/PD indices

*f*AUC

_{24}/MIC,

*fC*

_{max}/MIC, and %

*fT*

_{>MIC}, where the latter is equivalent to the percentage of time that

*C*

_{eff}> 1.

Software.The SQLite database engine (version 3.8.7.1; SQLite Development Team [https://www.sqlite.org]) was used to extract and organize data from the TB Alliance files. The GNU MCSim modeling and simulation suite (62) (version 5.6.5 [https://www.gnu.org/software/mcsim/]) was used for numerical evaluation of the PK model equations, including MC and MCMC simulations. MCSim uses LSODES (63) as the differential equation solver and the Metropolis-Hastings algorithm (21) for MCMC simulations, which are implemented as C programs, and were compiled using gcc (version 4.9.2 [https://gcc.gnu.org/]). R statistical software (version 3.3.3; R Development Team [https://www.R-project.org/]) was used for descriptive statistics, NCA, and analysis of the posterior probability distributions using the CODA package (59) (https://cran.r-project.org/web/packages/coda). The operating system was Linux (version 3.16.0-4-amd64, Debian distribution [https://www.debian.org]).

## ACKNOWLEDGMENTS

I thank Stephen Murray (Global Alliance for TB Drug Development [TB Alliance]), Khisi Mdluli (TB Alliance), Anna Upton (TB Alliance), Carl Mendel (TB Alliance), Bob Stafford (Critical Path to TB Drug Regimens [CPTR]), Debra Hanna (CPTR), and Klaus Romero (CPTR) for providing and facilitating the acquisition of the clinical trial data. Also, I thank Frédéric Bois (INERIS, France), David Salinger (Certara), and David Hermann (Bill and Melinda Gates Foundation) for helpful discussions related to the PK model and data and Anne Lenaerts (Colorado State University) and Véronique Dartois (Public Health Research Institute, Rutgers University) for helpful discussions on pretomanid. I also thank Andreas Diacon (TASK Applied Science and Stellenbosh University) and Jerry Nedelman (TB Alliance) for their careful reading of the manuscript and helpful comments and suggestions.

HHS, National Institutes of Health (NIH), National Institute of Allergy and Infectious Diseases (NIAID), provided funding to Michael A. Lyons under grant number R01AI125454.

## FOOTNOTES

- Received 15 November 2017.
- Returned for modification 4 January 2018.
- Accepted 9 April 2018.
- Accepted manuscript posted online 16 April 2018.

- Copyright © 2018 American Society for Microbiology.