Longitudinal Pharmacokinetic-Pharmacodynamic Biomarkers Correlate With Treatment Outcome in Drug-Sensitive Pulmonary Tuberculosis: A Population Pharmacokinetic-Pharmacodynamic Analysis

Abstract Background This study aims to explore relationships between baseline demographic covariates, plasma antibiotic exposure, sputum bacillary load, and clinical outcome data to help improve future tuberculosis (TB) treatment response predictions. Methods Data were available from a longitudinal cohort study in Malawian drug-sensitive TB patients on standard therapy, including steady-state plasma antibiotic exposure (154 patients), sputum bacillary load (102 patients), final outcome (95 patients), and clinical details. Population pharmacokinetic and pharmacokinetic-pharmacodynamic models were developed in the software package NONMEM. Outcome data were analyzed using univariate logistic regression and Cox proportional hazard models in R, a free software for statistical computing. Results Higher isoniazid exposure correlated with increased bacillary killing in sputum (P < .01). Bacillary killing in sputum remained fast, with later progression to biphasic decline, in patients with higher rifampicin area under the curve (AUC)0-24 (P < .01). Serial sputum colony counting negativity at month 2 (P < .05), isoniazid CMAX (P < .05), isoniazid CMAX/minimum inhibitory concentration ([MIC] P < .01), and isoniazid AUC0-24/MIC (P < .01) correlated with treatment success but not with remaining free of TB. Slower bacillary killing (P < .05) and earlier progression to biphasic bacillary decline (P < .01) both correlate with treatment failure. Posttreatment recurrence only correlated with slower bacillary killing (P < .05). Conclusions Patterns of early bacillary clearance matter. Static measurements such as month 2 sputum conversion and pharmacokinetic parameters such as CMAX/MIC and AUC0-24/MIC were predictive of treatment failure, but modeling of quantitative longitudinal data was required to assess the risk of recurrence. Pooled individual patient data analyses from larger datasets are needed to confirm these findings.


Further pharmacokinetic methods
Pharmacokinetic parameters were MU-transformed: Individual parameter estimates (P i ) constituted a typical population estimate (θ) and random between patient variability (η). The Iterative Two Stage estimation method was used to identify intial values for the parameter search, stochastic approximation expectation maximization was used to estimate parameters and importance sampling was used to calculate the objective function (-2 log-likelihood; -2LL) and the covariance matrix.
Discrimination between two hierarchical models was based on changes in the objective function value (-2LL, with drops of more than 3.84 or 6.63 points considered significant at p<0.05 or p<0.01 for the inclusion of 1 degree of freedom), precision in parameter estimates (relative standard error, RSE %, and confidence intervals, calculated as 2.5 and 97.5 percentile of the data, both derived from 1,000 non-parametric bootstraps), graphical analysis of model accuracy and prediction (e.g. goodness of fit plots and visual predictive checks), and physiological and micro-biological plausibility. Goodness of fit plots comprise graphical representations of observed vs. individual level model predictions and normalized predictive distribution errors vs. population level model predictions. Visual predictive checks comprise 2,000 newly simulated studies using the developed model. 90% confidence intervals around the simulated 2.5, 50 th and 97.5 percentiles are overlayed with the observed 2.5, 50 th and 97.5 and percentiles and observations. Parameter estimates were based on two compartment disposition models for isoniazid and ethambutol and one compartment disposition models for rifampicin and pyrazinamide. Rifampicin and ethambutol absorption were described using transit absorption models. Isoniazid and pyrazinamide absorption were described using first-order absorption models. Bodyweight was incorporated as a covariate on clearance and volume estimates using allometry, centralised around 70 kg patient for rifampicin and pyrazinamide and 63 kg and 50 kg for isoniazid and ethambutol. Rifampicin clearance estimates were centralised around male patients. Clearance and apparent distribution volume of the central compartment were estimated with absorption, peripheral distribution volume and inter-compartment clearance fixed to isoniazid [1], rifampicin [2], pyrazinamide [3] and ethambutol [4] literature values. This approach supported characterisation of the entire pharmacokinetic profiles (i.e. absorption, distribution and elimination) which was not possible based on the study data alone. For isoniazid, Q, V P and k a in the population pharmacokinetic model were fixed to literature values from a healthy volunteer population [1] as fixing parameter estimates to literature values from a patient population [5] resulted in unrealistically long terminal half-lives. Moreover, isoniazid elimination clearance parameters were not accounted for NAT2 acetylator status. Residual variability was described using proportional error model for isonizaid, rifampicin and ethambutol and a combined proportional/additive model for pyrazinamide.

S3 Fig.: Stratified pharmacokinetic visual predictive checks
Simulation based (n=2,000) VPCs for isoniazid, stratified by treatment outcome. Open circles represent observations, solid and dashed black lines represent observed 2.5, 50 th and 97.5 percentiles. Shaded areas represent the 90% confidence intervals around the simulated 2.5, 50 th and 97.5 percentiles. Cured: patients that had no recurrent TB during 12 month follow-up after cure at EOT, Failed: patients that failed treatment at EOT, Recurrence: patients that had a recurrent infection during the 12 month follow-up after cure at EOT, and excluded, loss to follow-up or died: patients that were excluded for treatment failure analysis, were loss to or did not enther the follow-up and patients that died.
Simulation based (n=2,000) VPCs for rifampicin, stratified by treatment outcome. Open circles represent observations, solid and dashed black lines represent observed 2.5, 50 th and 97.5 percentiles. Shaded areas represent the 90% confidence intervals around the simulated 2.5, 50 th and 97.5 percentiles. Cured: patients that had no recurrent TB during 12 month follow-up after cure at EOT, Failed: patients that failed treatment at EOT, Recurrence: patients that had a recurrent infection during the 12 month follow-up after cure at EOT, and excluded, loss to follow-up or died: patients that were excluded for treatment failure analysis, were loss to or did not enther the follow-up and patients that died.
Simulation based (n=2,000) VPCs for pyrazinamide, stratified by treatment outcome. Open circles represent observations, solid and dashed black lines represent observed 2.5, 50 th and 97.5 percentiles. Shaded areas represent the 90% confidence intervals around the simulated 2.5, 50 th and 97.5 percentiles. Cured: patients that had no recurrent TB during 12 month follow-up after cure at EOT, Failed: patients that failed treatment at EOT, Recurrence: patients that had a recurrent infection during the 12 month follow-up after cure at EOT, and excluded, loss to follow-up or died: patients that were excluded for treatment failure analysis, were loss to or did not enther the follow-up and patients that died.
Simulation based (n=2,000) VPCs for ethambutol, stratified by treatment outcome. Open circles represent observations, solid and dashed black lines represent observed 2.5, 50 th and 97.5 percentiles. Shaded areas represent the 90% confidence intervals around the simulated 2.5, 50 th and 97.5 percentiles. Cured: patients that had no recurrent TB during 12 month follow-up after cure at EOT, Failed: patients that failed treatment at EOT, Recurrence: patients that had a recurrent infection during the 12 month follow-up after cure at EOT, and excluded, loss to follow-up or died: patients that were excluded for treatment failure analysis, were loss to or did not enther the follow-up and patients that died.

Further pharmacokinetic-pharmacodynamic methods
Population PKPD models were developed using the ADVAN6 subroutine NONMEM and colony count number below the limit of quantification were handled with the M3 method. [6] Sputum bacillary load data above the limit of quantification was estimated and the likelihood that sputum bacillary load data was below the limit of quantification was maximised which is the standard procedure to account for data below limit of quantification. Except for CFU baseline , which followed normal distribution as the power of base 10 was estimated, all other PKPD parameters followed log-normal distribution: Individual parameter estimates (P i ) constituted a typical population estimate (θ) and random between patient variability (η). A single differential equation and a proportional bacterial killing rate (k net ) was used to describe the sputum bacillary load data with baseline sputum bacillary load as initial condition estimated: Effective bacterial killing on log 10 transformed displayed a bi-phasic distribution in some cases which was accomodated by an exponential model: The time dependency in the equation was represented by θ T 1/2 , the magnitude of decreasing early bacillary clearance over time by θ β and the underlying sputum bacillary effect by θ LAM . Criteria to discriminate between two hierarchical PKPD models were identical to the criteria used for the development of pharmacokinetic models.
The same criteria as described under the further pharmacokinetic method sections were used for discrimination between two hierarchical models.

S5 Fig.: Stratified pharmacokinetic-pharmacodynamic visual predictive checks
Simulation based (n=2,000) VPCs for sputum bacterial load, stratified by treatment outcome. Open circles represent observations, solid and dashed black lines represent observed 2.5, 50 th and 97.5 percentiles. Shaded areas represent the 90% confidence intervals around the simulated 2.5, 50 th and 97.5 percentiles. Cured: patients that had no recurrent TB during 12 month follow-up after cure at EOT, Failed: patients that failed treatment at EOT, Recurrence: patients that had a recurrent infection during the 12 month follow-up after cure at EOT, and excluded, loss to follow-up or died: patients that were excluded for treatment failure analysis, were loss to or did not enther the follow-up and patients that died.