The Potential for Treatment Shortening With Higher Rifampicin Doses: Relating Drug Exposure to Treatment Response in Patients With Pulmonary Tuberculosis

We used advanced model-based methods to characterize the relationship between individual rifampicin exposure and antituberculosis treatment response. With data from a trial investigating high-dose rifampicin, a significant relation could be derived, and the clinical impact of increased doses was predicted.


Population for simulations of clinical impact
The virtual population (n=10000) used as the basis for the simulations of clinical impact was created by sampling from parametric covariate distributions mimicking the distributions observed in the study data. The two non-treatment related covariates included in the final model was baseline bacterial load and proportion of missing samples. For baseline bacterial load a Box-Cox transformed normal distribution (SD 0.35, Box-Cox parameter 0.7) around the median observed time to positivity (4.37 days) was used. If a simulated value was higher than 42 days it was truncated to 42 days. For the proportion of missing sample results, a three-level uniform distribution was used: 59% of the subjects missing between 0 and 20% of the planned samples, 28% missing between 20 and 40% and 13% missing between 40 and 60%. For comparison, simulations were also conducted assuming 0% missing sample results for all subjects. The same sampling schedule as in the original study was implemented and all subjects were assumed to remain in the study until week 26 (no dropout).

Pharmacokinetic modeling
The previously developed population PK model generally fitted the data well. The model includes a single distribution compartment, absorption through a dynamic transit compartment model, and a Michelis-Menten function limiting the clearance at high concentrations. The previously described nonlinear increase in bioavailability with higher doses was not supported in this dataset and therefore simplified to a linear relationship. The relative bioavailability was fixed to 1 for a dose of 450 mg, thereafter increasing with the estimated slope coefficient. Further modifications to the original model included a reduction of the number of random effects, and an addition of a correlation between inter-individual variability in mean transit time and bioavailability. Samples below the limit of quantification (BLQ) were excluded in the estimation step. The model's ability to adequately predict BLQ samples was assessed by evaluating the full dataset including BLQ samples using the final estimated parameters and the M3 method (i.e. quantifying probability of a sample being BLQ).
Allometric scaling with fat-free mass as size descriptor, and coefficients fixed to the expected values (0.75 and 1 for clearance and volume of distribution, respectively) were included. Fat-free mass performed slightly better than total body weight. Gender and presence of lung cavitation did not have a statistically significant impact on clearance or volume of distribution. HIV-infection could not be evaluated due to the low number of HIV-positive patients included. There was a statistically significant but small effect of country on volume of distribution (13% lower in South Africa than Tanzania). Given the lack of a scientific rational and clinical significance, this effect was not included in the final model.
The final parameter estimates with their uncertainty are reported in Table S1. The good fit of the model to the observed concentrations and the proportion BLQ samples is demonstrated in the visual predictive check in Figure S1. The NONMEM code detailing the parameterization is included last in this supplementary material. Table S1. Maximum likelihood estimates of parameter values from the final model including uncertainty determined by the covariance step implemented in NONMEM. The typical values of the maximal elimination rate and the volume of distribution are representative for a patient with fat-free mass of 44.6 kg. Abbreviations: V max , maximal elimination rate; k m , rifampicin concentration at which the elimination is halfmaximal; IIV, inter-individual variability; CV, coefficient of variance * Not calculated, relative standard error of corresponding covariance estimate was 32.8% Figure S1. Visual predictive check of observed concentrations (upper panels) and the proportion of samples below the limit of quantification (lower panels), per dose group. In the upper panels blue rings represent the observed rifampicin concentrations, the lines represent the 2.5 th , 50 th and 97.5 th percentiles of the observed data, and the shaded areas are the 95% confidence intervals of the same percentiles based on data simulated by the final model. In the lower panels the blue rings represent the observed proportions samples below the limit of quantification per bin (indicated by the yellow tick marks), and the shaded area represents the 95% confidence intervals of the same proportions based on data simulated by the final model. Figure S2. Histogram of individual model predicted rifampicin AUC 0-24h at day 28 plotted in panels per dose level (10, 20 and 35 mg/kg) and colored according to absolute rifampicin dose (mg).

Results TSCC liquid cultures
The goodness of fit for different base hazard models is shown in Figure S3, comparing two standard distributions (constant and Weibul hazard) to the selected surge function. The poor fit of the standard models to the observed data is apparent. Figure S3. Visual predictive check of evaluated base hazard distributions in the time-to-event model describing TSCC based on liquid cultures, including constant, Weibul and the selected surge function. The solid lines are the Kaplan-Meier curves based on the observed data, vertical tick-marks in the signifies censored data, and the shaded area outlines the 95% prediction interval based on model simulations.
Covariates included in the final model were baseline time to positivity, proportion unavailable culture results, rifampicin exposure, and substitution of ethambutol with moxifloxacin or SQ109. Gender, country, study site, x-ray scoring, presence of cavitation, and pyrazinamide exposure were all significant in univariate analysis, but not in multivariate analysis and therefore not included in the final model. Body weight and isoniazid exposure were not significant at all.
The parameters of the final model were defined according to the equations following below. SA is the surge amplitude, PT is the peak time, SW is the surge width, p denotes the population value and i the individual value. The covariates are denoted with P miss for the proportion unavailable culture results, B TTP for baseline time to positivity, RIF AUC for rifampicin exposure quantified by AUC 0-24h (imputed for patients with missing PK data), and MX and SQ for having ethambutol replaced with moxifloxacin or SQ109, respectively (categorical covariates with value 1 if yes, 0 otherwise). The estimated coefficients for the respective relationships are denoted with θ and the covariate name. The statistical significance of each covariate relationship was demonstrated by the increase in objective function value (OFV, defined as minus two time the logarithm of the likelihood) after univariate deletion from the final model with single imputation of rifampicin exposure (Table S2). Given the study design, having moxifloxacin or SQ109 were mutually exclusive. These covariates were therefore only tested together to avoid biasing the typical estimates for patients without substitution of ethambutol. The final parameter estimates after the multiple imputation procedure, including parameter uncertainty, are listed in Table S3. The parameters were estimated with good precision (relative standard errors <30%), with an exception for the coefficients determining effect of moxifloxacin or SQ109 substitution (relative standard errors ~50%).

Results TSCC solid cultures
The best base hazard model for TSCC derived from solid cultures was a Weibull defined by a base and a shape parameter. The covariates found to have a significant impact on the base parameter were baseline bacterial load (power relation, relative to median observed baseline TTP) and rifampicin exposure (linear relation, same centering applied as in the model for liquid cultures, see equations above). The final parameters with uncertainty are listed in Table S4. The model fit is demonstrated in Figure S8.