Greater Early Bactericidal Activity at Higher Rifampicin Doses Revealed by Modeling and Clinical Trial Simulations

Greater Early Bactericidal Activity at Higher Rifampicin Doses Revealed by Modeling and Clinical... Abstract Background The currently recommended rifampicin dose (10 mg/kg) for treating tuberculosis is suboptimal. The PanACEA HIGHRIF1 trial evaluated the pharmacokinetics and early bactericidal activity of rifampicin doses of up to 40 mg/kg. Conventional statistical analyses revealed no significant exposure-response relationship. Our objectives were to explore the exposure-response relationship for high-dose rifampicin by using pharmacokinetic-pharmacodynamic modeling and to predict the early bactericidal activity of 50 mg/kg rifampicin. Methods Data included time to Mycobacterium tuberculosis positivity of liquid cultures of sputum specimens from 83 patients with tuberculosis who were treated with 10 mg/kg rifampicin (n = 8; reference arm) or 20, 25, 30, 35, or 40 mg/kg rifampicin (n = 15/arm) for 7 days. We used a semimechanistic time-to-event approach to model the time-to-positivity data. Rifampicin exposure and baseline time to culture positivity were explored as covariates. Results The baseline time to culture positivity was a significant covariate on the predicted initial bacterial load, and rifampicin exposure was a significant covariate on the bacterial kill rate in sputum resulting in increased early bactericidal activity. The 90% prediction interval for the predicted median day 7 increase in time to positivity for 50 mg/kg rifampicin was 7.25–10.3 days. Conclusions A significant exposure-response relationship was found between rifampicin exposure and early bactericidal activity. Clinical trial simulations showed greater early bactericidal activity for 50 mg/kg rifampicin. Clinical Trials Registration NCT01392911. Pharmacodynamics, tuberculosis, pharmacokinetics, patients, time to positivity, early bactericidal activity, models, bactericidal effect, Mycobacterium tuberculosis Since the concept of increasing the rifampicin dose for treating tuberculosis was reintroduced, a battery of trials has been conducted to optimize treatment of pulmonary tuberculosis and tuberculous meningitis [1–9]. Despite this, a question remains: what is the optimal dose of rifampicin [10, 11]? The answer remains unknown, but recent clinical trials have provided important insight. The PanACEA HIGHRIF1 trial [4] studied the short-term safety, pharmacokinetics, and antimycobacterial activity of rifampicin doses of up to 40 mg/kg. No statistically significant relationship was determined between rifampicin exposure and early bactericidal activity [4] in humans despite several lines of evidence derived from in vitro and animal experiments suggesting a clear relationship between exposure and mycobacterial killing [12–15]. Early bactericidal activity can be quantified using time to positivity in liquid culture, which is defined as the time from the start of incubation of a sputum specimen in a liquid culture system to the detection of a positive signal A high bacterial load is expected to lead to a short time to positivity and vice versa. Time to positivity reflects time-to-event data. For conventional statistical analysis, early bactericidal activity determined using time to positivity is usually analyzed in the context of a series of data points from daily sputum cultures as the change in time to positivity per day of treatment by regression-based methods [16, 17]. Two semimechanistic pharmacokinetic-pharmacodynamic models exist that treat time to positivity as time-to-event data [18, 19]. Model-based pharmacokinetic-pharmacodynamic analysis has been shown to be more powerful for defining the exposure-response relationship than conventional statistical methods [20]. Semimechanistic pharmacokinetic-pharmacodynamic models also allow for extrapolation by simulating new scenarios, such as predicting the early bactericidal activity of higher-than-observed doses, which can be used to design future clinical trials. Our objective was to use a semimechanistic time-to-event approach to explore the exposure-response relationship for early bactericidal activity, determined using the time to Mycobacterium tuberculosis positivity, in patients with pulmonary tuberculosis treated with high-dose rifampicin (up to 40 mg/kg) and then to simulate the early bactericidal activity of 45 and 50 mg/kg rifampicin, to inform the clinical development process of optimizing a higher rifampicin dose. METHODS Ethics The study was approved by local ethical review boards and by the Medicines Control Council of South Africa and was conducted according to good clinical practice. All patients provided written informed consent before enrollment in the study. Patient Data Modeling was performed on 1-week repeated time-to-positivity data measured in sputum specimens from patients recruited in the HIGHRIF1 trial, a prospective open-label multiple rising dose trial (clinical trials registration NCT01392911) [4]. Smear-positive patients with pulmonary tuberculosis were treated with 10 mg/kg rifampicin (n = 8; reference arm) or 20, 25, 30, 35, or 40 mg/kg rifampicin (n = 15/arm) as monotherapy daily for 7 days. The total study duration was 14 days, with standard doses of isoniazid, pyrazinamide, and ethambutol therapy added to high-dose rifampicin treatment on days 8–14. In this analysis, only data until day 7 were used, to define the exposure-response relationship for rifampicin alone. Overnight sputum sampling was performed on 2 consecutive days at baseline and then daily for 7 days. The time to positivity was determined in duplicate for each sample, using a standardized liquid culture system (BD Bactec MGIT 960 Mycobacterial Growth Indicator Tube system; Becton-Dickinson, Sparks, MD) in a single laboratory. The HIGHRIF1 trial is described in detail elsewhere [4]. Data Analysis Time-to-positivity data were analyzed with a time-to-event approach, using the nonlinear mixed-effects modeling software NONMEM 7.3 [21] with the Laplacian estimation method. Data handling and visualization were done in R, version 3.4.3 [22]. Model diagnostic evaluations were performed in Xpose 4.6.0 [23, 24], with visual predictive checks performed using PsN 4.6.12 [23, 25]. Models were compared on the basis of the objective function value (OFV), using the likelihood ratio test at a 5% significance level. Time-to-positivity replicates at each time point were analyzed without averaging. The baseline time to positivity was included in the model as a covariate (see below). Structural Model The starting point for model development was a previously developed semimechanistic time-to-event model for time to positivity [19]. Briefly, the model structure was derived from underlying knowledge about (1) how the amount of viable tuberculosis bacteria changes in human sputum over time, referred to as the “sputum model”; (2) how tuberculosis bacteria are known to grow in a liquid culture, referred to as the “mycobacterial growth model”; and (3) how the mycobacterial growth relates to the probability of achieving a positive signal event in the MGIT system, referred to as the “hazard model.” The starting model included drug effect without an exposure-response relationship. Sputum models with 1 and 2 mycobacterial subpopulations were tested. The bacterial load in the single mycobacterial subpopulation model was described by  B(tt)sputum=B0,sputum×e−kkill×tt where B0,sputum is the predicted bacterial load at the start of treatment, kkill is the first-order rifampicin bacterial kill rate, and tt is the time after the start of treatment. For the 2-subpopulation model, the bacterial loads of the first (B1) and second (B2) mycobacterial subpopulations were described by   B1(tt)sputum=B10,sputum×e−kkill,1×tt and  B2(tt)sputum=B20,sputum×e−kkill,2×tt where  B(tt)sputum=B1(tt)sputum+B2(tt)sputum where B10,sputum and B20,sputum denote the predicted bacterial loads at the start of treatment for subpopulations 1 and 2, respectively. Parameters kkill,1 and kkill,2 describe the first-order rifampicin bacterial kill rates of subpopulations 1 and 2, respectively. For the mycobacterial growth model in the liquid culture container, a logistic growth model was used, where the change in the bacterial load in the liquid culture (Bculture) over time is described by  dBculturedtc=kG×(Bmax−B(tc)culture)×Bculture where the initial bacterial load in the liquid culture was assumed to be equal to the number of bacteria in sputum at the time of sputum sampling, according to  B(tc=0)culture=B(tt=sampling time point)sputum where kG is a predicted maximal mycobacterial growth rate in the liquid, Bmax is the maximal bacterial load in the liquid culture, and tc is the time after inoculation of the liquid culture. Models with 2 subpopulations in the liquid culture, with different growth rates for each subpopulation and both with and without a possible transfer between subpopulations, were explored. A lag time for the start of growth in the liquid culture was explored as a single lag time for both the 1- and 2-subpopulation models. Time dependencies in kG were explored, including linearly decreasing kG with the duration of treatment and an exponential decline from a baseline value of kG (kG,base) to a steady-state value of kG (kG,ss) according to  k(tt)G=kG,base+(kG,ss−kG,base)×(1−e−kG,k×tt) where kG,k is the first-order time-dependent decrease of kG,base. For the hazard model, the bacterial load in the liquid culture at any given time point was equal to the hazard, h(tc), for the liquid culture to turn into a positive signal, described by  h(tc)=B(tc)culture which was used in a next step to calculate the cumulative hazard according to  H(tc)=∫0tch(tc)dt This finally allowed calculation of the survival, which is the probability of a sample without a positive signal at time tc, using the following equation:  S(tc)=e−H(tc) Covariate Model The individual mean baseline time to positivity was not included in the estimation but was evaluated as a covariate on the predicted bacterial load at the start of treatment (B0,sputum or B10,sputum and B20,sputum) as a power relationship. The area under the plasma concentration-time curve between 0 and 24 hours (AUC0-24h) at day 7 was evaluated as a covariate on the rifampicin kill rate parameters (kkill or kkill,1 and kkill,2). The AUC0-24h was chosen over the maximum concentration (Cmax) because the AUC is normally used in pharmacokinetic-pharmacodynamic analyses of rifampicin. Cmax and AUC0-24h are probably highly correlated and would therefore perform similarly when explored in a pharmacokinetic-pharmacodynamic model. Since only once-daily dosing was included in the current study design, it would probably be difficult to distinguish between Cmax and AUC0-24h. The AUC0-24h was calculated for each subject on the basis of concentration measurements at 0, 0.5, 1, 1.5, 2, 3, 4, 6, 8, 12, and 24 hours, using the linear-log trapezoidal rule in Winnonlin, version 5.3 (Pharsight, Mountain View, CA), as described elsewhere [4]. Concentrations were measured using validated ultra performance liquid chromatography (accuracy, <4%; limit of quantification, 0.13 mg/L). Stochastic Model Interindividual variability was investigated in all parameters for the sputum model, as well as for the estimated lag time for the growth in the mycobacterial growth model. Interoccasion variability in sputum sampling was investigated as random variability between occasions for the bacterial load inoculated in the mycobacterial growth model [19]. Model Evaluation The final semimechanistic time-to-event model (ie, the chosen model after structural, covariate, and stochastic model evaluations) was evaluated by performing a 1000-sample bootstrap stratified on dose group to attain parameter uncertainty. A posterior predictive check was performed by comparing the median time to positivity calculated from 1000 simulated trials to the observed median time to positivity. Clinical Trial Simulation of Pharmacokinetics and Time to Positivity After Receipt of 45 or 50 mg/kg Rifampicin The final semimechanistic time-to-event model was used for clinical trial simulation of time to positivity following receipt of 45 or 50 mg/kg rifampicin once daily for 7 days. Pharmacokinetics as the driver for increasing time to positivity was simulated for 45 and 50 mg/kg, and the day 7 AUC0-24h was calculated by means of the linear-log trapezoidal rule in ncappc 0.2.1.1, within R [26], from 1000 simulated data sets, using a pharmacokinetic model developed with data from the same patients used in this analysis [27]. To simulate pharmacokinetics, patient covariates were sampled from the observed population in a bootstrap procedure. The AUC0-24h values from the 1000 simulations were used to predict the time to positivity after receipt of the 45 and 50 mg/kg rifampicin regimens. Baseline times to positivity for the simulations were sampled from a log-normal distribution centered around 4.34 days and with a standard deviation of 0.32 days (estimated from the observed data set). The same study design as for the HIGHRIF1 trial was used (ie, 15 individuals/dose) [4]. RESULTS Patients and Data In total, 83 patients and 1102 time-to-positivity measurements were analyzed. A few samples (5.2%) were excluded from the analysis; 52 samples (collected on various treatment days) were contaminated, and 8 samples were negative for M. tuberculosis (all were collected before day 7 and were followed by positive samples collected on later treatment days). Patient characteristics are summarized in Table 1. Table 1. Baseline Patient Characteristics, by Rifampicin Dose Parameter  Overall (n = 83)  10 mg/kg (n = 8)  20 mg/kg (n = 15)  25 mg/kg (n = 15)  30 mg/kg (n = 15)  35 mg/kg (n = 15)  40 mg/kg (n = 15)  Weight, kg  53.9 (40.2–84.2)  56.9 (46.8–64.9)  52.6 (41.8–62.7)  52.8 (40.2–67.9)  54.0 (45.7–84.2)  57.0 (40.5–74.0)  58.9 (46.7–64.8)  Age, y  31.0 (18.0–59.0)  27.5 (19.0–49.0)  27.0 (18.0–46.0)  25.0 (19.0–46.0)  40.0 (19.0–59.0)  37.0 (21.0–59.0)  34.0 (23.0–58.0)  Body mass indexa  19.4 (14.7–30.9)  20.5 (15.8–26.3)  18.6 (16.8–26.2)  19.3 (15.1–25.2)  20.9 (16.4–30.9)  19.4 (14.7–25.2)  19.4 (17.2–19.4)  Male sex  59 (71.1)  6 (75.0)  11 (73.3)  10 (66.7)  11 (73.3)  10 (66.7)  11 (73.3)  Raceb                 Black  38 (45.8)  3 (37.5)  7 (46.7)  4 (26.4)  9 (60.0)  5 (33.3)  10 (66.7)   Colored  45 (54.2)  5 (62.5)  8 (53.3)  11 (73.3)  6 (40.0)  10 (66.7)  5 (33.3)  HIV infection  3 (3.6)  0 (0.0)  0 (0.0)  0 (0.0)  2 (13.3)  1 (6.7)  0 (0.0)  Baseline time to positivity, d  4.0 (2.2–18.2)  4.0 (3.3–5.2)  4.9 (3.0–9.1)  4.0 (3.4–6.5)  4.0 (2.9–6.3)  3.9 (2.6–18.2)  4.0 (2.2–7.6)  Day 7 AUC0-24h, h·mg/L  241 (34–847)  43 (34–53)  155 (96–221)  178 (134–380)  298 (177–781)  321 (145–555)  357 (201–847)  Parameter  Overall (n = 83)  10 mg/kg (n = 8)  20 mg/kg (n = 15)  25 mg/kg (n = 15)  30 mg/kg (n = 15)  35 mg/kg (n = 15)  40 mg/kg (n = 15)  Weight, kg  53.9 (40.2–84.2)  56.9 (46.8–64.9)  52.6 (41.8–62.7)  52.8 (40.2–67.9)  54.0 (45.7–84.2)  57.0 (40.5–74.0)  58.9 (46.7–64.8)  Age, y  31.0 (18.0–59.0)  27.5 (19.0–49.0)  27.0 (18.0–46.0)  25.0 (19.0–46.0)  40.0 (19.0–59.0)  37.0 (21.0–59.0)  34.0 (23.0–58.0)  Body mass indexa  19.4 (14.7–30.9)  20.5 (15.8–26.3)  18.6 (16.8–26.2)  19.3 (15.1–25.2)  20.9 (16.4–30.9)  19.4 (14.7–25.2)  19.4 (17.2–19.4)  Male sex  59 (71.1)  6 (75.0)  11 (73.3)  10 (66.7)  11 (73.3)  10 (66.7)  11 (73.3)  Raceb                 Black  38 (45.8)  3 (37.5)  7 (46.7)  4 (26.4)  9 (60.0)  5 (33.3)  10 (66.7)   Colored  45 (54.2)  5 (62.5)  8 (53.3)  11 (73.3)  6 (40.0)  10 (66.7)  5 (33.3)  HIV infection  3 (3.6)  0 (0.0)  0 (0.0)  0 (0.0)  2 (13.3)  1 (6.7)  0 (0.0)  Baseline time to positivity, d  4.0 (2.2–18.2)  4.0 (3.3–5.2)  4.9 (3.0–9.1)  4.0 (3.4–6.5)  4.0 (2.9–6.3)  3.9 (2.6–18.2)  4.0 (2.2–7.6)  Day 7 AUC0-24h, h·mg/L  241 (34–847)  43 (34–53)  155 (96–221)  178 (134–380)  298 (177–781)  321 (145–555)  357 (201–847)  Data are median values (ranges) or no. (%) of patients. Abbreviations: AUC0-24h, area under the plasma concentration-time curve during 24 hours; HIV, human immunodeficiency virus. aCalculated as the weight in kilograms divided by the height in meters squared. b“Black” refers to African natives, and “colored” refers to a population group genetically descended from Southeast Asia. View Large Table 1. Baseline Patient Characteristics, by Rifampicin Dose Parameter  Overall (n = 83)  10 mg/kg (n = 8)  20 mg/kg (n = 15)  25 mg/kg (n = 15)  30 mg/kg (n = 15)  35 mg/kg (n = 15)  40 mg/kg (n = 15)  Weight, kg  53.9 (40.2–84.2)  56.9 (46.8–64.9)  52.6 (41.8–62.7)  52.8 (40.2–67.9)  54.0 (45.7–84.2)  57.0 (40.5–74.0)  58.9 (46.7–64.8)  Age, y  31.0 (18.0–59.0)  27.5 (19.0–49.0)  27.0 (18.0–46.0)  25.0 (19.0–46.0)  40.0 (19.0–59.0)  37.0 (21.0–59.0)  34.0 (23.0–58.0)  Body mass indexa  19.4 (14.7–30.9)  20.5 (15.8–26.3)  18.6 (16.8–26.2)  19.3 (15.1–25.2)  20.9 (16.4–30.9)  19.4 (14.7–25.2)  19.4 (17.2–19.4)  Male sex  59 (71.1)  6 (75.0)  11 (73.3)  10 (66.7)  11 (73.3)  10 (66.7)  11 (73.3)  Raceb                 Black  38 (45.8)  3 (37.5)  7 (46.7)  4 (26.4)  9 (60.0)  5 (33.3)  10 (66.7)   Colored  45 (54.2)  5 (62.5)  8 (53.3)  11 (73.3)  6 (40.0)  10 (66.7)  5 (33.3)  HIV infection  3 (3.6)  0 (0.0)  0 (0.0)  0 (0.0)  2 (13.3)  1 (6.7)  0 (0.0)  Baseline time to positivity, d  4.0 (2.2–18.2)  4.0 (3.3–5.2)  4.9 (3.0–9.1)  4.0 (3.4–6.5)  4.0 (2.9–6.3)  3.9 (2.6–18.2)  4.0 (2.2–7.6)  Day 7 AUC0-24h, h·mg/L  241 (34–847)  43 (34–53)  155 (96–221)  178 (134–380)  298 (177–781)  321 (145–555)  357 (201–847)  Parameter  Overall (n = 83)  10 mg/kg (n = 8)  20 mg/kg (n = 15)  25 mg/kg (n = 15)  30 mg/kg (n = 15)  35 mg/kg (n = 15)  40 mg/kg (n = 15)  Weight, kg  53.9 (40.2–84.2)  56.9 (46.8–64.9)  52.6 (41.8–62.7)  52.8 (40.2–67.9)  54.0 (45.7–84.2)  57.0 (40.5–74.0)  58.9 (46.7–64.8)  Age, y  31.0 (18.0–59.0)  27.5 (19.0–49.0)  27.0 (18.0–46.0)  25.0 (19.0–46.0)  40.0 (19.0–59.0)  37.0 (21.0–59.0)  34.0 (23.0–58.0)  Body mass indexa  19.4 (14.7–30.9)  20.5 (15.8–26.3)  18.6 (16.8–26.2)  19.3 (15.1–25.2)  20.9 (16.4–30.9)  19.4 (14.7–25.2)  19.4 (17.2–19.4)  Male sex  59 (71.1)  6 (75.0)  11 (73.3)  10 (66.7)  11 (73.3)  10 (66.7)  11 (73.3)  Raceb                 Black  38 (45.8)  3 (37.5)  7 (46.7)  4 (26.4)  9 (60.0)  5 (33.3)  10 (66.7)   Colored  45 (54.2)  5 (62.5)  8 (53.3)  11 (73.3)  6 (40.0)  10 (66.7)  5 (33.3)  HIV infection  3 (3.6)  0 (0.0)  0 (0.0)  0 (0.0)  2 (13.3)  1 (6.7)  0 (0.0)  Baseline time to positivity, d  4.0 (2.2–18.2)  4.0 (3.3–5.2)  4.9 (3.0–9.1)  4.0 (3.4–6.5)  4.0 (2.9–6.3)  3.9 (2.6–18.2)  4.0 (2.2–7.6)  Day 7 AUC0-24h, h·mg/L  241 (34–847)  43 (34–53)  155 (96–221)  178 (134–380)  298 (177–781)  321 (145–555)  357 (201–847)  Data are median values (ranges) or no. (%) of patients. Abbreviations: AUC0-24h, area under the plasma concentration-time curve during 24 hours; HIV, human immunodeficiency virus. aCalculated as the weight in kilograms divided by the height in meters squared. b“Black” refers to African natives, and “colored” refers to a population group genetically descended from Southeast Asia. View Large Semimechanistic Time-to-Event Model The final semimechanistic time-to-event model included 1 mycobacterial subpopulation, both for the sputum and mycobacterial growth models. The latter included a time-varying, exponentially declining kG. Figure 1 shows the dynamics within each submodel for a typical patient receiving 30 mg/kg. A statistically significant exposure-response relationship was identified: the parameter kkill was found to increase linearly with increasing AUC0-24h (yielding increased early bactericidal activity at higher rifampicin exposures). The baseline time to positivity was a significant covariate on the initial bacterial load in sputum, where a long time to positivity gave a low initial bacterial load. The final model did not include any random interindividual or interoccasion variability because it was not supported by the data. Figure 1. View largeDownload slide Dynamics of the sputum model (A), mycobacterial growth model (B), and hazard model (C) for a typical patient receiving a rifampicin dose of 30 mg/kg, with an area under the plasma concentration-time curve between 0 and 24 hours of 298 h·mg/L and a baseline time to positivity of 4 days. Open squares show the dynamics of an early (day 1) sample, and open triangles show the dynamics for a late (day 7) sample. Bsputum, predicted bacterial load in sputum; Bculture, predicted bacterial load in liquid culture. Figure 1. View largeDownload slide Dynamics of the sputum model (A), mycobacterial growth model (B), and hazard model (C) for a typical patient receiving a rifampicin dose of 30 mg/kg, with an area under the plasma concentration-time curve between 0 and 24 hours of 298 h·mg/L and a baseline time to positivity of 4 days. Open squares show the dynamics of an early (day 1) sample, and open triangles show the dynamics for a late (day 7) sample. Bsputum, predicted bacterial load in sputum; Bculture, predicted bacterial load in liquid culture. Implementation of 2 mycobacterial subpopulations in sputum was statistically significant as compared to having 1 subpopulation (dOFV = −37.5; P < .00001). However, adding a 2-subpopulation model to a model with time-varying kG was not significant, whereas a model with a 1-subpopulation model and an exponential decline of kG was significantly better than a model with only 1 subpopulation (dOFV = −106.1; P < .00001). The AUC0-24h was found to significantly increase kkill with a linear relationship (dOFV = −88.7; P < .00001). An Emax or a sigmoidal Emax model did not decrease OFV as compared to the linear model. The baseline time to positivity was a significant covariate on the initial bacterial load (dOFV = −357.0; P < .00001), which was described using a power relationship. Model Evaluation The final semimechanistic time-to-event model described the observed data well according to a posterior predictive check (Figure 2). The predicted median time to positivity, based on the final model, agreed well with the observed median time to positivity in all dose groups. This was also seen when performing a visual predictive check (Supplementary Figure 1). The parameter estimates and corresponding precision are shown in Table 2. The parameter precision was low overall. Table 2. Parameter Estimates From the Final Semimechanistic Time-to-Event Model Model, Parameter  Description  Estimate (90% Confidence Intervala)  Sputum model       B0,sputum (risk·day-1)b  Baseline bacterial load  1.40 × 10–4 (1.67 × 10–5–8.78 × 10–4)   ΘTTP  Effect of baseline time to positivity on B0  −7.13 (−9.30 to −5.18)   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 model       kG,base (day-1)  Baseline mycobacterial growth rate  4.90 (3.18–6.52)   kG,ss (day-1)  Steady-dstate mycobacterial growth rate  2.74 (1.57–3.78)   kG,k (day-1)  Rate constant for decrease of mycobacterial growth rate  0.580 (.387–.870)   Bmax (risk·day-1)b  Maximal bacterial load in liquid container  0.523 (.459–.665)  Model, Parameter  Description  Estimate (90% Confidence Intervala)  Sputum model       B0,sputum (risk·day-1)b  Baseline bacterial load  1.40 × 10–4 (1.67 × 10–5–8.78 × 10–4)   ΘTTP  Effect of baseline time to positivity on B0  −7.13 (−9.30 to −5.18)   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 model       kG,base (day-1)  Baseline mycobacterial growth rate  4.90 (3.18–6.52)   kG,ss (day-1)  Steady-dstate mycobacterial growth rate  2.74 (1.57–3.78)   kG,k (day-1)  Rate constant for decrease of mycobacterial growth rate  0.580 (.387–.870)   Bmax (risk·day-1)b  Maximal bacterial load in liquid container  0.523 (.459–.665)  The mathematical structure for the final model is as follows: B(tt)sputum=B0,sputum×(TTPbaselinemedian(TTPbaseline))ΘTTP×e−kkill×AUC0−24h×tt (sputum model), dBculturedtc=(kG,base+(kG,ss−kG,base)×(1−e−kG,k×tt))×(Bmax−B(tc)culture)×Bculture (mycobacterial growth model), and h(tc)=B(tc)culture (hazard model). aObtained from a 1000-sample nonparametric bootstrap. bRisk refers to risk of a positive signal from the liquid culture system. View Large Table 2. Parameter Estimates From the Final Semimechanistic Time-to-Event Model Model, Parameter  Description  Estimate (90% Confidence Intervala)  Sputum model       B0,sputum (risk·day-1)b  Baseline bacterial load  1.40 × 10–4 (1.67 × 10–5–8.78 × 10–4)   ΘTTP  Effect of baseline time to positivity on B0  −7.13 (−9.30 to −5.18)   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 model       kG,base (day-1)  Baseline mycobacterial growth rate  4.90 (3.18–6.52)   kG,ss (day-1)  Steady-dstate mycobacterial growth rate  2.74 (1.57–3.78)   kG,k (day-1)  Rate constant for decrease of mycobacterial growth rate  0.580 (.387–.870)   Bmax (risk·day-1)b  Maximal bacterial load in liquid container  0.523 (.459–.665)  Model, Parameter  Description  Estimate (90% Confidence Intervala)  Sputum model       B0,sputum (risk·day-1)b  Baseline bacterial load  1.40 × 10–4 (1.67 × 10–5–8.78 × 10–4)   ΘTTP  Effect of baseline time to positivity on B0  −7.13 (−9.30 to −5.18)   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 model       kG,base (day-1)  Baseline mycobacterial growth rate  4.90 (3.18–6.52)   kG,ss (day-1)  Steady-dstate mycobacterial growth rate  2.74 (1.57–3.78)   kG,k (day-1)  Rate constant for decrease of mycobacterial growth rate  0.580 (.387–.870)   Bmax (risk·day-1)b  Maximal bacterial load in liquid container  0.523 (.459–.665)  The mathematical structure for the final model is as follows: B(tt)sputum=B0,sputum×(TTPbaselinemedian(TTPbaseline))ΘTTP×e−kkill×AUC0−24h×tt (sputum model), dBculturedtc=(kG,base+(kG,ss−kG,base)×(1−e−kG,k×tt))×(Bmax−B(tc)culture)×Bculture (mycobacterial growth model), and h(tc)=B(tc)culture (hazard model). aObtained from a 1000-sample nonparametric bootstrap. bRisk refers to risk of a positive signal from the liquid culture system. View Large Figure 2. View largeDownload slide Posterior predictive check for median time to positivity in each observed rifampicin dose group. Shaded areas are 90% prediction intervals from 1000 simulated trials. Figure 2. View largeDownload slide Posterior predictive check for median time to positivity in each observed rifampicin dose group. Shaded areas are 90% prediction intervals from 1000 simulated trials. Clinical Trial Simulation of Pharmacokinetics and Time to Positivity After 45 and 50 mg/kg Rifampicin The predictions of early bactericidal activity after receipt of 45 and 50 mg/kg rifampicin are summarized in Figure 3 and Table 3 as 90% prediction intervals for the median change in the baseline time to positivity at day 7. The observed median values are included to provide a point of reference. The median simulated day 7 AUC0-24h values (Table 3) displayed larger relative increases in AUC0-24h than the relative increases in dose, owing to dose-dependent bioavailability and saturable elimination [4, 27]. Table 3. Predicted Day 7 Change From the Baseline Time to Positivity and Predicted Day 7 Area Under the Plasma Concentration-Time Curve During 24 Hours (AUC0-24h) Dose, mg/kg  Change From Baseline Time to Positivity, d, Median  Day 7 AUC0-24h, h·mg/L, Median  Observed  Predicteda  Predicted  Percentage Increase From 10-mg/kg Dose  10  2.38  2.11–3.97  42.8  …  20  3.87  3.03–4.49  139.2  225.2  25  4.31  3.26–4.85  172.7  303.5  30  5.42  3.63–5.16  226.3  429.4  35  4.51  4.07–5.76  286.2  568.7  40  5.89  4.37–6.30  338.7  691.4  45  …  4.86–6.85  413.2  865.4  50  …  5.32–7.48  481.4  1024.8  Dose, mg/kg  Change From Baseline Time to Positivity, d, Median  Day 7 AUC0-24h, h·mg/L, Median  Observed  Predicteda  Predicted  Percentage Increase From 10-mg/kg Dose  10  2.38  2.11–3.97  42.8  …  20  3.87  3.03–4.49  139.2  225.2  25  4.31  3.26–4.85  172.7  303.5  30  5.42  3.63–5.16  226.3  429.4  35  4.51  4.07–5.76  286.2  568.7  40  5.89  4.37–6.30  338.7  691.4  45  …  4.86–6.85  413.2  865.4  50  …  5.32–7.48  481.4  1024.8  a90% prediction interval, based on 1000 simulated data sets. View Large Table 3. Predicted Day 7 Change From the Baseline Time to Positivity and Predicted Day 7 Area Under the Plasma Concentration-Time Curve During 24 Hours (AUC0-24h) Dose, mg/kg  Change From Baseline Time to Positivity, d, Median  Day 7 AUC0-24h, h·mg/L, Median  Observed  Predicteda  Predicted  Percentage Increase From 10-mg/kg Dose  10  2.38  2.11–3.97  42.8  …  20  3.87  3.03–4.49  139.2  225.2  25  4.31  3.26–4.85  172.7  303.5  30  5.42  3.63–5.16  226.3  429.4  35  4.51  4.07–5.76  286.2  568.7  40  5.89  4.37–6.30  338.7  691.4  45  …  4.86–6.85  413.2  865.4  50  …  5.32–7.48  481.4  1024.8  Dose, mg/kg  Change From Baseline Time to Positivity, d, Median  Day 7 AUC0-24h, h·mg/L, Median  Observed  Predicteda  Predicted  Percentage Increase From 10-mg/kg Dose  10  2.38  2.11–3.97  42.8  …  20  3.87  3.03–4.49  139.2  225.2  25  4.31  3.26–4.85  172.7  303.5  30  5.42  3.63–5.16  226.3  429.4  35  4.51  4.07–5.76  286.2  568.7  40  5.89  4.37–6.30  338.7  691.4  45  …  4.86–6.85  413.2  865.4  50  …  5.32–7.48  481.4  1024.8  a90% prediction interval, based on 1000 simulated data sets. View Large Figure 3. View largeDownload slide Model predictions of the day 7 median change from baseline time to positivity for different doses of rifampicin monotherapy. The shaded area is a 90% prediction interval based on 1000 simulated trials. No model fit was performed for this plot; the observed data are just overlaid over the predictions. Figure 3. View largeDownload slide Model predictions of the day 7 median change from baseline time to positivity for different doses of rifampicin monotherapy. The shaded area is a 90% prediction interval based on 1000 simulated trials. No model fit was performed for this plot; the observed data are just overlaid over the predictions. The final semimechanistic time-to-event model predicted a bacterial kill rate in sputum of 0.0608 days-1 (90% confidence interval [CI], .0345–.0882 days-1) at a median predicted AUC0-24h of 42.8 hours·mg/L for 10 mg/kg rifampicin, which is considerably lower than 0.481 days-1 (90% CI, .273–.698 days-1) at 338.7 hours·mg/L for 40 mg/kg rifampicin. This corresponds to bacterial elimination half-lives of 11.4 and 1.44 days, respectively. In other words, the kill rate of the 40-mg/kg regimen was 7.9 times faster than that of the 10-mg/kg regimen, and the AUC0-24h for the 40-mg/kg regimen was 7.9 times higher than that of the 10-mg/kg regimen. For 50 mg/kg, the model predicted a median AUC0-24h of 481 hours·mg/L, which corresponds to a bacterial kill rate of 0.684 days-1 (90% CI, .388–.991 days-1; half-life of bacterial elimination, 1.01 days). The exposure predictions are summarized in more detail in Supplementary Figure 2. Supplementary Table 1 summarizes the simulated AUC0-24h values. Supplementary Figure 3 summarizes the complete time course of the predicted median time to positivity. DISCUSSION Our semimechanistic time-to-event model was developed to describe early bactericidal activity, using time-to-positivity measurements from patients with pulmonary tuberculosis treated with 10–40 mg/kg rifampicin. A statistically significant exposure-response relationship was detected between rifampicin and the bacterial kill rate in sputum, resulting in greater early bactericidal activity at higher exposures. The exposure-response relationship was not detected using conventional statistical analysis. One likely explanation for this is that, in contrast to conventional statistical analyses, we used pharmacokinetic-pharmacodynamic modeling, which has been shown to be more powerful than conventional statistical methods. Another possible explanation is that we used a time-to-event approach, which is reflective of time-to-positivity data. The final model described the observed data well and was used for clinical trial simulations to predict early bactericidal activity following receipt of 50 mg/kg rifampicin. The clinical trial simulations of 45 and 50 mg/kg predicted a further increase in early bactericidal activity, compared with 40 mg/kg (the highest observed dose). The predicted pharmacokinetic exposure (AUC0-24h) at day 7, which drove the increase in early bactericidal activity, yielded a disproportionally greater increase than the increase in dose (Table 3) [27]. The predicted early bactericidal activity, expressed as a day 7 median increase in time to positivity, was 4.37–6.30 days (90% prediction interval) for 40 mg/kg rifampicin, compared with 2.11–3.97 days for 10 mg/kg rifampicin (Table 3). The early bactericidal activity for 40 mg/kg is clearly greater than that for 10 mg/kg, but this increase in early bactericidal activity (about 2-fold) is smaller than the relative increase in predicted exposure (almost 8-fold) between 10 and 40 mg/kg (Table 3). This may appear unexpectedly low since the final model includes a linear exposure-response relationship between exposure and bacterial kill rate in sputum, which means, for example, that an 8-fold greater AUC0-24h will yielded an 8-fold increase in bacterial kill rate. However, the bacterial kill rate in sputum does not have a linear relationship with the day 7 increase in time to positivity. In this work, the bacterial loads in sputum and liquid culture are reported as a probability per unit time (ie, the risk of a sample testing positive per day), which is difficult to interpret. This is because the model was built using only time-to-positivity measurements. The MGIT manual states that the liquid culture container contains approximately 105–106 colony-forming units/mL when the system signals a positive finding, which may reflect the Bmax (ie, the maximal bacterial load in the liquid culture container). The numbers presented as a risk per unit time bear no meaning as such, but they can be viewed on a relative scale by looking at the percentage change in bacterial load from the initial load. The data support a linear exposure-response relationship between the rifampicin AUC0-24h and the bacterial kill rate in sputum. This implies that the model predicts an increased time to positivity for any increase in AUC0-24h. However, the model cannot predict a dose for which no further increase in early bactericidal activity is expected, nor can it predict limitations arising from intolerability or adverse events with higher doses. The Emax model [28 p1057] can be used to predict maximal effect doses, but it was not supported by the data. When the Emax model cannot be supported in favor of a linear model, it may indicate that the data (or doses/exposures) do not cover the upper end of a sigmoidal exposure-response curve. Thus, our results indicate that 40 mg/kg is located in the ascending part of the exposure-response curve, which agrees with findings from in vitro, in vivo, and clinical studies [13, 29]. Once data for 50 mg/kg become available, the model can be updated to see whether an Emax model can be identified. Our results suggest overlapping distributions of individual predicted times to positivity between 45 and 50 mg/kg (Figure 3), which were also reflected in the simulated pharmacokinetic exposures (Supplementary Figure 2). Given this large overlap in response (and exposure), it may be rational to include only 50 mg/kg in a future clinical trial. This exemplifies a strength of modeling and simulation and how it can be used to improve the design of clinical trials. The pharmacokinetic parameters of the nonlinear relation of elimination with respect to dose were estimated with high precision [27]. As such, the predicted exposures at high doses are regarded as reliable. Interindividual variability or interoccasion variability were not supported by the final model, which may be because the variability was low or because the data were unable to support such variability. However, variability was included through baseline time to positivity and through rifampicin exposure, which were included as covariates in the final model. Similar model structures for other models of time to positivity exist [18, 19]. Chigutsa et al [18] included 2 mycobacterial subpopulations, whereas our model includes 1. In contrast to our study (83 patients during 1 week), Chigutsa et al performed a longer and larger trial (140 patients during 8 weeks), using standard drug combination. A biphasic pattern in the time-to-positivity data over time on treatment is probably necessary to support two mycobacterial subpopulations. Time-to-positivity data following rifampicin in monotherapy may be less biphasic than the standard drug combination modeled elsewhere [18], which gave insufficient support for 2 mycobacterial subpopulations in our model. To detect biphasic killing, the treatment must have pronounced killing of multiple mycobacterial subpopulations, which may be the case for the standard combination therapy but not for rifampicin monotherapy. The mycobacterial growth rate in the MGIT system decreased with time in our model, similar to the report by Chigutsa et al [18]. In the model by Svensson and Karlsson [19], the growth rate was constant. Despite the use of time to positivity to develop the latter model, the predicted bacterial load was reported as the number of bacteria per milliliter of sputum. This contrasts with our model, in which the bacterial load is presented in terms of a probability per unit time. Svensson and Karlsson were able to use the number of bacteria per milliliter because many samples in their study were negative and because they made a series of assumptions that facilitated this choice [19]. In our data set, 8 samples were negative, which was too few to allow us to use the approach by Svensson and Karlsson and predict the bacterial load in terms of the number of bacteria per milliliter. Simpler models for time-to-positivity data use linear or bilinear regression with time as the independent variable and treat time to positivity as a continuous variable including repeated measurements [16, 30–32]. Different treatments, doses or exposures can be explored as predictors for coefficients for increase in time to positivity. However, these simpler regression-based models have been shown to be less powerful than model-based pharmacokinetic-pharmacodynamic methods for finding exposure-response relationship for tuberculosis [20]. This is further supported by our semimechanistic time-to-event analysis which could demonstrate exposure-response relationship, but the conventional regression-based statistical analysis did not [4]. Day 7 AUC0-24h was a covariate for the rate of decline of bacterial load in sputum. Rifampicin has time-dependent pharmacokinetics (due to autoinduction), and the AUC0-24h will gradually decrease from day 1 and onward [27]. This was a potential source of bias since the extent and time course of autoinduction may differ between doses. We have however shown (in the same patients) that autoinduction is similar between dose groups (extent and time course) [27]. In this work, we chose not to use the predicted AUC0-24h on day 1 as this only shifts the value for the coefficient for the bacterial decline (kkill) without altering the predictions. The noncompartmental analysis AUC0-24h (ie, non–model based) was used here as a secondary summary variable for the pharmacokinetic exposure and input to the semimechanistic time-to-event model. Alternatively, model-based AUC0-24h could be used as input, using the previously developed population pharmacokinetic model [27]. The noncompartmental analysis AUC0-24h was however calculated from a full pharmacokinetic curve and with such rich sampling, noncompartmental analysis AUC0-24h is expected to perform similar to model-based AUC0-24h. The model was built on time-to-positivity data from patients treated for 7 days with daily rifampicin. We have used the model for extrapolation in terms of predicting early bactericidal activity for 7 days for an increased dose (50 mg/kg), but we are unable to predict activity longer than 7 days. While our findings are certainly not discouraging for the exploration of even higher doses, no association with sterilizing activity can be made. This study defines a statistically significant short-term exposure-response relationship for up to 40 mg/kg rifampicin and shows that a further increase in early bactericidal activity can be expected beyond 40 mg/kg. In conclusion, this study has established the exposure-response relationship between rifampicin exposure of 10–40 mg/kg and an increase in early bactericidal activity, determined using time to positivity. These results give further weight to studying higher doses of rifampicin in longer and larger clinical trials. Model-based clinical trial simulations of pharmacokinetics and time to positivity following receipt of 50 mg/kg rifampicin predict a further increase in early bactericidal activity, compared with 40 mg/kg rifampicin. Supplementary Data Supplementary materials are available at The Journal of Infectious Diseases online. Consisting of data provided by the authors to benefit the reader, the posted materials are not copyedited and are the sole responsibility of the authors, so questions or comments should be addressed to the corresponding author. Acknowledgments. We thank the patients and site staff for their participation in the underlying study. Financial support. This work was supported by the Swedish Research Council (grant 521-2011-3442 to R. J. S. and U. S. H. S.), the Innovative Medicines Initiative Joint Undertaking (award 115337, with contribution from the European Union’s Seventh Framework Programme [FP7/2007–2013] and the European Federation of Pharmaceutical Industries and Associations [in-kind contribution]), the European and Developing Countries Clinical Trials Partnership (awards IP.2007.32011.011, IP.2007.32011.012, and IP.2007.32011.013), the Netherlands-African Partnership for Capacity Development and Clinical Interventions Against Poverty-Related Diseases, and the Bill and Melinda Gates Foundation. Potential conflicts of interest. All authors: No reported conflicts of interest. All authors have submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest. Conflicts that the editors consider relevant to the content of the manuscript have been disclosed. 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Greater Early Bactericidal Activity at Higher Rifampicin Doses Revealed by Modeling and Clinical Trial Simulations

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Oxford University Press
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© The Author(s) 2018. Published by Oxford University Press for the Infectious Diseases Society of America. All rights reserved. For permissions, e-mail: journals.permissions@oup.com.
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0022-1899
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1537-6613
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10.1093/infdis/jiy242
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Abstract

Abstract Background The currently recommended rifampicin dose (10 mg/kg) for treating tuberculosis is suboptimal. The PanACEA HIGHRIF1 trial evaluated the pharmacokinetics and early bactericidal activity of rifampicin doses of up to 40 mg/kg. Conventional statistical analyses revealed no significant exposure-response relationship. Our objectives were to explore the exposure-response relationship for high-dose rifampicin by using pharmacokinetic-pharmacodynamic modeling and to predict the early bactericidal activity of 50 mg/kg rifampicin. Methods Data included time to Mycobacterium tuberculosis positivity of liquid cultures of sputum specimens from 83 patients with tuberculosis who were treated with 10 mg/kg rifampicin (n = 8; reference arm) or 20, 25, 30, 35, or 40 mg/kg rifampicin (n = 15/arm) for 7 days. We used a semimechanistic time-to-event approach to model the time-to-positivity data. Rifampicin exposure and baseline time to culture positivity were explored as covariates. Results The baseline time to culture positivity was a significant covariate on the predicted initial bacterial load, and rifampicin exposure was a significant covariate on the bacterial kill rate in sputum resulting in increased early bactericidal activity. The 90% prediction interval for the predicted median day 7 increase in time to positivity for 50 mg/kg rifampicin was 7.25–10.3 days. Conclusions A significant exposure-response relationship was found between rifampicin exposure and early bactericidal activity. Clinical trial simulations showed greater early bactericidal activity for 50 mg/kg rifampicin. Clinical Trials Registration NCT01392911. Pharmacodynamics, tuberculosis, pharmacokinetics, patients, time to positivity, early bactericidal activity, models, bactericidal effect, Mycobacterium tuberculosis Since the concept of increasing the rifampicin dose for treating tuberculosis was reintroduced, a battery of trials has been conducted to optimize treatment of pulmonary tuberculosis and tuberculous meningitis [1–9]. Despite this, a question remains: what is the optimal dose of rifampicin [10, 11]? The answer remains unknown, but recent clinical trials have provided important insight. The PanACEA HIGHRIF1 trial [4] studied the short-term safety, pharmacokinetics, and antimycobacterial activity of rifampicin doses of up to 40 mg/kg. No statistically significant relationship was determined between rifampicin exposure and early bactericidal activity [4] in humans despite several lines of evidence derived from in vitro and animal experiments suggesting a clear relationship between exposure and mycobacterial killing [12–15]. Early bactericidal activity can be quantified using time to positivity in liquid culture, which is defined as the time from the start of incubation of a sputum specimen in a liquid culture system to the detection of a positive signal A high bacterial load is expected to lead to a short time to positivity and vice versa. Time to positivity reflects time-to-event data. For conventional statistical analysis, early bactericidal activity determined using time to positivity is usually analyzed in the context of a series of data points from daily sputum cultures as the change in time to positivity per day of treatment by regression-based methods [16, 17]. Two semimechanistic pharmacokinetic-pharmacodynamic models exist that treat time to positivity as time-to-event data [18, 19]. Model-based pharmacokinetic-pharmacodynamic analysis has been shown to be more powerful for defining the exposure-response relationship than conventional statistical methods [20]. Semimechanistic pharmacokinetic-pharmacodynamic models also allow for extrapolation by simulating new scenarios, such as predicting the early bactericidal activity of higher-than-observed doses, which can be used to design future clinical trials. Our objective was to use a semimechanistic time-to-event approach to explore the exposure-response relationship for early bactericidal activity, determined using the time to Mycobacterium tuberculosis positivity, in patients with pulmonary tuberculosis treated with high-dose rifampicin (up to 40 mg/kg) and then to simulate the early bactericidal activity of 45 and 50 mg/kg rifampicin, to inform the clinical development process of optimizing a higher rifampicin dose. METHODS Ethics The study was approved by local ethical review boards and by the Medicines Control Council of South Africa and was conducted according to good clinical practice. All patients provided written informed consent before enrollment in the study. Patient Data Modeling was performed on 1-week repeated time-to-positivity data measured in sputum specimens from patients recruited in the HIGHRIF1 trial, a prospective open-label multiple rising dose trial (clinical trials registration NCT01392911) [4]. Smear-positive patients with pulmonary tuberculosis were treated with 10 mg/kg rifampicin (n = 8; reference arm) or 20, 25, 30, 35, or 40 mg/kg rifampicin (n = 15/arm) as monotherapy daily for 7 days. The total study duration was 14 days, with standard doses of isoniazid, pyrazinamide, and ethambutol therapy added to high-dose rifampicin treatment on days 8–14. In this analysis, only data until day 7 were used, to define the exposure-response relationship for rifampicin alone. Overnight sputum sampling was performed on 2 consecutive days at baseline and then daily for 7 days. The time to positivity was determined in duplicate for each sample, using a standardized liquid culture system (BD Bactec MGIT 960 Mycobacterial Growth Indicator Tube system; Becton-Dickinson, Sparks, MD) in a single laboratory. The HIGHRIF1 trial is described in detail elsewhere [4]. Data Analysis Time-to-positivity data were analyzed with a time-to-event approach, using the nonlinear mixed-effects modeling software NONMEM 7.3 [21] with the Laplacian estimation method. Data handling and visualization were done in R, version 3.4.3 [22]. Model diagnostic evaluations were performed in Xpose 4.6.0 [23, 24], with visual predictive checks performed using PsN 4.6.12 [23, 25]. Models were compared on the basis of the objective function value (OFV), using the likelihood ratio test at a 5% significance level. Time-to-positivity replicates at each time point were analyzed without averaging. The baseline time to positivity was included in the model as a covariate (see below). Structural Model The starting point for model development was a previously developed semimechanistic time-to-event model for time to positivity [19]. Briefly, the model structure was derived from underlying knowledge about (1) how the amount of viable tuberculosis bacteria changes in human sputum over time, referred to as the “sputum model”; (2) how tuberculosis bacteria are known to grow in a liquid culture, referred to as the “mycobacterial growth model”; and (3) how the mycobacterial growth relates to the probability of achieving a positive signal event in the MGIT system, referred to as the “hazard model.” The starting model included drug effect without an exposure-response relationship. Sputum models with 1 and 2 mycobacterial subpopulations were tested. The bacterial load in the single mycobacterial subpopulation model was described by  B(tt)sputum=B0,sputum×e−kkill×tt where B0,sputum is the predicted bacterial load at the start of treatment, kkill is the first-order rifampicin bacterial kill rate, and tt is the time after the start of treatment. For the 2-subpopulation model, the bacterial loads of the first (B1) and second (B2) mycobacterial subpopulations were described by   B1(tt)sputum=B10,sputum×e−kkill,1×tt and  B2(tt)sputum=B20,sputum×e−kkill,2×tt where  B(tt)sputum=B1(tt)sputum+B2(tt)sputum where B10,sputum and B20,sputum denote the predicted bacterial loads at the start of treatment for subpopulations 1 and 2, respectively. Parameters kkill,1 and kkill,2 describe the first-order rifampicin bacterial kill rates of subpopulations 1 and 2, respectively. For the mycobacterial growth model in the liquid culture container, a logistic growth model was used, where the change in the bacterial load in the liquid culture (Bculture) over time is described by  dBculturedtc=kG×(Bmax−B(tc)culture)×Bculture where the initial bacterial load in the liquid culture was assumed to be equal to the number of bacteria in sputum at the time of sputum sampling, according to  B(tc=0)culture=B(tt=sampling time point)sputum where kG is a predicted maximal mycobacterial growth rate in the liquid, Bmax is the maximal bacterial load in the liquid culture, and tc is the time after inoculation of the liquid culture. Models with 2 subpopulations in the liquid culture, with different growth rates for each subpopulation and both with and without a possible transfer between subpopulations, were explored. A lag time for the start of growth in the liquid culture was explored as a single lag time for both the 1- and 2-subpopulation models. Time dependencies in kG were explored, including linearly decreasing kG with the duration of treatment and an exponential decline from a baseline value of kG (kG,base) to a steady-state value of kG (kG,ss) according to  k(tt)G=kG,base+(kG,ss−kG,base)×(1−e−kG,k×tt) where kG,k is the first-order time-dependent decrease of kG,base. For the hazard model, the bacterial load in the liquid culture at any given time point was equal to the hazard, h(tc), for the liquid culture to turn into a positive signal, described by  h(tc)=B(tc)culture which was used in a next step to calculate the cumulative hazard according to  H(tc)=∫0tch(tc)dt This finally allowed calculation of the survival, which is the probability of a sample without a positive signal at time tc, using the following equation:  S(tc)=e−H(tc) Covariate Model The individual mean baseline time to positivity was not included in the estimation but was evaluated as a covariate on the predicted bacterial load at the start of treatment (B0,sputum or B10,sputum and B20,sputum) as a power relationship. The area under the plasma concentration-time curve between 0 and 24 hours (AUC0-24h) at day 7 was evaluated as a covariate on the rifampicin kill rate parameters (kkill or kkill,1 and kkill,2). The AUC0-24h was chosen over the maximum concentration (Cmax) because the AUC is normally used in pharmacokinetic-pharmacodynamic analyses of rifampicin. Cmax and AUC0-24h are probably highly correlated and would therefore perform similarly when explored in a pharmacokinetic-pharmacodynamic model. Since only once-daily dosing was included in the current study design, it would probably be difficult to distinguish between Cmax and AUC0-24h. The AUC0-24h was calculated for each subject on the basis of concentration measurements at 0, 0.5, 1, 1.5, 2, 3, 4, 6, 8, 12, and 24 hours, using the linear-log trapezoidal rule in Winnonlin, version 5.3 (Pharsight, Mountain View, CA), as described elsewhere [4]. Concentrations were measured using validated ultra performance liquid chromatography (accuracy, <4%; limit of quantification, 0.13 mg/L). Stochastic Model Interindividual variability was investigated in all parameters for the sputum model, as well as for the estimated lag time for the growth in the mycobacterial growth model. Interoccasion variability in sputum sampling was investigated as random variability between occasions for the bacterial load inoculated in the mycobacterial growth model [19]. Model Evaluation The final semimechanistic time-to-event model (ie, the chosen model after structural, covariate, and stochastic model evaluations) was evaluated by performing a 1000-sample bootstrap stratified on dose group to attain parameter uncertainty. A posterior predictive check was performed by comparing the median time to positivity calculated from 1000 simulated trials to the observed median time to positivity. Clinical Trial Simulation of Pharmacokinetics and Time to Positivity After Receipt of 45 or 50 mg/kg Rifampicin The final semimechanistic time-to-event model was used for clinical trial simulation of time to positivity following receipt of 45 or 50 mg/kg rifampicin once daily for 7 days. Pharmacokinetics as the driver for increasing time to positivity was simulated for 45 and 50 mg/kg, and the day 7 AUC0-24h was calculated by means of the linear-log trapezoidal rule in ncappc 0.2.1.1, within R [26], from 1000 simulated data sets, using a pharmacokinetic model developed with data from the same patients used in this analysis [27]. To simulate pharmacokinetics, patient covariates were sampled from the observed population in a bootstrap procedure. The AUC0-24h values from the 1000 simulations were used to predict the time to positivity after receipt of the 45 and 50 mg/kg rifampicin regimens. Baseline times to positivity for the simulations were sampled from a log-normal distribution centered around 4.34 days and with a standard deviation of 0.32 days (estimated from the observed data set). The same study design as for the HIGHRIF1 trial was used (ie, 15 individuals/dose) [4]. RESULTS Patients and Data In total, 83 patients and 1102 time-to-positivity measurements were analyzed. A few samples (5.2%) were excluded from the analysis; 52 samples (collected on various treatment days) were contaminated, and 8 samples were negative for M. tuberculosis (all were collected before day 7 and were followed by positive samples collected on later treatment days). Patient characteristics are summarized in Table 1. Table 1. Baseline Patient Characteristics, by Rifampicin Dose Parameter  Overall (n = 83)  10 mg/kg (n = 8)  20 mg/kg (n = 15)  25 mg/kg (n = 15)  30 mg/kg (n = 15)  35 mg/kg (n = 15)  40 mg/kg (n = 15)  Weight, kg  53.9 (40.2–84.2)  56.9 (46.8–64.9)  52.6 (41.8–62.7)  52.8 (40.2–67.9)  54.0 (45.7–84.2)  57.0 (40.5–74.0)  58.9 (46.7–64.8)  Age, y  31.0 (18.0–59.0)  27.5 (19.0–49.0)  27.0 (18.0–46.0)  25.0 (19.0–46.0)  40.0 (19.0–59.0)  37.0 (21.0–59.0)  34.0 (23.0–58.0)  Body mass indexa  19.4 (14.7–30.9)  20.5 (15.8–26.3)  18.6 (16.8–26.2)  19.3 (15.1–25.2)  20.9 (16.4–30.9)  19.4 (14.7–25.2)  19.4 (17.2–19.4)  Male sex  59 (71.1)  6 (75.0)  11 (73.3)  10 (66.7)  11 (73.3)  10 (66.7)  11 (73.3)  Raceb                 Black  38 (45.8)  3 (37.5)  7 (46.7)  4 (26.4)  9 (60.0)  5 (33.3)  10 (66.7)   Colored  45 (54.2)  5 (62.5)  8 (53.3)  11 (73.3)  6 (40.0)  10 (66.7)  5 (33.3)  HIV infection  3 (3.6)  0 (0.0)  0 (0.0)  0 (0.0)  2 (13.3)  1 (6.7)  0 (0.0)  Baseline time to positivity, d  4.0 (2.2–18.2)  4.0 (3.3–5.2)  4.9 (3.0–9.1)  4.0 (3.4–6.5)  4.0 (2.9–6.3)  3.9 (2.6–18.2)  4.0 (2.2–7.6)  Day 7 AUC0-24h, h·mg/L  241 (34–847)  43 (34–53)  155 (96–221)  178 (134–380)  298 (177–781)  321 (145–555)  357 (201–847)  Parameter  Overall (n = 83)  10 mg/kg (n = 8)  20 mg/kg (n = 15)  25 mg/kg (n = 15)  30 mg/kg (n = 15)  35 mg/kg (n = 15)  40 mg/kg (n = 15)  Weight, kg  53.9 (40.2–84.2)  56.9 (46.8–64.9)  52.6 (41.8–62.7)  52.8 (40.2–67.9)  54.0 (45.7–84.2)  57.0 (40.5–74.0)  58.9 (46.7–64.8)  Age, y  31.0 (18.0–59.0)  27.5 (19.0–49.0)  27.0 (18.0–46.0)  25.0 (19.0–46.0)  40.0 (19.0–59.0)  37.0 (21.0–59.0)  34.0 (23.0–58.0)  Body mass indexa  19.4 (14.7–30.9)  20.5 (15.8–26.3)  18.6 (16.8–26.2)  19.3 (15.1–25.2)  20.9 (16.4–30.9)  19.4 (14.7–25.2)  19.4 (17.2–19.4)  Male sex  59 (71.1)  6 (75.0)  11 (73.3)  10 (66.7)  11 (73.3)  10 (66.7)  11 (73.3)  Raceb                 Black  38 (45.8)  3 (37.5)  7 (46.7)  4 (26.4)  9 (60.0)  5 (33.3)  10 (66.7)   Colored  45 (54.2)  5 (62.5)  8 (53.3)  11 (73.3)  6 (40.0)  10 (66.7)  5 (33.3)  HIV infection  3 (3.6)  0 (0.0)  0 (0.0)  0 (0.0)  2 (13.3)  1 (6.7)  0 (0.0)  Baseline time to positivity, d  4.0 (2.2–18.2)  4.0 (3.3–5.2)  4.9 (3.0–9.1)  4.0 (3.4–6.5)  4.0 (2.9–6.3)  3.9 (2.6–18.2)  4.0 (2.2–7.6)  Day 7 AUC0-24h, h·mg/L  241 (34–847)  43 (34–53)  155 (96–221)  178 (134–380)  298 (177–781)  321 (145–555)  357 (201–847)  Data are median values (ranges) or no. (%) of patients. Abbreviations: AUC0-24h, area under the plasma concentration-time curve during 24 hours; HIV, human immunodeficiency virus. aCalculated as the weight in kilograms divided by the height in meters squared. b“Black” refers to African natives, and “colored” refers to a population group genetically descended from Southeast Asia. View Large Table 1. Baseline Patient Characteristics, by Rifampicin Dose Parameter  Overall (n = 83)  10 mg/kg (n = 8)  20 mg/kg (n = 15)  25 mg/kg (n = 15)  30 mg/kg (n = 15)  35 mg/kg (n = 15)  40 mg/kg (n = 15)  Weight, kg  53.9 (40.2–84.2)  56.9 (46.8–64.9)  52.6 (41.8–62.7)  52.8 (40.2–67.9)  54.0 (45.7–84.2)  57.0 (40.5–74.0)  58.9 (46.7–64.8)  Age, y  31.0 (18.0–59.0)  27.5 (19.0–49.0)  27.0 (18.0–46.0)  25.0 (19.0–46.0)  40.0 (19.0–59.0)  37.0 (21.0–59.0)  34.0 (23.0–58.0)  Body mass indexa  19.4 (14.7–30.9)  20.5 (15.8–26.3)  18.6 (16.8–26.2)  19.3 (15.1–25.2)  20.9 (16.4–30.9)  19.4 (14.7–25.2)  19.4 (17.2–19.4)  Male sex  59 (71.1)  6 (75.0)  11 (73.3)  10 (66.7)  11 (73.3)  10 (66.7)  11 (73.3)  Raceb                 Black  38 (45.8)  3 (37.5)  7 (46.7)  4 (26.4)  9 (60.0)  5 (33.3)  10 (66.7)   Colored  45 (54.2)  5 (62.5)  8 (53.3)  11 (73.3)  6 (40.0)  10 (66.7)  5 (33.3)  HIV infection  3 (3.6)  0 (0.0)  0 (0.0)  0 (0.0)  2 (13.3)  1 (6.7)  0 (0.0)  Baseline time to positivity, d  4.0 (2.2–18.2)  4.0 (3.3–5.2)  4.9 (3.0–9.1)  4.0 (3.4–6.5)  4.0 (2.9–6.3)  3.9 (2.6–18.2)  4.0 (2.2–7.6)  Day 7 AUC0-24h, h·mg/L  241 (34–847)  43 (34–53)  155 (96–221)  178 (134–380)  298 (177–781)  321 (145–555)  357 (201–847)  Parameter  Overall (n = 83)  10 mg/kg (n = 8)  20 mg/kg (n = 15)  25 mg/kg (n = 15)  30 mg/kg (n = 15)  35 mg/kg (n = 15)  40 mg/kg (n = 15)  Weight, kg  53.9 (40.2–84.2)  56.9 (46.8–64.9)  52.6 (41.8–62.7)  52.8 (40.2–67.9)  54.0 (45.7–84.2)  57.0 (40.5–74.0)  58.9 (46.7–64.8)  Age, y  31.0 (18.0–59.0)  27.5 (19.0–49.0)  27.0 (18.0–46.0)  25.0 (19.0–46.0)  40.0 (19.0–59.0)  37.0 (21.0–59.0)  34.0 (23.0–58.0)  Body mass indexa  19.4 (14.7–30.9)  20.5 (15.8–26.3)  18.6 (16.8–26.2)  19.3 (15.1–25.2)  20.9 (16.4–30.9)  19.4 (14.7–25.2)  19.4 (17.2–19.4)  Male sex  59 (71.1)  6 (75.0)  11 (73.3)  10 (66.7)  11 (73.3)  10 (66.7)  11 (73.3)  Raceb                 Black  38 (45.8)  3 (37.5)  7 (46.7)  4 (26.4)  9 (60.0)  5 (33.3)  10 (66.7)   Colored  45 (54.2)  5 (62.5)  8 (53.3)  11 (73.3)  6 (40.0)  10 (66.7)  5 (33.3)  HIV infection  3 (3.6)  0 (0.0)  0 (0.0)  0 (0.0)  2 (13.3)  1 (6.7)  0 (0.0)  Baseline time to positivity, d  4.0 (2.2–18.2)  4.0 (3.3–5.2)  4.9 (3.0–9.1)  4.0 (3.4–6.5)  4.0 (2.9–6.3)  3.9 (2.6–18.2)  4.0 (2.2–7.6)  Day 7 AUC0-24h, h·mg/L  241 (34–847)  43 (34–53)  155 (96–221)  178 (134–380)  298 (177–781)  321 (145–555)  357 (201–847)  Data are median values (ranges) or no. (%) of patients. Abbreviations: AUC0-24h, area under the plasma concentration-time curve during 24 hours; HIV, human immunodeficiency virus. aCalculated as the weight in kilograms divided by the height in meters squared. b“Black” refers to African natives, and “colored” refers to a population group genetically descended from Southeast Asia. View Large Semimechanistic Time-to-Event Model The final semimechanistic time-to-event model included 1 mycobacterial subpopulation, both for the sputum and mycobacterial growth models. The latter included a time-varying, exponentially declining kG. Figure 1 shows the dynamics within each submodel for a typical patient receiving 30 mg/kg. A statistically significant exposure-response relationship was identified: the parameter kkill was found to increase linearly with increasing AUC0-24h (yielding increased early bactericidal activity at higher rifampicin exposures). The baseline time to positivity was a significant covariate on the initial bacterial load in sputum, where a long time to positivity gave a low initial bacterial load. The final model did not include any random interindividual or interoccasion variability because it was not supported by the data. Figure 1. View largeDownload slide Dynamics of the sputum model (A), mycobacterial growth model (B), and hazard model (C) for a typical patient receiving a rifampicin dose of 30 mg/kg, with an area under the plasma concentration-time curve between 0 and 24 hours of 298 h·mg/L and a baseline time to positivity of 4 days. Open squares show the dynamics of an early (day 1) sample, and open triangles show the dynamics for a late (day 7) sample. Bsputum, predicted bacterial load in sputum; Bculture, predicted bacterial load in liquid culture. Figure 1. View largeDownload slide Dynamics of the sputum model (A), mycobacterial growth model (B), and hazard model (C) for a typical patient receiving a rifampicin dose of 30 mg/kg, with an area under the plasma concentration-time curve between 0 and 24 hours of 298 h·mg/L and a baseline time to positivity of 4 days. Open squares show the dynamics of an early (day 1) sample, and open triangles show the dynamics for a late (day 7) sample. Bsputum, predicted bacterial load in sputum; Bculture, predicted bacterial load in liquid culture. Implementation of 2 mycobacterial subpopulations in sputum was statistically significant as compared to having 1 subpopulation (dOFV = −37.5; P < .00001). However, adding a 2-subpopulation model to a model with time-varying kG was not significant, whereas a model with a 1-subpopulation model and an exponential decline of kG was significantly better than a model with only 1 subpopulation (dOFV = −106.1; P < .00001). The AUC0-24h was found to significantly increase kkill with a linear relationship (dOFV = −88.7; P < .00001). An Emax or a sigmoidal Emax model did not decrease OFV as compared to the linear model. The baseline time to positivity was a significant covariate on the initial bacterial load (dOFV = −357.0; P < .00001), which was described using a power relationship. Model Evaluation The final semimechanistic time-to-event model described the observed data well according to a posterior predictive check (Figure 2). The predicted median time to positivity, based on the final model, agreed well with the observed median time to positivity in all dose groups. This was also seen when performing a visual predictive check (Supplementary Figure 1). The parameter estimates and corresponding precision are shown in Table 2. The parameter precision was low overall. Table 2. Parameter Estimates From the Final Semimechanistic Time-to-Event Model Model, Parameter  Description  Estimate (90% Confidence Intervala)  Sputum model       B0,sputum (risk·day-1)b  Baseline bacterial load  1.40 × 10–4 (1.67 × 10–5–8.78 × 10–4)   ΘTTP  Effect of baseline time to positivity on B0  −7.13 (−9.30 to −5.18)   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 model       kG,base (day-1)  Baseline mycobacterial growth rate  4.90 (3.18–6.52)   kG,ss (day-1)  Steady-dstate mycobacterial growth rate  2.74 (1.57–3.78)   kG,k (day-1)  Rate constant for decrease of mycobacterial growth rate  0.580 (.387–.870)   Bmax (risk·day-1)b  Maximal bacterial load in liquid container  0.523 (.459–.665)  Model, Parameter  Description  Estimate (90% Confidence Intervala)  Sputum model       B0,sputum (risk·day-1)b  Baseline bacterial load  1.40 × 10–4 (1.67 × 10–5–8.78 × 10–4)   ΘTTP  Effect of baseline time to positivity on B0  −7.13 (−9.30 to −5.18)   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 model       kG,base (day-1)  Baseline mycobacterial growth rate  4.90 (3.18–6.52)   kG,ss (day-1)  Steady-dstate mycobacterial growth rate  2.74 (1.57–3.78)   kG,k (day-1)  Rate constant for decrease of mycobacterial growth rate  0.580 (.387–.870)   Bmax (risk·day-1)b  Maximal bacterial load in liquid container  0.523 (.459–.665)  The mathematical structure for the final model is as follows: B(tt)sputum=B0,sputum×(TTPbaselinemedian(TTPbaseline))ΘTTP×e−kkill×AUC0−24h×tt (sputum model), dBculturedtc=(kG,base+(kG,ss−kG,base)×(1−e−kG,k×tt))×(Bmax−B(tc)culture)×Bculture (mycobacterial growth model), and h(tc)=B(tc)culture (hazard model). aObtained from a 1000-sample nonparametric bootstrap. bRisk refers to risk of a positive signal from the liquid culture system. View Large Table 2. Parameter Estimates From the Final Semimechanistic Time-to-Event Model Model, Parameter  Description  Estimate (90% Confidence Intervala)  Sputum model       B0,sputum (risk·day-1)b  Baseline bacterial load  1.40 × 10–4 (1.67 × 10–5–8.78 × 10–4)   ΘTTP  Effect of baseline time to positivity on B0  −7.13 (−9.30 to −5.18)   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 model       kG,base (day-1)  Baseline mycobacterial growth rate  4.90 (3.18–6.52)   kG,ss (day-1)  Steady-dstate mycobacterial growth rate  2.74 (1.57–3.78)   kG,k (day-1)  Rate constant for decrease of mycobacterial growth rate  0.580 (.387–.870)   Bmax (risk·day-1)b  Maximal bacterial load in liquid container  0.523 (.459–.665)  Model, Parameter  Description  Estimate (90% Confidence Intervala)  Sputum model       B0,sputum (risk·day-1)b  Baseline bacterial load  1.40 × 10–4 (1.67 × 10–5–8.78 × 10–4)   ΘTTP  Effect of baseline time to positivity on B0  −7.13 (−9.30 to −5.18)   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 model       kG,base (day-1)  Baseline mycobacterial growth rate  4.90 (3.18–6.52)   kG,ss (day-1)  Steady-dstate mycobacterial growth rate  2.74 (1.57–3.78)   kG,k (day-1)  Rate constant for decrease of mycobacterial growth rate  0.580 (.387–.870)   Bmax (risk·day-1)b  Maximal bacterial load in liquid container  0.523 (.459–.665)  The mathematical structure for the final model is as follows: B(tt)sputum=B0,sputum×(TTPbaselinemedian(TTPbaseline))ΘTTP×e−kkill×AUC0−24h×tt (sputum model), dBculturedtc=(kG,base+(kG,ss−kG,base)×(1−e−kG,k×tt))×(Bmax−B(tc)culture)×Bculture (mycobacterial growth model), and h(tc)=B(tc)culture (hazard model). aObtained from a 1000-sample nonparametric bootstrap. bRisk refers to risk of a positive signal from the liquid culture system. View Large Figure 2. View largeDownload slide Posterior predictive check for median time to positivity in each observed rifampicin dose group. Shaded areas are 90% prediction intervals from 1000 simulated trials. Figure 2. View largeDownload slide Posterior predictive check for median time to positivity in each observed rifampicin dose group. Shaded areas are 90% prediction intervals from 1000 simulated trials. Clinical Trial Simulation of Pharmacokinetics and Time to Positivity After 45 and 50 mg/kg Rifampicin The predictions of early bactericidal activity after receipt of 45 and 50 mg/kg rifampicin are summarized in Figure 3 and Table 3 as 90% prediction intervals for the median change in the baseline time to positivity at day 7. The observed median values are included to provide a point of reference. The median simulated day 7 AUC0-24h values (Table 3) displayed larger relative increases in AUC0-24h than the relative increases in dose, owing to dose-dependent bioavailability and saturable elimination [4, 27]. Table 3. Predicted Day 7 Change From the Baseline Time to Positivity and Predicted Day 7 Area Under the Plasma Concentration-Time Curve During 24 Hours (AUC0-24h) Dose, mg/kg  Change From Baseline Time to Positivity, d, Median  Day 7 AUC0-24h, h·mg/L, Median  Observed  Predicteda  Predicted  Percentage Increase From 10-mg/kg Dose  10  2.38  2.11–3.97  42.8  …  20  3.87  3.03–4.49  139.2  225.2  25  4.31  3.26–4.85  172.7  303.5  30  5.42  3.63–5.16  226.3  429.4  35  4.51  4.07–5.76  286.2  568.7  40  5.89  4.37–6.30  338.7  691.4  45  …  4.86–6.85  413.2  865.4  50  …  5.32–7.48  481.4  1024.8  Dose, mg/kg  Change From Baseline Time to Positivity, d, Median  Day 7 AUC0-24h, h·mg/L, Median  Observed  Predicteda  Predicted  Percentage Increase From 10-mg/kg Dose  10  2.38  2.11–3.97  42.8  …  20  3.87  3.03–4.49  139.2  225.2  25  4.31  3.26–4.85  172.7  303.5  30  5.42  3.63–5.16  226.3  429.4  35  4.51  4.07–5.76  286.2  568.7  40  5.89  4.37–6.30  338.7  691.4  45  …  4.86–6.85  413.2  865.4  50  …  5.32–7.48  481.4  1024.8  a90% prediction interval, based on 1000 simulated data sets. View Large Table 3. Predicted Day 7 Change From the Baseline Time to Positivity and Predicted Day 7 Area Under the Plasma Concentration-Time Curve During 24 Hours (AUC0-24h) Dose, mg/kg  Change From Baseline Time to Positivity, d, Median  Day 7 AUC0-24h, h·mg/L, Median  Observed  Predicteda  Predicted  Percentage Increase From 10-mg/kg Dose  10  2.38  2.11–3.97  42.8  …  20  3.87  3.03–4.49  139.2  225.2  25  4.31  3.26–4.85  172.7  303.5  30  5.42  3.63–5.16  226.3  429.4  35  4.51  4.07–5.76  286.2  568.7  40  5.89  4.37–6.30  338.7  691.4  45  …  4.86–6.85  413.2  865.4  50  …  5.32–7.48  481.4  1024.8  Dose, mg/kg  Change From Baseline Time to Positivity, d, Median  Day 7 AUC0-24h, h·mg/L, Median  Observed  Predicteda  Predicted  Percentage Increase From 10-mg/kg Dose  10  2.38  2.11–3.97  42.8  …  20  3.87  3.03–4.49  139.2  225.2  25  4.31  3.26–4.85  172.7  303.5  30  5.42  3.63–5.16  226.3  429.4  35  4.51  4.07–5.76  286.2  568.7  40  5.89  4.37–6.30  338.7  691.4  45  …  4.86–6.85  413.2  865.4  50  …  5.32–7.48  481.4  1024.8  a90% prediction interval, based on 1000 simulated data sets. View Large Figure 3. View largeDownload slide Model predictions of the day 7 median change from baseline time to positivity for different doses of rifampicin monotherapy. The shaded area is a 90% prediction interval based on 1000 simulated trials. No model fit was performed for this plot; the observed data are just overlaid over the predictions. Figure 3. View largeDownload slide Model predictions of the day 7 median change from baseline time to positivity for different doses of rifampicin monotherapy. The shaded area is a 90% prediction interval based on 1000 simulated trials. No model fit was performed for this plot; the observed data are just overlaid over the predictions. The final semimechanistic time-to-event model predicted a bacterial kill rate in sputum of 0.0608 days-1 (90% confidence interval [CI], .0345–.0882 days-1) at a median predicted AUC0-24h of 42.8 hours·mg/L for 10 mg/kg rifampicin, which is considerably lower than 0.481 days-1 (90% CI, .273–.698 days-1) at 338.7 hours·mg/L for 40 mg/kg rifampicin. This corresponds to bacterial elimination half-lives of 11.4 and 1.44 days, respectively. In other words, the kill rate of the 40-mg/kg regimen was 7.9 times faster than that of the 10-mg/kg regimen, and the AUC0-24h for the 40-mg/kg regimen was 7.9 times higher than that of the 10-mg/kg regimen. For 50 mg/kg, the model predicted a median AUC0-24h of 481 hours·mg/L, which corresponds to a bacterial kill rate of 0.684 days-1 (90% CI, .388–.991 days-1; half-life of bacterial elimination, 1.01 days). The exposure predictions are summarized in more detail in Supplementary Figure 2. Supplementary Table 1 summarizes the simulated AUC0-24h values. Supplementary Figure 3 summarizes the complete time course of the predicted median time to positivity. DISCUSSION Our semimechanistic time-to-event model was developed to describe early bactericidal activity, using time-to-positivity measurements from patients with pulmonary tuberculosis treated with 10–40 mg/kg rifampicin. A statistically significant exposure-response relationship was detected between rifampicin and the bacterial kill rate in sputum, resulting in greater early bactericidal activity at higher exposures. The exposure-response relationship was not detected using conventional statistical analysis. One likely explanation for this is that, in contrast to conventional statistical analyses, we used pharmacokinetic-pharmacodynamic modeling, which has been shown to be more powerful than conventional statistical methods. Another possible explanation is that we used a time-to-event approach, which is reflective of time-to-positivity data. The final model described the observed data well and was used for clinical trial simulations to predict early bactericidal activity following receipt of 50 mg/kg rifampicin. The clinical trial simulations of 45 and 50 mg/kg predicted a further increase in early bactericidal activity, compared with 40 mg/kg (the highest observed dose). The predicted pharmacokinetic exposure (AUC0-24h) at day 7, which drove the increase in early bactericidal activity, yielded a disproportionally greater increase than the increase in dose (Table 3) [27]. The predicted early bactericidal activity, expressed as a day 7 median increase in time to positivity, was 4.37–6.30 days (90% prediction interval) for 40 mg/kg rifampicin, compared with 2.11–3.97 days for 10 mg/kg rifampicin (Table 3). The early bactericidal activity for 40 mg/kg is clearly greater than that for 10 mg/kg, but this increase in early bactericidal activity (about 2-fold) is smaller than the relative increase in predicted exposure (almost 8-fold) between 10 and 40 mg/kg (Table 3). This may appear unexpectedly low since the final model includes a linear exposure-response relationship between exposure and bacterial kill rate in sputum, which means, for example, that an 8-fold greater AUC0-24h will yielded an 8-fold increase in bacterial kill rate. However, the bacterial kill rate in sputum does not have a linear relationship with the day 7 increase in time to positivity. In this work, the bacterial loads in sputum and liquid culture are reported as a probability per unit time (ie, the risk of a sample testing positive per day), which is difficult to interpret. This is because the model was built using only time-to-positivity measurements. The MGIT manual states that the liquid culture container contains approximately 105–106 colony-forming units/mL when the system signals a positive finding, which may reflect the Bmax (ie, the maximal bacterial load in the liquid culture container). The numbers presented as a risk per unit time bear no meaning as such, but they can be viewed on a relative scale by looking at the percentage change in bacterial load from the initial load. The data support a linear exposure-response relationship between the rifampicin AUC0-24h and the bacterial kill rate in sputum. This implies that the model predicts an increased time to positivity for any increase in AUC0-24h. However, the model cannot predict a dose for which no further increase in early bactericidal activity is expected, nor can it predict limitations arising from intolerability or adverse events with higher doses. The Emax model [28 p1057] can be used to predict maximal effect doses, but it was not supported by the data. When the Emax model cannot be supported in favor of a linear model, it may indicate that the data (or doses/exposures) do not cover the upper end of a sigmoidal exposure-response curve. Thus, our results indicate that 40 mg/kg is located in the ascending part of the exposure-response curve, which agrees with findings from in vitro, in vivo, and clinical studies [13, 29]. Once data for 50 mg/kg become available, the model can be updated to see whether an Emax model can be identified. Our results suggest overlapping distributions of individual predicted times to positivity between 45 and 50 mg/kg (Figure 3), which were also reflected in the simulated pharmacokinetic exposures (Supplementary Figure 2). Given this large overlap in response (and exposure), it may be rational to include only 50 mg/kg in a future clinical trial. This exemplifies a strength of modeling and simulation and how it can be used to improve the design of clinical trials. The pharmacokinetic parameters of the nonlinear relation of elimination with respect to dose were estimated with high precision [27]. As such, the predicted exposures at high doses are regarded as reliable. Interindividual variability or interoccasion variability were not supported by the final model, which may be because the variability was low or because the data were unable to support such variability. However, variability was included through baseline time to positivity and through rifampicin exposure, which were included as covariates in the final model. Similar model structures for other models of time to positivity exist [18, 19]. Chigutsa et al [18] included 2 mycobacterial subpopulations, whereas our model includes 1. In contrast to our study (83 patients during 1 week), Chigutsa et al performed a longer and larger trial (140 patients during 8 weeks), using standard drug combination. A biphasic pattern in the time-to-positivity data over time on treatment is probably necessary to support two mycobacterial subpopulations. Time-to-positivity data following rifampicin in monotherapy may be less biphasic than the standard drug combination modeled elsewhere [18], which gave insufficient support for 2 mycobacterial subpopulations in our model. To detect biphasic killing, the treatment must have pronounced killing of multiple mycobacterial subpopulations, which may be the case for the standard combination therapy but not for rifampicin monotherapy. The mycobacterial growth rate in the MGIT system decreased with time in our model, similar to the report by Chigutsa et al [18]. In the model by Svensson and Karlsson [19], the growth rate was constant. Despite the use of time to positivity to develop the latter model, the predicted bacterial load was reported as the number of bacteria per milliliter of sputum. This contrasts with our model, in which the bacterial load is presented in terms of a probability per unit time. Svensson and Karlsson were able to use the number of bacteria per milliliter because many samples in their study were negative and because they made a series of assumptions that facilitated this choice [19]. In our data set, 8 samples were negative, which was too few to allow us to use the approach by Svensson and Karlsson and predict the bacterial load in terms of the number of bacteria per milliliter. Simpler models for time-to-positivity data use linear or bilinear regression with time as the independent variable and treat time to positivity as a continuous variable including repeated measurements [16, 30–32]. Different treatments, doses or exposures can be explored as predictors for coefficients for increase in time to positivity. However, these simpler regression-based models have been shown to be less powerful than model-based pharmacokinetic-pharmacodynamic methods for finding exposure-response relationship for tuberculosis [20]. This is further supported by our semimechanistic time-to-event analysis which could demonstrate exposure-response relationship, but the conventional regression-based statistical analysis did not [4]. Day 7 AUC0-24h was a covariate for the rate of decline of bacterial load in sputum. Rifampicin has time-dependent pharmacokinetics (due to autoinduction), and the AUC0-24h will gradually decrease from day 1 and onward [27]. This was a potential source of bias since the extent and time course of autoinduction may differ between doses. We have however shown (in the same patients) that autoinduction is similar between dose groups (extent and time course) [27]. In this work, we chose not to use the predicted AUC0-24h on day 1 as this only shifts the value for the coefficient for the bacterial decline (kkill) without altering the predictions. The noncompartmental analysis AUC0-24h (ie, non–model based) was used here as a secondary summary variable for the pharmacokinetic exposure and input to the semimechanistic time-to-event model. Alternatively, model-based AUC0-24h could be used as input, using the previously developed population pharmacokinetic model [27]. The noncompartmental analysis AUC0-24h was however calculated from a full pharmacokinetic curve and with such rich sampling, noncompartmental analysis AUC0-24h is expected to perform similar to model-based AUC0-24h. The model was built on time-to-positivity data from patients treated for 7 days with daily rifampicin. We have used the model for extrapolation in terms of predicting early bactericidal activity for 7 days for an increased dose (50 mg/kg), but we are unable to predict activity longer than 7 days. While our findings are certainly not discouraging for the exploration of even higher doses, no association with sterilizing activity can be made. This study defines a statistically significant short-term exposure-response relationship for up to 40 mg/kg rifampicin and shows that a further increase in early bactericidal activity can be expected beyond 40 mg/kg. In conclusion, this study has established the exposure-response relationship between rifampicin exposure of 10–40 mg/kg and an increase in early bactericidal activity, determined using time to positivity. These results give further weight to studying higher doses of rifampicin in longer and larger clinical trials. Model-based clinical trial simulations of pharmacokinetics and time to positivity following receipt of 50 mg/kg rifampicin predict a further increase in early bactericidal activity, compared with 40 mg/kg rifampicin. Supplementary Data Supplementary materials are available at The Journal of Infectious Diseases online. Consisting of data provided by the authors to benefit the reader, the posted materials are not copyedited and are the sole responsibility of the authors, so questions or comments should be addressed to the corresponding author. Acknowledgments. We thank the patients and site staff for their participation in the underlying study. Financial support. This work was supported by the Swedish Research Council (grant 521-2011-3442 to R. J. S. and U. S. H. S.), the Innovative Medicines Initiative Joint Undertaking (award 115337, with contribution from the European Union’s Seventh Framework Programme [FP7/2007–2013] and the European Federation of Pharmaceutical Industries and Associations [in-kind contribution]), the European and Developing Countries Clinical Trials Partnership (awards IP.2007.32011.011, IP.2007.32011.012, and IP.2007.32011.013), the Netherlands-African Partnership for Capacity Development and Clinical Interventions Against Poverty-Related Diseases, and the Bill and Melinda Gates Foundation. Potential conflicts of interest. All authors: No reported conflicts of interest. All authors have submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest. Conflicts that the editors consider relevant to the content of the manuscript have been disclosed. 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The Journal of Infectious DiseasesOxford University Press

Published: Apr 28, 2018

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