Model-Based Evaluation of Higher Doses of Rifampin Using a Semimechanistic Model Incorporating Autoinduction and Saturation of Hepatic Extraction

Abstract

Rifampin is a key sterilizing drug in the treatment of tuberculosis (TB). It induces its own metabolism, but neither the onset nor the extent of autoinduction has been adequately described. Currently, the World Health Organization recommends a rifampin dose of 8 to 12 mg/kg of body weight, which is believed to be suboptimal, and higher doses may potentially improve treatment outcomes. However, a nonlinear increase in exposure may be observed because of saturation of hepatic extraction and hence this should be taken into consideration when a dose increase is implemented. Intensive pharmacokinetic (PK) data from 61 HIV-TB-coinfected patients in South Africa were collected at four visits, on days 1, 8, 15, and 29, after initiation of treatment. Data were analyzed by population nonlinear mixed-effects modeling. Rifampin PKs were best described by using a transit compartment absorption and a well-stirred liver model with saturation of hepatic extraction, including a first-pass effect. Autoinduction was characterized by using an exponential-maturation model: hepatic clearance almost doubled from the baseline to steady state, with a half-life of around 4.5 days. The model predicts that increases in the dose of rifampin result in more-than-linear drug exposure increases as measured by the 24-h area under the concentration-time curve. Simulations with doses of up to 35 mg/kg produced results closely in line with those of clinical trials.

INTRODUCTION

Rifampin is a key drug in the treatment of tuberculosis (TB), and the World Health Organization (WHO) currently recommends weight-adjusted doses of 8 to 12 mg/kg daily. Despite its being used in the treatment of TB for nearly 50 years, there is evidence that current rifampin exposures may be suboptimal. Rifampin's efficacy is exposure dependent (1–3); therefore, the efficacy and toxicity of higher doses are under investigation. Recent reports show that larger doses of rifampin are well tolerated by humans (4) and may improve treatment outcomes, as well as reduce the treatment duration from the current 6 months (5, 6).

Rifampin is mainly hepatically cleared, and it undergoes extensive first-pass metabolism (7), whose saturation with higher doses has been reported since early pharmacokinetic (PK) studies (8). Thus, when the rifampin dose is increased above a certain level, a more-than-proportional increase in the plasma rifampin concentration results. Rifampin also induces its own metabolism via the pregnane X receptor (9), a phenomenon known as clearance autoinduction, resulting in less exposure at steady state than after a single dose.

Previous studies have proposed rifampin PK models (10), but those trying to characterize clearance autoinduction have done so mostly by relying on only two PK sampling occasions (11), which limited their ability to characterize the process. Nonlinearity in a dose-exposure relationship suggesting saturation of rifampin clearance has been reported (8). However, a population PK model has not jointly described the autoinduction and hepatic extraction (E_H) of rifampin. In this study, we analyzed rich data from an intensive sampling scheme to develop a rifampin PK model for TB patients that accounts for both clearance autoinduction and saturation of E_H. This model was then employed to explore changes in rifampin exposure when doses are increased beyond the currently recommended range.

MATERIALS AND METHODS

Study design and patient selection.

Extensive details of this study, including design, patient selection, and dose administration, have been reported before (12). Two four-drug fixed-dose combinations (FDCs) were administered; each tablet contained 150 mg of rifampin, 75 mg of isoniazid, 400 mg of pyrazinamide, and 275 mg of ethambutol. Patients received weight-adjusted doses for 5 days a week, from Monday to Friday, according to WHO guidelines (13), except 10 patients who received medication for 7 days a week. Thus, patients weighing 30 to 37 kg at the start of treatment received two FDC tablets per dose, while those weighing 38 to 54, 55 to 70, or >70 kg received three, four, or five FDC tablets, respectively. Efavirenz (EFV)-based antiretroviral therapy (ART) was initiated in two-thirds of the patients on day 15 after the start of TB treatment. Patients were excluded if they had evidence of a preexisting disease likely to affect the response to or assessment of treatment effects or represent contraindications of the study medication.

Specimen collection and drug quantitation.

Participants were admitted for PK blood sampling on the 1st, 8th, 15th, and 29th days of TB treatment after an overnight fast. Blood samples were taken immediately before dosing and 1, 2, 4, 6, 8, and 12 h after dose administration. Additionally, a sample was collected at approximately 12 h before the 15th dose. Details of plasma separation and storage and quantitation of drug concentrations were as reported before (12). The lower limit of quantitation was 0.1 mg/liter.

PK analysis.

Population PK analysis was used to describe the concentration data in NONMEM version 7.3 software (14) by using the algorithm first-order conditional estimation with eta-epsilon interaction (FOCE-I). Perl-speaks-NONMEM, Xpose, and Pirana were used for model diagnostics and to track model development (15). Additional diagnostic plots and postmodeling analysis were performed with R version 3.1.2 (16) via RStudio version 0.98.1091 (17).

Several disposition models were evaluated, including one-compartment first-order elimination and a well-stirred liver model, with and without saturation of E_H (18) characterized by Michaelis-Menten parameterization. To characterize rifampin absorption, a first-order model with and without lag time and a chain of transit compartments were assessed (19). Different approaches were used to describe autoinduction of rifampin: estimating a different clearance value at each PK sampling occasion, using an enzyme induction model (11), or using an exponential maturation model with clearance increasing with time on treatment (20).

Between-subject variability (BSV) and between-occasion variability (BOV) were assumed to follow a log-normal distribution. A PK profile was treated as a separate occasion: four sampling occasions with intensive sampling and three catering for concentrations obtained prior to dosing on days 8, 15, and 29. Allometric scaling was applied to all disposition parameters, with allometric exponents fixed to 0.75 for clearance parameters and 1 for volume parameters, as described by Anderson and Holford (21). Total body weight (TBW) and fat-free mass (FFM) were evaluated on each of these parameters. All samples (including predose after day 1) with concentrations below the limit of quantitation (BLQ) were handled by the M6 method (22). This means that they were replaced with half the lower limit of quantitation (LLQ), except for consecutive values in a series, for which the trailing BLQ values were ignored for the fit but included in the diagnostic plots. Predose concentrations from day 1 were excluded from the fit after it was verified that they were BLQ, as expected. Overall, a combined additive and proportional error model was used to describe unexplained residual variability. The effect of covariates on PK parameters was assessed by exploring proportional changes with a linear model for continuous variables and additive covariate model for categorical variables (23).

Model building was guided by change in the objective function value (OFV, assumed to be approximately χ² distributed), inspection of diagnostic plots including a prediction-corrected visual predictive check (VPC) (24), and physiological plausibility.

The final model was used to simulate larger doses of rifampin in a reference cohort of in silico TB patients created with demographic data of 870 TB patients in South Africa and West Africa (200 repetitions). With the same weight bands as described above and a tablet strength of 150 mg of rifampin, daily doses of 15, 20, 25, 30, and 35 mg/kg were evaluated, assuming drug administration every day of the week. The model-based 24-h area under the concentration-time curve (AUC_0–24) and maximum concentration (C_max) were derived at the first dose and at steady state. The probability of target attainment (PTA) for each rifampin daily dose at each specific MIC was calculated as the proportion of simulated patients with a steady-state AUC_0–24/MIC ratio of at least 271, a cutoff value that has been shown to correlate well with the bactericidal activity of rifampin against Mycobacterium tuberculosis (5). The MICs were derived from the distribution of M. tuberculosis MICs in South African isolates (25). The selected PTA was plotted against the range of MICs to describe the killing effects of different doses of rifampin. The cumulative fraction of response (CFR) was computed by using equation 1 for the reference MIC distribution and expressed as a percentage to assess the overall PTA for each dose (26).

$${\text{CFR}}_{\text{dose}}=\underset{i\hspace{0.17em}=\hspace{0.17em}1}{\overset{n}{\mathrm{\Sigma }}}{\text{PTA}}_i\cdot {\text{F}}_i$$ (1)

The subscript i shows the MICs ranked from the lowest to the highest for the population of microorganisms. PTA_i is the PTA for each MIC, and F_i is the fraction of the population of microorganisms at each MIC. Simulations were also used to explore changes in 24-h trough levels associated with higher doses of rifampin.

RESULTS

Demographics.

In total, 61 patients were recruited into the study. Their baseline characteristics are presented in Table 1, and further information can be found in the previous report (12). The median weight, FFM, and height were 55.2 kg, 42.2 kg, and 1.59 m, respectively. The median age of the patients was 32 years, and their ages ranged from 18 to 47 years. Rifampin concentrations in 1,342 plasma samples were included in the analysis, and 140 (10%) of these, mostly in predose samples, were below the limit of quantitation. Of the 61 patients, 41 started EFV-based ART on day 15.

TABLE 1.

Baseline characteristics of patients

Characteristic	Value
Total no.	61
No. (%) of females	33 (54)
No. (%) undergoing ART	41 (67)
No. (%) treated 5 days/wk	51 (84)
Median age, yr (range)	32 (18–47)
Median wt, kg (range)	55.2 (34.4–98.7)
Median ht, m (range)	1.59 (1.41–1.81)
Median FFM, kg (range)	42.2 (28.0–57.6)
Median albumin level, g/liter (range)	26 (15–43)
Median creatinine level, μmol/liter (range)	74 (53–155)
Median viral load, 103 copies/ml (range)	86 (0.05–13,000)
Median no. of CD4+ cells/μl of blood (range)	254 (12–500)

Structural model.

Rifampin PKs were best characterized by a well-stirred liver model, with absorption through a chain of transit compartments. A schematic diagram of the final model is shown in Fig. 1. Inclusion of saturation of E_H further improved the model (a 216-point drop in the OFV, 1 degree of freedom, P < 0.001). In the final model, rifampin clearance and bioavailability are both dependent on E_H. E_H is influenced by the unbound fraction of rifampin (f_u), hepatic plasma flow rate (Q_H), and intrinsic clearance (CL_int), which changes with time on treatment because of autoinduction. CL_int was saturable and followed Michaelis-Menten kinetics; that is, the rate of elimination had a maximum saturation value (CL_int,max) dependent on the Michaelis constant (K_m). More details of the model, including all of the equations describing saturable elimination, are included in the Appendix.

FIG 1.

Schematic diagram of the final model. V is the volume of the observation/central compartment, and NN is number of absorption transit compartments.

Rifampin autoinduction was characterized by applying an exponential-maturation model to CL_int,max so that this increased with time on treatment from a baseline value of ${\text{CL}}_{\mathrm{int},\max }^0$ to a steady-state value of ${\text{CL}}_{\mathrm{int},\max }^{\text{ss}}$ as follows:

$${\text{CL}}_{\mathrm{int},\max }={\text{CL}}_{\mathrm{int},\max }^0+({\text{CL}}_{\mathrm{int},\max }^{\text{ss}}-{\text{CL}}_{\mathrm{int},\max }^0)\cdot (1-e^{-\frac{\ln (2)}{{t_{1/2}}_{\text{ind}}}\times t})$$ (2)

The model was used to estimate the half-life of the induction process (${t_{1/2}}_{\text{ind}}$). The typical value of prehepatic bioavailability (F_prehep) was fixed to a reference value of 1 and allowed to vary between occasions. Typical values of the volume of the liver (V_H) and hepatic plasma flow (Q_H) were fixed to 1 liter and 50 liters/h, respectively, and allometric scaling was included to account for size differences. The fraction of unbound rifampin (f_u) was fixed to 20% (8). Different typical values of V_H, Q_H, and f_u were explored by sensitivity analysis, and the model was found to be robust.

Allometric scaling of all disposition parameters, including those for the well-stirred hepatic model (CL_int, hepatic plasma flow, volume of the liver and the central compartment), was best characterized by using fat-free mass (FFM) compared to TBW (a 40-point decrease in the Akaike information criterion [AIC]) in addition to a 27-point drop in the AIC when allometric scaling was applied by using TBW. The median FFM of 42 kg was used as a reference. EFV coadministration was not found to affect rifampin PKs.

Parameter estimates of the final model.

A VPC provided in Fig. 2 shows that the simulated concentrations mirror the observed values well and that the model correctly captures the decrease in rifampin exposure with time on treatment because of autoinduction. The parameter estimates of the final model and their precision obtained with a 200-sample nonparametric bootstrap are presented in Table 2. The maximum CL_int almost doubled from the first day of treatment to steady state; for a typical individual, it increased from 93 to 176 liters/h. The half-life of the induction process was estimated to be 4.5 days. The model estimated that a K_m concentration (bound plus unbound) of 3.4 mg/liter will result in half the maximum CL_int. The final model included BSV in clearance (23%) and the volume of the observation compartment (14%) and included BOV in clearance (22%), bioavailability (11%), the absorption rate constant (K_a) (81%), and the mean transit time (MTT) (63%). A combined additive (0.07 mg/liter) plus proportional (11%) error model was supported by the data.

FIG 2.

Prediction-corrected VPC stratified by day after treatment initiation. Open circles are the observed concentrations. The middle continuous line is the 50th percentile of the observed data, and the upper and lower dashed lines are the 95th and 5th percentiles of the observed data, respectively. The shaded regions represent the 95% prediction intervals of the 5th, 50th, and 95th percentiles.

TABLE 2.

Values estimated by the final model

Parameter	Estimate	Bootstrap 90% CIa
${\text{CL}}_{\text{int},\text{max}}^0$ (liters/h)b	93.2	83.7–108.1
V (liters)b	50.1	47.7–52.8
Ka (/h)	1.96	1.7–2.2
MTT (h)	0.71	0.67–0.78
NNc	19.3	18.1–22.2
Fd	1 fixed
${\text{CL}}_{\mathrm{int},\max }^{\text{ss}}$ (liters/h)b	176	159–210
${t_{1/2}}_{\text{ind}}$ (days)	4.5	4.1–4.9
VH (liters)b	1 fixed
QH (liters/h)b	50 fixed
fu	0.2 fixed
Km (mg/liter)e	3.35	3.0–3.56
BSV (%)
CL	22.5	19.1–26.1
V	14.2	11.5–16.2
BOV (%)
CL	21.9	18.3–25.7
F	11.0	9.6–13.6
ka	81.2	72.8–88.4
MTT	62.7	57.0–75.4
Error
Additive (mg/liter)	0.064	0.059–0.07
Coefficient of variation (%)	10.8	10.0–12.8

^aCI, confidence interval.

^bThis parameter has been adjusted by allometric scaling, and the values reported refer to a subject with an FFM of 42 kg (the median value of the cohort).

^cNN, number of absorption transit compartments.

^dF, bioavailability.

^eTotal concentration (bound plus unbound).

Simulations.

Model-simulated rifampin exposures on days 1 and 29 after TB treatment initiation for our reference cohort of 870 TB patients are shown in Table 3. Changes in the AUC_0–24 from the first day of treatment due to autoinduction for a reference male in the data set (median weight of 55 kg and height of 1.65 m) are presented in Fig. 3a for the current 10-mg/kg dose and larger doses of up to 35 mg/kg. Figure 3b shows the concentration-time PK profiles for the same male patient at full induction.

TABLE 3.

Simulated exposures at first dose and steady state by dose^a

Dose (mg/kg)	First dose		Steady-state dose
	Cmax (mg/liter)	AUC0–24 (mg · h/liter)	Cmin (mg/liter)	Cmax (mg/liter)	AUC0–24 (mg · h/liter)
10	8.0 (4.7–12.6)	71.1 (35.1–140.3)	0.005 (0.0001–0.13)	6.9 (3.6–11.6)	39.3 (19.0–81.3)
15	13.5 (8.2–20.9)	150 (74.0–282.3)	0.023 (0.0003–0.78)	12.1 (6.7–19.7)	84.6 (40.0–180.5)
20	17.4 (10.8–27.0)	217.1 (107.1–403.5)	0.06 (0.001–2.67)	16.1 (9.0–26.8)	127.0 (58.3–298.0)
25	23.2 (14.7–35.3)	326.3 (166.7–573.8)	0.26 (0.002–15.78)	22.3 (12.8–46.9)	207.0 (92.7–735.8)
30	27.2 (17.2–41.7)	407.9 (211.0–709.1)	0.72 (0.005–86.82)	27.3 (15.5–123.2)	280.6 (119.3–2,543.5)
35	33.1 (21.3–50.1)	531.1 (287.0–893.2)	2.96 (0.015–251.8)	35.8 (19.9–291.1)	425.2 (169.5–6,532.5)

^aData are medians (90% ranges).

FIG 3.

(a) Change in the AUC_0–24 from the first day of treatment to day 29 for a typical male patient (median weight of 55 kg and height of 1.65 m) daily administered 600 mg and larger doses of up to 2,100 mg (3.5 times larger). (b) Simulated concentration-time profile on day 29 after TB treatment initiation for a typical male patient.

As expected, a nonlinear increase in exposure with increasing doses is predicted. At steady state, with the currently recommended dose of 10 mg/kg as the reference, increases in exposure were 2.2-fold for 15 mg/kg, 3.2-fold for 20 mg/kg, 5.3-fold for 25 mg/kg, 7.1-fold for 30 mg/kg, and 10.8-fold for 35 mg/kg. At a dose of ≥25 mg/kg, the simulations predict a median trough concentration (C_min) of >0.3 mg/liter, higher than the LLQ of 0.1 mg/liter in this study. The changes in exposure during the first days of treatment are a result of the balance between the effect of autoinduction and that of accumulation after multiple consecutive doses. Our model predicts that, for doses of >20 mg/kg, the daily exposures from the first dose on will significantly increase during the first days and then decrease to levels lower than that of the first day because of autoinduction.

Moreover, with the current dosing recommendations based on total weight, the model predicts that patients in lower-weight bands are exposed to lower drug levels, as shown in Fig. 4. In the TB patient population used in our simulation, subjects with weights of 30 to 37 kg had, on average, 44% less rifampin exposure than those with weights of >70 kg.

FIG 4.

Distribution of exposures (AUC_0–24) at steady state (day 29) based on the currently recommended doses. The simulated exposures are shown in box plots with the individual values observed in the present study superimposed in closed circles.

The PTA results are shown in Fig. 5. At the current MICs prevalent in the South African population of drug-sensitive TB patients (0.016 to 0.5 mg/liter), the current rifampin dose of 10 mg/kg alone is predicted to have a PTA of slightly above 60% for a median MIC of 0.125 mg/liter, so larger doses of rifampin are likely to be more effective. For M. tuberculosis strains with higher MICs, the currently recommended doses are predicted to be ineffective. The predicted CFR for a daily dose of 10 mg/kg was 65%, and increasing the dose to 15 mg/kg achieves a CFR of 90%. A further increase to 20 mg/kg will result in a CFR of 96%. Doses of at least 25 mg/kg will achieve an overall PTA of >99%.

FIG 5.

Probabilities of target (steady-state AUC_0–24/MIC ratio of 271) attainment over a range of MICs (plotted on a log₂ scale) with different doses in milligrams per kilogram of body weight.

DISCUSSION

A population PK model of rifampin describing autoinduction and saturation of E_H was developed and used to simulate larger doses of rifampin of up to 35 mg/kg of body weight.

Autoinduction of rifampin clearance has been previously described on the basis of results of both traditional noncompartmental analysis (NCA) (7, 27) and population PKs (11). To our knowledge, previous reports were based on two sampling occasions (first dose and steady state), while our data comprised four sampling occasions starting from treatment initiation and we could characterize rifampin autoinduction by using an exponential-maturation model, enabling us to estimate the half-life of the process. The model suggests that, on average, clearance of rifampin almost doubles from the first day of treatment to steady state, and the induction process takes around 2 weeks to reach 90% of the fully induced state. The duration of the process differs from that reported in other studies, possibly because of the richness of data and the dosing strategies used (daily versus intermittent dosing) (11, 28). Though the induction half-life estimated by our model is shorter than that reported by Smythe et al., the extent of the autoinduction effect on clearance is roughly the same.

E_H was described by using a well-stirred liver model, and its saturation was characterized by using Michaelis-Menten kinetics. This model confirms findings of previous studies showing saturation of rifampin clearance already at doses of about ≥450 mg (1, 8, 29). The proposed PK model with saturable E_H could mechanistically explain three different phenomena seen in the present data and/or previously reported in other studies: nonlinearity of rifampin exposure with dose, underexposure of lower-weight patients by the current weight band approach, and a correlation between faster rifampin absorption and greater bioavailability.

Previous studies and recent clinical trials show the nonproportionality of the dose-exposure relationship (30, 31). This means that the rifampin exposure level for doses larger than the current recommendation is greater than that expected if the dose-exposure relationship were linear. Our model mechanistically explains this nonproportionality by using saturable E_H. For example, simulations based on our model show that doubling of the dose is associated with more than double the exposure. This could be explained by saturation of the beta-esterase metabolizing enzymes and/or p-glycoprotein after oral administration with a reduction in the first-pass effect and increased bioavailability. With the currently used doses, the effect of saturation is evident only on first-pass metabolism and not on systemic clearance. With larger doses, however, our model predicts that systemic clearance will also be affected by the saturation effect, resulting in, inter alia, nonnegligible accumulation of rifampin between consecutive doses. Our results showing nonproportionality of the dose-exposure relationship are in line with previous studies evaluating doses of rifampin of 15 to 20 mg/kg (29, 32) and more recently up to 35 mg/kg (4). Ruslami et al. predicted a 65% larger AUC_0–24 for patients receiving 13 mg/kg than for those receiving 10 mg/kg (32), and Boeree et al. recently showed that increasing the dose to 35 mg/kg results in a 10-fold increase in the AUC_0–24 (4). Simulations based on our model closely mirror the exposures detected by Boeree et al., as shown in Fig. 6, which provides a visual comparison of the C_max and AUC_0–24 on day 14.

FIG 6.

Comparison of simulated exposure (C_max and AUC_0–24, median and 90% range) on day 14 after TB treatment initiation and exposure (C_max and AUC_0–24, geometric mean and range) obtained from reference 4.

Although our model predictions for larger rifampin doses closely mirror the median exposure values observed in recent trials, the simulations for 30 and 35 mg/kg showed alarmingly large variability and predictions of extremely high values in some individuals (Table 3). These results could be due to the limits of the extrapolation capability of our model, since it was developed on the basis of data obtained with a 10-mg/kg dose. Despite this caveat, greater variability in exposure is to be expected when increasing the dose of a drug that exhibits saturation kinetics, because relatively small changes in the dose may be enough to reach the “tipping point” for some patients but not for others. Boeree et al. also reported increased variability in exposure with larger doses (4), although not to the extent that our model predicted. It is interesting that in our simulations, the patients with extremely high exposure values were mostly women with high body weights, whom our model found to be relatively overexposed even on the basis of the current guidelines, as discussed below. In the present simulations, it was assumed that the level of autoinduction remains the same even at higher rifampin concentrations. The consistency of our predictions with the values observed in clinical trials supports this assumption.

Before the inclusion of saturable E_H, the model detected a positive effect of the total dose on bioavailability; that is, patients in the higher-weight bands receiving larger absolute doses had greater bioavailability than patients in the lower-weight bands. This suggests that doses intended to achieve the same dose in milligrams per kilogram of body weight across weight bands are not appropriate and lower-weight patients should be prescribed larger doses. This finding is driven by saturation of first-pass metabolism, which was more evident for patients in the highest-weight band, the relatively increased clearance per unit of body size described by allometric scaling theory, and FFM being the most appropriate body size descriptor for scaling of clearance, which is consistent with previous evidence (11, 33). Geiseler et al. showed that daily dosing of a number of anti-TB drugs, including rifampin, should be based on the ideal body weight rather than the TBW (34). This argument has implications in settings where a significant proportion of the population is overweight, and it could cause differences in exposure among patients receiving the same dose (milligrams per kilogram) in different weight bands. This was indeed the case in our study cohort, which contained several women with high body mass indexes who were found to achieve greater exposures. This is in keeping with previous NCA results based on the same data set (12), which showed that patients in the lower-weight bands, as well as males, have lower drug exposure levels than other patients do.

Similar to findings described by Jeremiah et al. (33), a negative correlation between absorption MTT and bioavailability was observed, so that faster absorption was associated with increased bioavailability. Upon inclusion of the saturable E_H model, this phenomenon could be explained mechanistically as follows: higher absorption rates achieve higher rifampin concentrations in the liver, thus saturating the clearance and reducing the extent of first-pass extraction, resulting in greater exposure.

Rifampin exposure levels greater than those achieved with the current dosing have been shown to correlate with better treatment outcomes (35, 36); hence, the increased rifampin exposure due to saturation is likely to be beneficial to patients. On the basis of the range of MICs obtained from a South African study (25), our simulation suggests that the currently recommended dose may not be adequate for some patients. The PTA for the currently recommended dose was 63% for a median MIC of 0.125 mg/liter. This result corroborates the notion that increasing rifampin doses is likely to result in improved responses to treatment, which might allow shorter treatment times. On the basis of Monte Carlo simulations of exposure with the current weight and dosing and the reported MICs, a dose of 20 mg/kg is expected to achieve a CFR of >95%.

The model presented here has some limitations. It was developed on the basis of data obtained only with a 10-mg/kg dose, so the extrapolation becomes less reliable as our simulations explore much larger doses such as 30 or 35 mg/kg. Though we could not establish a relationship between autoinduction and the administration schedule (5 versus 7 days/week), there is no guarantee that the extent of autoinduction will be similar for other intermittent-dosing schedules, for example, dosing two or three times a week. Similarly, our data could not be used to predict whether larger doses of rifampin will result in higher levels of autoinduction. Predicted PTAs should be interpreted while keeping in mind that the cutoff values used for PTA determination were obtained from a murine model (5) and extrapolation to humans may not be accurate for a number of factors, including differences in the lesions: more granuloma as well as cavity formations in humans (37, 38).

In conclusion, the model developed here describes autoinduction of clearance and saturation of E_H of rifampin. The model was used to simulate doses larger than those currently recommended, and a more-than-proportional increase in exposure in relation to the dose was observed. Doses larger than those currently recommended are likely to be more effective against the M. tuberculosis strains considered in this study. Since it was not possible to characterize whether higher rifampin concentrations may affect the extent of autoinduction, further research is necessary to address this question. Moreover, the effect of increased rifampin exposure on the PKs of coadministered drugs, in particular, the companion anti-TB and antiretroviral drugs, would need to be assessed. Alternative dosing strategies based on FFM need to be explored to reduce differences in exposure among TB patients, and this is likely to become even more critical with higher doses, with which even greater variability is expected.

APPENDIX

STRUCTURAL MODEL WITH SATURABLE E_H

The model structure depicted in Fig. 1 is explained in detail below.

Upon oral administration, rifampin is transferred into the absorption compartment via transits compartments, and from there, it reaches the liver, where it is subjected to first-pass metabolism. It is then transferred into the central compartment, from which it recirculates to the liver because of blood circulation. The site of drug clearance, characterized with a well-stirred model, is the liver. Clearance is determined by hepatic plasma flow (Q_H) and the E_H ratio as follows:

$${\text{CL}}_H=Q_H\cdot E_H$$ (A1)

The E_H ratio is defined as follows:

$$E_H=\frac{{\text{CL}}_{\mathrm{int}}\cdot f_u}{{\text{CL}}_{\mathrm{int}}\cdot f_u+Q_H}$$ (A2)

where CL_H is the saturable intrinsic hepatic clearance and f_u is the unbound fraction of rifampin. Saturable CL_int is defined by Michaelis-Menten parameterization as follows:

$${\text{CL}}_{\mathrm{int}}=\frac{{\text{CL}}_{\mathrm{int},\max }\cdot C_H}{C_H+K_m}$$ (A3)

where CL_int,max is the maximum CL_int, C_H is the concentration of rifampin in the liver, and K_m is the Michaelis constant, a parameter that governs saturable hepatic elimination and denotes the rifampin concentration at which the CL_int is half its maximal value. To stabilize the model during estimation of K_m, the parameter was estimated on a log scale. CL_int,max was autoinduced in accordance with equation 1.

Funding Statement

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.