**DOI:**10.1128/AAC.00461-07

## ABSTRACT

This article describes the population pharmacokinetics of rifampin in South African pulmonary tuberculosis patients. Three datasets containing 2,913 rifampin plasma concentration-time data points, collected from 261 South African pulmonary tuberculosis patients aged 18 to 72 years and weighing 28.5 to 85.5 kg and receiving regular daily treatment that included administration of rifampin (450 to 600 mg) for at least 10 days, were pooled. A compartmental pharmacokinetic model was developed using nonlinear mixed-effects modeling. Variability in the shape of the absorption curve was described using a flexible transit compartment model, in which a delay in the onset of absorption and a gradually changing absorption rate were modeled as the passage of drug through a chain of hypothetical compartments, ultimately reaching the absorption compartment. A previously described implementation was extended to allow its application to multiple-dosing data. The typical population estimate of oral clearance was 19.2 liters·h^{−1}, while the volume of distribution was estimated to be 53.2 liters. Interindividual variability was estimated to be 52.8% for clearance and 43.4% for volume of distribution. Interoccasional variability was estimated for CL/F (22.5%) and mean transit time during absorption (67.9%). The use of single-drug formulations was found to increase both the mean transit time (by 104%) and clearance (by 23.6%) relative to fixed-dose-combination use. A strong correlation between clearance and volume of distribution suggested substantial variability in bioavailability, which could have clinical implications, given the dependence of treatment effectiveness on exposure. The final model successfully described rifampin pharmacokinetics in the population studied and is suitable for simulation in this context.

Rifampin (RIF) is an essential component of first-line tuberculosis (TB) pharmacotherapy. Its antimycobacterial utility against *Mycobacterium tuberculosis* infections is characterized by high sterilizing activity (i.e., high ability to eliminate semidormant or persisting organisms in TB lesions). In addition, it prevents the emergence of resistance to its companion drugs (38).

The treatment success rate in South Africa was 68% in 2002 compared to 65% in 2001 and 66% in 2000 (69). These rates are still unsatisfactory compared with the World Health Organization target of 85% (70). The adoption of the Directly Observed Treatment (Short-Course) (DOTS) methodology of the World Health Organization in most treatment centers in South Africa and the country's relatively strong healthcare infrastructure are the major pillars upon which South Africa's National TB treatment program depends. In addition to poor patient adherence, suboptimal dosing (in combination with highly variable bioavailability) has been suggested to be a factor that might be worthy of investigation to increase TB treatment success rates (9, 37, 65). Increased interindividual variability (IIV) or interoccasional variability (IOV) may affect the efficacy of the drug by increasing the likelihood of subtherapeutic concentrations. This, potentially complicated by RIF's well-reported autoinduction of its own metabolism (3, 31, 32, 74), could lead to delayed or incomplete responses to treatment and an increase in the risk of the emergence of drug resistance. In this article, we develop a nonlinear mixed-effects model to characterize the variability in the population pharmacokinetic parameters of RIF and to identify any contributing covariate factors, with a view to better understanding this risk.

## MATERIALS AND METHODS

Patients.Data from three clinical studies of pulmonary TB patients were pooled to form the data set used in the analysis (Table 1). Patients were recruited from the D. P. Marais South African National Tuberculosis Association Centre, a short distance outside urban Cape Town, South Africa, and Brewelskloof Hospital, in the Breede Valley. Both centers are located in South Africa's Western Cape province. The study participants were males and nonpregnant females over the age of 18. All subjects were subjected to fasting from 10 p.m. on the evenings prior to blood sampling and provided full written informed consent prior to inclusion in the studies. Ethical approval for all the studies was granted by the research ethics committees of the University of Cape Town, South Africa, and the participating study centers. All formulations used during the study were those usually administered at the centers concerned and were approved for use in the country by the national medicines regulatory authority, with a single exception, which is discussed further on.

South African TB treatment guidelines at the time of the study (2002 to 2003) were based on the World Health Organization's DOTS TB control strategy (33, 40). RIF was administered in combination with isoniazid for a total of 6 months of treatment. In the first 2 months, known as the intensive phase, pyrazinamide and ethambutol (and, in some cases, streptomycin) were added to the regimen. All sites followed international published guidelines on RIF dosing, using crude weight criteria: subjects weighing less than 50 kg received either 450 mg or 480 mg daily, depending upon the formulations available, whereas those weighing more than 50 kg received 600 mg daily (5). The mean dose given across all 261 subjects was 10.6 ± 1.43 mg·kg^{−1}.

The first subset, which we refer to as DPM1, comprised data from 91 pulmonary TB patients treated with a RIF-using drug regimen for a minimum of 10 days. Twelve patients received 450 mg of RIF/day orally, 28 patients received 480 mg of RIF/day orally, and 51 patients received 600 mg of RIF/day orally, Monday to Friday. The mean dose in this group was 10.4 ± 1.22 mg·kg^{−1}. Three blood samples for RIF pharmacokinetics were taken twice weekly, on Tuesdays and Fridays, at random times between 0 and 12 h postdose, producing a total of 12 samples taken over four occasions. In addition to RIF, patients received their concomitant prescribed medications as usual. Details of these treatments were carefully noted for possible inclusion in the analysis to identify covariates affecting the pharmacokinetics of RIF.

The second data subset (DPM2) included data from 31 pulmonary TB patients treated with first-line TB therapy for at least 14 days prior to the start of the study. Subjects in this group who had had a previous hepatic, renal, or gastrointestinal disorder(s) and who had a recent history of concomitant illness, blood donation, or substance abuse were excluded. All patients weighed 50 kg or more and received 600 mg of RIF/day orally from Monday to Friday. The mean dose in this group was 10.1 ± 1.18 mg·kg^{−1}. Blood samples for RIF pharmacokinetics were taken predose and subsequently at 0.25, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 4.0, 6.0, 8.0, 12.0, and 24.0 h postdose on Tuesdays on up to four occasions over a 6-week period. Patients in DPM2 received their other prescribed medications as usual except for the days of pharmacokinetic blood sampling, when only RIF and other components of antimycobacterial therapy were administered. On a single occasion, a subset of patients in this group (*n* = 22) received a formulation not approved by the national regulatory agency. However, it was shown to be bioequivalent to the reference formulation, and data from this treatment group were included in the DPM2 subset on that basis.

The third and final subset (BKH) included 139 pulmonary TB patients who were admitted at the end of the 2-month intensive phase of treatment which included RIF therapy (36). A total of 98 patients received 450 mg of RIF/day orally, and 41 patients received 600 mg of RIF/day orally, on a daily basis, without a weekend drug holiday. The mean dose in this subset was 10.9 ± 1.55 mg·kg^{−1}. Blood samples for the determination of RIF pharmacokinetics were taken on the study day (Thursday) predose and subsequently at 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 4.0, 6.0, and 8.0 h postdose. In addition to RIF, patients received their other prescribed medications as usual. Subjects in this category were sampled on one day only.

Covariate information and full medical histories were recorded for each patient during the initial interview and by examination of their clinical case records. Information gathered included age, weight, height, body mass index, gender, phase of treatment (intensive or continuation), details of previous TB episodes, the date that RIF treatment was started, and use of concomitant medication, alcohol, tobacco, and drugs of abuse. Adherence to treatment on the pharmacokinetic study days was confirmed by direct observation of drug ingestion.

Specimen collection and storage.Venous blood samples for determination of RIF pharmacokinetics were collected into lithium heparin vacuum tubes (Vacuette, Greiner Bio-One International AG, Kremsmuenster, Austria) through an intravenous cannula (Introcan; B. Braun AG, Melsungen, Germany) (1.1 by 32 mm) inserted into an arm vein. The samples were stored for up to 20 min in darkness on ice before being centrifuged using a benchtop centrifuge (Sigma 3E-1; Sigma, Osterode am Harz, Germany) at 1,500 × *g* for 10 min at ambient temperature. The plasma was subsequently harvested into labeled 1.5-ml microcentrifuge tubes (Greiner Bio-One International, Kremsmuenster, Austria) and stored at −80°C until analysis.

Patients were requested to undergo voluntary testing for the presence of human immunodeficiency virus (HIV) (10 subjects declined) by use of an automated enzyme-linked immunosorbent assay method (AxSYM HIV Ag/Ab combo; Abbott Diagnostics, Germany). Counseling was provided pre- and posttest for all subjects. Confirmatory testing was carried out for subjects whose initial screening result was positive by use of Enzygnost Anti-HIV 1/2 Plus (Dade Behring, Liederbach, Germany), a second enzyme-linked immunosorbent assay.

Bioanalytics.Plasma concentrations of RIF were determined by high-performance liquid chromatography (HPLC) by use of UV detection (60). The HPLC system consisted of a Discovery C8 analytical column of dimensions 15 cm by 4.6 mm and a 5-μm particle diameter (Supelco, Bellefonte, PA) in conjunction with a reverse-phase guard column (packed with Pelliguard LC-8 [Upchurch Scientific, Oak Harbor, WA]) (2.5 cm by 0.46 cm). The mobile phase consisted of acetonitrile (BDH, Poole, United Kingdom) and 0.1% trifluoroacetic acid (Riedel-de Haën, Seelze, Germany) in a 60:40 ratio. The UV detection wavelength was 270 nm, and the flow rate was 2.0 ml min^{−1}. A 50-μl volume of sample was injected directly onto the column, and the retention time was approximately 3.45 min.

Frozen plasma samples were allowed to thaw in a water bath at ambient temperature. The C18 solid-phase extraction column (Bond Elut; Varian, Palo Alto, CA) (3.0 ml bed volume) was primed with 1 ml of 0.5 mM potassium phosphate buffer (pH 4.5), and 0.5 ml of plasma was applied to the column. The sample was drawn onto the column and allowed to stand for 10 min. The column was washed with 1 ml of the phosphate buffer. Bound RIF was eluted into a tinted analytical vial by use of 0.5 ml of acetonitrile (BDH, Poole, United Kingdom) and 0.5 ml methanol (BDH). All solvents were of HPLC grade.

Standard curves were linear and provided a detection range of 0.3 to 25 mg · liter^{−1}. Quality-control samples of 0.75 mg · liter^{−1}, 10 mg · liter^{−1}, and 20 mg · liter^{−1} were interspersed between the samples. The coefficient of variation for intraday precision was 8.57% and for interday precision was 9.21%. Mean (± standard deviation) recovery was assessed by measuring the RIF concentration obtained from spiked plasma samples corresponding to points on standard curves in mobile phase and was found to be 89.3 ± 6.78%. Apart from the assessment of recovery, plasma was used as the matrix for standard curves and quality-control samples.

Pharmacokinetic data analysis.A total of 2,913 concentration-time observations of 261 subjects were available for modeling. Model building was conducted using NONMEM software (version VI, level 1.0 beta) (6), as implemented on a computing cluster running Red Hat Linux 7.0 (Mandrakesoft, Paris, France) with GNU Fortran (g77) 2.96, a component of GCC 2.96 (Free Software Foundation, Boston, MA). Model-building steps and associated analysis data were managed using the software utilities Census (68) and Xpose version 4.0 (23). The first-order conditional estimation method, with ε-η interaction, was used for the estimation of typical population pharmacokinetic parameters, random interindividual variability (IIV) and random interoccasional variability (IOV) in these parameters, and residual variability between observed and predicted plasma concentrations. Correlations between variability components were also tested.

Model selection was achieved by use of the objective function value (OFV), a goodness-of-fit estimate which is calculated using minus twice the log likelihood of the data, as well as by examination of relative standard error values and goodness-of-fit plots. Differences between the objective functions of a full and a reduced model are approximately chi-square distributed, with *n* degrees of freedom, where *n* is the number of parameters fixed in the reduced model. A drop of >3.84 in the objective function after addition of a single model parameter, corresponding to a 5% significance level with a single degree of freedom, was regarded as significant.

One- and two-compartment models with linear absorption and elimination, models incorporating lag times, and models incorporating sequential zero- and first-order absorption (20) were fitted to the data during the initial stage of model building. Elimination was assumed to take place from the central plasma compartment in all models tested. The absorption model was subsequently modified as described later. IIV values for all parameters were modeled as exponential variance parameters. IOV was modeled following the method of Karlsson and Sheiner (24). Residual variability, arising from unspecified within-subject variability, model misspecification, and experimental error, was described using a slope-intercept model comprising additive and constant coefficient-of-variation components.

Two approaches were tested to develop the model for RIF pharmacokinetics. In the first, an enzyme turnover model was adapted to try to characterize autoinduction in RIF metabolism (18). Using this framework, the dependence of enzyme formation on the concentration of drug in the central compartment, along with the effect of enzyme levels on clearance, was tested.

Absorption, which a graphical inspection of the data revealed to be highly variable, was modeled using a method proposed by Savic et al. that envisages absorption as a multiple-step process occurring as the drug travels through a number of hypothetical “transit” compartments (42, 56, 59). Transit compartments were used to mimic a delay in absorption onset and a gradual increase in absorption rate in a more physiologically plausible manner than that offered by the use of lag times. Drug transfer from the final transit compartment to the central compartment occurred through an absorption compartment, from which drug was absorbed according to the first-order rate constant *k _{a}*. The optimal (noninteger) number of transit compartments (

*n*) was estimated using equation 1, in which

*dA*

_{1}*/dt*is the rate of drug change in the absorption compartment, “Dose” is amount of drug administered (in milligrams),

*F*is bioavailability,

*k*

_{tr}is a transit rate constant describing movement of drug between transit compartments

*n*− 1 and

*n*(in hours),

*t*is time (in hours),

*k*is the first-order absorption rate constant, and Γ(

_{a}*n*) is the gamma function, which extends the factorial expression

*n!*to noninteger, complex, and real numbers. $$mathtex$$\[\frac{dA_{1}}{dt}{=}\mathrm{Dose}{\cdot}F{\cdot}k_{\mathrm{tr}}{\cdot}\frac{(k_{\mathrm{tr}}{\cdot}t)^{n}{\cdot}e^{{-}k_{\mathrm{tr}}\ {\cdot}\ t}}{{\Gamma}(n)}{-}k_{a}{\cdot}A_{1}\]$$mathtex$$(1) $$mathtex$$\[{\Gamma}(n){=}\sqrt{2{\pi}}{\cdot}n^{n\ {+}\ 0.5}{\cdot}e^{{-}n}\]$$mathtex$$(2) The Stirling approximation was used to compute Γ(

*n*) numerically (equation 2). $$mathtex$$\[k_{\mathrm{tr}}{=}\frac{n{+}1}{\mathrm{MTT}}\]$$mathtex$$(3) The rate constant

*k*was calculated from an estimate of the mean transit time (MTT [in hours]), the average amount of time spent by a drug molecule traveling from the first transit compartment to the absorption compartment, as indicated in equation 3.

_{tr}The transit compartment approach as originally proposed allowed application of the model for single-dose data only, since the nature of the differential equations used in implementing the model allowed the initial conditions of the system (the dose administered) to be set at time 0 only and did not allow for the introduction of new drug boluses into the system at later time points. In order to apply this model to a repeated-dose design, modifications were required. Time *t* in equation 1, the actual time at which a given sample was drawn, was changed to time after dose (*t*_{ad}) by subtracting the time of the last dose (*t*_{dose}) from *t* (equation 4). In this way, each dosing event happened at time 0, meeting the requirements of the original model and thus allowing the transit model to accommodate multiple-dosing schemes.
$$mathtex$$\[\frac{dA_{1}}{dt}{=}\mathrm{Dose}{\cdot}F{\cdot}k_{\mathrm{tr}}{\cdot}\frac{(k_{\mathrm{tr}}{\cdot}t_{ad})^{n}{\cdot}e^{{-}k_{\mathrm{tr}}\ {\cdot}\ t_{ad}}}{{\Gamma}(n)}{-}k_{a}{\cdot}A_{1}\]$$mathtex$$(4)

An enzyme turnover model (18) was adapted in an attempt to characterize autoinduction in RIF metabolism (31). By use of this framework, the dependence of enzyme formation on the concentration of drug in the plasma compartment, along with the effect of enzyme levels on clearance, was tested.

A number of potential covariate relationships for the pharmacokinetic parameters, including the demographic variables age, weight, sex, HIV status, study site, and choice of formulation type, were tested. The formulation type was either fixed-dose combination (FDC), in which RIF and other drugs were administered together in the same formulation to promote compliance, or single drug, in which RIF and other drugs were administered as separate tablets. Potential covariates were initially identified by using stepwise generalized additive modeling, as implemented in Xpose. The covariates selected in the generalized additive modeling analysis were tested in the model by stepwise addition using an OFV change of >3.84 (corresponding to a significance level of 5%) as the cutoff for inclusion followed by stepwise deletion using an OFV change of >10.84 (corresponding to a significance level of 0.1%) as a prerequisite for retaining a covariate in the model (34). The effects on RIF pharmacokinetics of significant covariate relations were explored using simulations. New individuals were simulated to represent the spectrum of possible covariate configurations (*n* = 1,000 of each permutation), and the resulting concentration-time data were plotted in combination with locally weighted least-square regression lines (calculated using locally weighted scatterplot smoothing [LOESS]) in order to detect differences (10).

The software tool Perl-speaks-NONMEM was used to run a nonparametric bootstrap of 800 iterations to provide unbiased estimates of the standard errors and the 95% confidence intervals of the estimated parameters (28, 29). The resampled datasets were stratified by location to ensure that they were suitably representative of the structure of the original pooled data set.

Model-based estimates of individual values of area under the concentration-time curve to 24 h (AUC_{0-24}) were calculated from empirical Bayes estimates of parameters as indicated in equation 5, where CL/*F* represents CL at steady state in liters per hour and “dose” represents the RIF dose in milligrams.
$$mathtex$$\[\mathrm{AUC}_{0-24}{=}\frac{\mathrm{Dose}}{(\mathrm{CL}/F)}\]$$mathtex$$(5) A visual predictive check was employed to characterize the model's simulation properties. The final model was used to simulate 400 new datasets based on the design of the original data set. For each of the original data points, a 95% prediction interval was obtained by extracting the 2.5% and 97.5% quantiles of their simulated distributions. These were then plotted against the observations.

## RESULTS

The pooled patient RIF plasma concentration-time data were best described by the transit-compartment absorption model, which was sufficiently flexible to allow for the acceptable fitting of almost all subjects. Two-compartment models provided no advantage in terms of improvement in diagnostic plots or change in OFV (ΔOFV = 0.169) and were discarded early in the model-building process. Models incorporating lag times and sequential zero- and first-order absorption processes produced substantially poorer fits than those provided by the transit model, as determined based on a graphical assessment of their ability to describe the data and the degree to which estimates of IIV for the key structural parameters were reduced, and were similarly rejected (Table 2).

The model was parameterized in terms of CL (CL/*F*, where *F* is unknown bioavailability), apparent volume of distribution (*V*) of the central compartment (*V*/*F*), absorption rate constant (*k _{a}*), MTT, and number of transit compartments (

*n*). While the fit provided by the enzyme turnover model was better than that seen with the simple first-order-input and combined zero- and first-order-absorption models, it failed to describe a number of individuals with particularly slow or atypical absorption characteristics. The data did not support the inclusion of both the complex model for absorption and an enzyme turnover model to account for autoinduction. Consequently, the disposition model was simplified to a one-compartment model parameterized in terms of CL/

*F*and

*V*/

*F*.

The final model itself is illustrated in Fig. 1. The rate of change of drug in the absorption compartment was determined by equation 1 as described earlier; in addition, the first term was log-transformed to reduce potential numerical instability during computation.
$$mathtex$$\[\frac{dA_{2}}{dt}{=}k_{a}{\cdot}A_{1}{-}\frac{\mathrm{CL}}{V}{\cdot}A_{2}\]$$mathtex$$(6) The rate of change of drug in the central compartment was determined by equation 6, in which *A*_{2} is the amount of drug in the compartment (in milligrams), CL is CL (in liters per hour), and *V* is in liters.

Variability in CL/*F* was separated into IIV (η_{CL/}* _{F}*; coefficient of variation [CV] = 52.8%) and IOV (κ

_{CL/}

*; CV = 22.5%). Parameters related to absorption exhibited the most variability. IIV in*

_{F}*k*was estimated to be 66.3%, in MTT 60.1%, and in

_{a}*n*156%, while IOV in

*MTT*was estimated at 67.9%. A strong (0.947) correlation between CL/

*F*and

*V*/

*F*was estimated.

Of the tested covariate relations, only the inclusion of the formulation type (single-drug formulation [SDF]or FDC) as a covariate for CL/*F* and MTT remained in the model after the conclusion of the stepwise deletion process (ΔOFV ≥ 10.83; *P* ≤ 0.001). There was a significant difference in CL results when subjects administered FDCs were compared with subjects administered SDFs; the estimated typical value of CL/*F* for subjects receiving SDFs was 23.6% greater than that estimated for subjects receiving FDCs, translating into slightly increased exposure for the FDC group. For patients who received their RIF as a SDF, MTT was 104% greater than for those who took FDC formulations, resulting in peak concentrations approximately 30 min later in those subjects. The relationship between choice of formulation type and CL/*F* was modeled as indicated in equation 7.
$$mathtex$$\[(\mathrm{CL}/F)_{ij}{=}[\mathrm{TV}(\mathrm{CL}/F)\ {\cdot}\ (1{+}{\theta}_{\mathrm{SDF},\ \mathrm{CL}/F}\ {\cdot}\ \mathrm{SDF})]{\times}\mathrm{exp}({\eta}_{\mathrm{CL}/F,i}{+}{\kappa}_{\mathrm{CL}/F,ij})\]$$mathtex$$(7) In equation 7, (CL/*F) _{ij}* is apparent CL in individual

*i*at occasion

*j*, TV(CL/

*F*) is the value of CL/

*F*in the population (assuming administration of an FDC), θ

_{SDF, CL/F}is the model parameter describing the effect of SDF use on CL, SDF is formulation type (0 for FDC, 1 for SDF), η

_{CL/}

_{F}_{,}

*is IIV for CL for individual*

_{i}*i*, and κ

_{CL/}

_{F}_{,}

*is IOV for CL for individual*

_{ij}*i*at occasion

*j*. The relationship between MTT and formulation type was expressed similarly. The impact of covariate effects on RIF pharmacokinetics is illustrated in Fig. 2.

Final estimates of the parameters, together with bootstrap estimates of standard errors and parameter confidence intervals, are presented in Table 3. Goodness-of-fit plots (Fig. 3) indicated a good fit of the model to the data, although the plot of observed concentrations against population predictions reveals that approximately 175 points (approximately 5% of observations) were being underpredicted by the population model (individual predictions < 0.2 mg · liter^{−1}). The distribution of the weighted residuals was unbiased with respect to time, indicating that this was probably not attributable to a systematic problem in the structural model. Plots of the observations, individual predictions, and population predictions for representative individuals (Fig. 4) confirmed that the final model adequately described the data, even when the “worst” fits, characterized by high individual-weighted residuals (IWRES) and population-weighted residuals (WRES), were selected for display. A visual predictive check of the final model appears as Fig. 5. Model-based predictions of AUC_{0-24} had a mean of 30.7 ± 13.2 mg·h liter^{−1} across all subjects and sampling occasions.

## DISCUSSION

The population pharmacokinetics of RIF in the studied patients were highly variable. The drug exhibited more variability in its population pharmacokinetics in the study group than has been reported for healthy volunteers (50). Loos et al. reported CL/*F* in a small German patient population to be 14.2 ± 9.70 liters · h^{−1} (31), but few other studies of RIF pharmacokinetics for similar patient groups in terms of CL/*F* and *V*/*F* have been reported in the literature. It is helpful, therefore, to look at exposure metrics instead. Model-derived estimates of AUC_{0-24} were generally lower than the values presented in published reports of studies of other populations of fully induced pulmonary TB patients (see Table 4), although they were consistent with those calculated in a separate noncompartmental analysis of the BKH subset of these data (36). Our results are similar to those collected during studies of HIV patient populations (16, 51), although fewer than 15% of the subjects included in our analysis were seropositive for the disease (Table 1).

Subpopulations with different absorption characteristics were evident from plots of the raw data and have also been previously described for healthy volunteers (50). Most commonly, these differences appeared to be related to the rate and extent of absorption. Several potential causes for this variability may be immediately discounted. No food intake was allowed until 2 h postdose, eliminating food effects as a possible source (46, 73), and no significant correlation was found with HIV coinfection (11, 16, 17, 47, 49, 58, 64). Other sources of this variability might be attributed to the fact that the studies were conducted during clinical treatment in a hospital setting. While concomitant drug intake was carefully monitored, the combinations of medications involved were too numerous (*n* = 41), and their frequencies within the population too low, to allow any effective investigation of their potential influence. None were previously reported to have influenced the pharmacokinetics of RIF. The influence of delayed gastric emptying and alterations in gastric pH (1, 44) and poor nutritional status (37) could not be determined using our study design. Other covariate effects, however, were available for model-based analysis, and we shall discuss these further on.

The core one-compartment model with linear elimination was similar to one used previously to model RIF in healthy volunteers (50). The transit compartment model provided a better fit to the data than the other absorption models tested, and it was therefore chosen as the most appropriate model for fitting the unusual absorption profiles seen in our data (Fig. 4). Previously, transit model (“tanks-in-series”) approaches have been used to describe signal transduction (62, 71), and similar approaches have been used to model absorption (12, 66). Weiss used the gamma distribution to model drug residence times (67), and since then, similar approaches have been applied to other areas (26, 55). The transit model assumes a gradual increase in the absorption rate, which results in a smoother initial rise in the plasma concentration toward the maximum. This is considered to be a better approximation of the underlying physiology than the use of first- or zero-order absorption models which include a lag-time parameter (*T*_{lag}). The lag-time parameter, which assumes an instantaneous shift from no absorption to maximal absorption, is physiologically implausible and is associated with computational difficulties. The transit compartment model offers advantages from a numerical point of view, since partial derivatives are defined for the predicted concentrations from the entire absorption profile (59). Here, we have extended this approach to account for multiple dosing. Addition of the transit model, while providing a better fit, did not, however, affect predictions of CL/*F* and *V*/*F*, which were largely independent of the method used to model absorption. The increase in the complexity of the absorption model was, however, offset by a proportional improvement in the model's ability to explain variability in the key structural parameters, justifying the additional computation overhead (Table 2).

Some caveats apply to the extended transit model for repeated doses that we present in this article. Our implementation assumes that the entirety of the bioavailable dose completely reaches the absorption compartment before the next dose is administered, as the system is reset at each dosing event. In this case, given once-daily dosing, this assumption was valid and was supported by the data. The utility of the method may be enhanced when subjects are subjected to fasting, owing to the increased rate of gastric emptying under these conditions.

The data did not support the inclusion of an enzyme turnover model for autoinduction, despite the fact that this phenomenon is well known to occur with RIF; repeated daily administration leads to accelerated clearance and decreased plasma concentrations (3, 31, 32, 74). The most likely explanation is that subjects were uniformly at a steady state for induction, having been recruited after at least 10 days of regular RIF treatment, and the weekend drug holiday was insufficiently large as an interruption to produce a change in elimination-related enzyme levels significant enough to produce a significant signal in the data. Literature reports indicate that a maximal state of induction is typically achieved within 7 to 10 days (2, 31, 54) and that between 3 and 7 days are required for a return to normal levels (21, 61).

A significant within-subject, between-occasion contribution to overall variability in CL/*F* and MTT was noted. While for the former, IOV was relatively small (22.5%), IOV for MTT was significantly larger (67.9%). Since few time-varying covariate data were available, no conclusions could be drawn regarding the origin of this component of variability for the sample population. However, allowing CL/*F* and MTT to vary according to sampling occasion significantly improved the fit and the model's predictive ability. The transit model parameters MTT and, especially, *n* (estimated to be 7.13 in the population but with a CV of 156%) exhibited substantial variability. While there is no physiological explanation for the value of *n*, which is purely empirical, variability in the overall shape of the absorption curve may be linked to both gastric pH and the rates of release of RIF from each of the specific formulations used. Indeed, formulation type was a critical predictor of RIF pharmacokinetics in this patient population, as we shall see.

A strong (0.947) correlation between CL/*F* and V/*F* was noted in the data. This was in all likelihood driven by variability in *F*. RIF is well known for displaying variability in both rate and extent of absorption when dosed orally (27, 35, 36, 41, 43, 52, 65), particularly when FDC and SDFs are compared. A variety of potential reasons for this have been investigated in the literature. It had long been speculated that this behavior was related to formulation dissolution and disintegration properties of oral formulations (45, 46), and recent work has suggested that this is indeed the case (4). The structure of the final model, however, was unable to support the direct estimation of IIV for *F*, owing to numerical issues related to the large number of model parameters (although, in principle, there is no reason why this should not work in other implementations of this model). No significant correlations were noted between CL/*F* and any of the absorption parameters (*k _{a}*, MTT, or

*n*).

There was evidence in our data, in the form of a strong covariate relationship between CL/*F* and formulation type, to support the idea of a formulation effect on bioavailability. The use of SDFs was associated with a statistically significant (23.6%) increase in CL/*F* relative to the typical value of the parameter for subjects for whom FDCs were used. The reasons for this are probably related to *F* rather than to CL, since it is unlikely that formulation would exert a direct effect on elimination processes, given the large quantity of clinical evidence for the relationship between *F* and formulation. With larger quantities of data, it may be possible confirm this directly.

RIF has an acidic pK_{a} of 1.7 and a basic pK_{a} of 7.9 (7). Consequently, it is highly soluble but poorly permeative under gastric pH (pH 1 to 3) and physiological conditions, but its solubility varies by 100-fold in this range. Solubility at duodenal pH (pH 4 to 6) is moderate to high and permeativity is high, and in the colon, both solubility and permeativity are high. In formulations in which the release rate is high, most of the dose is dissolved by the time gastric emptying occurs, resulting in rapid uptake from the duodenum. However, where release rate is slower or gastric pH is not optimal, less substrate is available at the absorption site, limiting uptake and producing a different shape (4) and adding to variability of both *n* and MTT, as well as of *F*, which we have already discussed. This determination is supported by the selection of a significant covariate effect linking RIF formulation type and MTT during the model-building process. According to the model, when RIF was administered as an SDF, MTT was 104% longer (at 0.865 h) than the typical value for the population. This relationship in our data appears to delay the time of peak concentration (*T*_{max}) for SDF users (see Fig. 2) and, while probably not clinically relevant, explains a portion, but not all, of the variability seen in the absorption phase.

In addition to the effect on *T*_{max}, the choice of a SDF appears to reduce the peak plasma concentration (*C*_{max}) through its effect on CL/*F*. The effect on CL/*F* also produces a net decrease in exposure, as represented by the AUC (see Fig. 2). It is, however, important to temper these findings with a brief discussion of potentially confounding factors. The BKH subgroup was treated almost uniformly with SDFs, while the DPM1 and DPM2 subgroups were mostly administered FDCs. In a further complication, 51 of the included BKH subjects (representing 13.1% of the total number of observations) were treated with formulations later found to be of inferior quality (35). Excluding these individuals, or including the use of the inferior formulations as a covariate with any of the model parameters, failed to produce a significant difference in the model fit or the parameter estimates, indicating that the majority of the observed formulation effect did not result from this source. Dosing of the studied patients was routinely carried out according to body weight, explaining the absence of a significant weight effect on any of the model parameters despite previously published evidence of this relationship (50).

The distribution of *n*, the number of transit compartments, was significantly skewed (see Table 3). This appears to be a natural characteristic of this parameter and was present in all stages of model development. When one considers that the final estimate of *n* is theoretically an optimum, higher values of which would make little difference to the fit in comparison to the effect of lower values, this behavior is not unexpected.

The visual predictive check (Fig. 5) indicated that the model slightly overpredicted the variability of the data. This can probably be explained in terms of the significant proportion of the population made up by patients with atypical absorption characteristics, which led to the large estimates of absorption-related variability we have observed and a concomitant overall increase in the variability of model-derived predictions (see Fig. 4 for examples). Also, more than 75% of the observations were recorded at 6 h postdose or less, concentrating the information content in this region. Given the degree of variability in the data, the increased uncertainty at times greater than 8 h postdose, when observations were sparser, was not unexpected. The median values of the observations and the predictions matched very closely, confirming that the model adequately captured the central trend. The poor agreement of the lower intervals at the 480-mg-dose level is probably attributable to the relatively low number of observations in this group (approximately 10.5% of the total). We may therefore conclude that the model is suitable for simulation using patient populations similar to those studied here, as long as it is borne in mind that simulations may overemphasize variability to a small degree and as long as one assumes that simulated subjects have been dosed according to weight, as was the case here.

It has been reported previously that RIF's antimicrobial killing properties are related to the ratio of the AUC to the MIC (22). This means that the effectiveness of RIF treatment is strongly related to *F* and CL, and as we have seen, both are somewhat variable. More recent research by Gumbo and colleagues (15) has suggested that the ratio of *C*_{max} to the MIC is important in preventing the emergence of resistance. Assuming a range of MICs of RIF, with respect to drug-susceptible clinical isolates of *M. tuberculosis*, of between 0.125 mg · liter^{−1} and 0.250 mg · liter^{−1} (19, 53), plasma concentrations in some individuals may not reach high enough levels to prevent the emergence of resistance or may not maintain high enough levels to ensure optimal bactericidal effect. As an illustration, the lowest measured peak concentration for the studied patients was 0.716 mg · liter^{−1}, which, when one considers that approximately 84 to 88% of RIF in blood is protein bound (8), translates to an estimated maximal unbound concentration of about 0.1 mg · liter^{−1}. In addition to oft-cited causes of treatment failure, such as poor compliance (14, 72), it follows that inadequate exposure to the drug may be playing a role in the poor cure rates seen in South African patients; low rifampin exposures for a demographically similar group of Indonesian patients have been also reported by van Crevel and colleagues (65). While a highly variable rate of absorption would be expected to have little effect on total exposure, its effect on *C*_{max} is considerable—slower absorption leads to lower peak plasma concentrations. These data add further support to the mounting clinical evidence that higher doses may be more effective, although the safety implications of increased exposure remain unclear (13, 22, 25, 30, 39, 48).

While the multidrug treatment strategy currently employed to combat pulmonary TB is undeniably effective for the majority of South African patients, the variability in RIF pharmacokinetics and generally lower exposures we have observed for our South African study population suggest that some patients routinely receive low concentrations of the drug. It is therefore vitally important in this context that further research be carried out in order to characterize the pharmacokinetic/pharmacodynamic relationship more clearly and thereby to enable the definition of the most appropriate dosing strategy for South African pulmonary TB patients and, indeed, for other populations as well.

## ACKNOWLEDGMENTS

This research was cofunded by the South African Medical Research Council and by the Division of Clinical Pharmacology of the Department of Medicine, Faculty of Health Sciences, University of Cape Town, South Africa.

We thank Jean van Dyk, Rudy Onia, Afia Fredericks, and Alicia Evans for their invaluable technical and logistical assistance. We also wish to thank Bernard Fourie, Director, Medical Research Council Tuberculosis Research Unit, South Africa, for allowing the use of some of the PK data included in this study.

We have identified no conflicts of interest.

## FOOTNOTES

- Received 3 April 2007.
- Returned for modification 10 June 2007.
- Accepted 31 March 2008.
↵▿ Published ahead of print on 7 April 2008.

- American Society for Microbiology