Factors Affecting the Pharmacokinetics of Pyrazinamide and Its Metabolites in Patients Coinfected with HIV and Implications for Individualized Dosing

ABSTRACT

Pyrazinamide is a first-line drug used in the treatment of tuberculosis. High exposure to pyrazinamide and its metabolites may result in hepatotoxicity, whereas low exposure to pyrazinamide has been correlated with treatment failure of first-line antitubercular therapy. The aim of this study was to describe the pharmacokinetics and metabolism of pyrazinamide in patients coinfected with tuberculosis and HIV. We further aimed to identify demographic and clinical factors which affect the pharmacokinetics of pyrazinamide and its metabolites in order to suggest individualized dosing regimens. Plasma concentrations of pyrazinamide, pyrazinoic acid, and 5-hydroxypyrazinamide from 63 Rwandan patients coinfected with tuberculosis and HIV were determined by liquid chromatography-tandem mass spectrometry followed by nonlinear mixed-effects modeling. Females had a close to 50% higher relative pyrazinamide bioavailability compared to males. The distribution volumes of pyrazinamide and both metabolites were lower in patients on concomitant efavirenz-based HIV therapy. Furthermore, there was a linear relationship between serum creatinine and oral clearance of pyrazinoic acid. Simulations indicated that increasing doses from 25 mg/kg of body weight to 35 mg/kg and 50 mg/kg in females and males, respectively, would result in adequate exposure with regard to suggested thresholds and increase probability of target attainment to >0.9 for a MIC of 25 mg/liter. Further, lowering the dose by 40% in patients with high serum creatinine would prevent accumulation of toxic metabolites. Individualized dosing is proposed to decrease variability in exposure to pyrazinamide and its metabolites. Reducing the variability in exposure may lower the risk of treatment failure and resistance development.

INTRODUCTION

Tuberculosis (TB) remains the most common cause of death in HIV-infected patients. Pyrazinamide (PZA) is a first-line drug used in combination with rifampin, isoniazid, and ethambutol to treat TB infection. The addition of PZA to the antitubercular cocktail reduced duration of TB therapy from 9 months to 6 months (1). The sterilizing properties of PZA render it a promising candidate for novel antitubercular combination regimens which may reduce length of therapy further (2).

PZA is mainly eliminated by hepatic metabolism, which forms pyrazinoic acid (POA) via microsomal deamidase and 5-hydroxypyrazinamide (OHPZA) via xanthine oxidase (3). These metabolites are mainly cleared renally, although both metabolites are further metabolized to 5-hydroxypyrazinoic acid (OHPOA) (4). Active POA is also formed from the parent drug by the tuberculosis bacteria (5). An animal study showed that direct administration of POA was less effective than administration of PZA, indicating that bacterially mediated POA is crucial for efficacy (6). However, Via et al. suggested that subinhibitory levels of host-mediated formation of POA could increase the risk of resistance to PZA and POA (2).

Subtherapeutic doses of anti-infective drugs may result in treatment failure and resistance development. Therapeutic targets (area under the plasma concentration-time curve [AUC]/MIC > 11.3 and AUC > 363 mg·h/liter) for PZA have been proposed (7, 8). Recently, Zheng et al. also suggested that low PZA AUC/MIC is associated with less effective elimination of bacteria (9). A study conducted in Botswanan TB/HIV patients concluded that low PZA exposure is a predictor of poor TB therapy outcome (10). Furthermore, studies have suggested that doses higher than the current standard of 25 mg/kg of body weight are required to reach therapeutic exposure targets of PZA (11, 12). A study conducted in mice and guinea pigs further suggested that PZA efficacy is dose dependent (13). The authors concluded that higher doses than the current standard doses could increase efficacy clinically. However, concern regarding PZA-related adverse events, such as hepatotoxicity, has limited the use of higher doses (4).

Variability in PZA pharmacokinetic parameters has been shown to be affected by patient characteristics such as sex and age (14, 15). The high variability in PZA and POA exposure could be reduced by individualized optimization of PZA doses, which potentially could decrease the number of patients at risk of treatment failure or toxicity. Hence, the present study aimed to describe the pharmacokinetics and metabolism of PZA in patients coinfected with TB and HIV. Moreover, we aimed to quantify the effect of clinical factors influencing the exposure of PZA and its metabolites to explore individualized dosing regimens.

RESULTS

PZA, POA, and OHPZA plasma concentration-time profiles from 63 patients coinfected with TB and HIV were analyzed in the present study. The total number of observations used were 1,244 (413 for PZA, 395 for POA, and 436 for OHPZA). Observations below the lower limits of quantification were ignored (n = 53 [4.3%]). OHPOA data were excluded from the present analysis due to a limited number of observations above the lower limit of quantification (n = 23 [6% of assayed samples]).

One-compartment models most adequately described the dispositions of PZA, POA, and OHPZA. Diagnostic plots are presented in the supplemental material. A visual predictive check indicated adequate predictive properties of the model (Fig. 1). Epsilon shrinkage of the final model was 9%.

FIG 1.

Prediction-corrected visual predictive check (n = 1,000) of the final population pharmacokinetic model of pyrazinamide, pyrazinoic acid, and 5-hydroxypyrazinamide stratified by sex. Circles represent observations, solid lines show the medians of observations, and dashed lines show the 90th and 10th percentiles of observations. Gray areas indicate the 95% confidence intervals of the predicted medians and percentiles.

The typical oral clearance of PZA was estimated at 4.8 liters/h, of which 45% led to formation of POA. Females had a significantly higher relative bioavailability than males (reduction in objective function value [ΔOFV] = −16.3). Concomitant antiretroviral therapy (ART) had a significant effect on the volume of distribution for PZA and both metabolites (ΔOFV = −21.6). Furthermore, serum creatinine had a significant linear effect on the oral clearance of POA (ΔOFV = −7.3). Estimated pharmacokinetic parameters of the final model are summarized in Table 1.

TABLE 1.

Parameters of pyrazinamide, pyrazinoic acid, and 5-hydroxypryazinamide in adult TB/HIV-coinfected patients estimated by the final population pharmacokinetic model^a

Parameter	Mean (% RSE)	95% confidence interval
PZA CL/F (liters/h)	4.7 (8.12)	4.08 to 5.5
PZA V/F (liter)	62.0 (7.47)	53.7 to 72.2
Ka (h−1)	3.5 (233)	2.01 to 9.6
F	1 FIX
POA CL/F (liters/h)	9.5 (9.52)	7.72 to 11.2
F POA	0.45 (4.75)	0.41 to 0.488
OHPZA CL/F (liters/h)	15.8 (8.25)	13.7 to 19.2
Effect of female sex on F	0.47 (27.8)	0.244 to 0.755
Effect of serum creatinine on POA CL/F	−0.0064 (28.7)	−0.00264 to −0.0104
Effect of study arm on PZA, POA and OHPZA V/F	−0.24 (27.1)	−0.091 to −0.385
PZA proportional error	0.32 (6.01)	0.281 to 0.36
POA proportional error	0.3 (7.38)	0.261 to 0.347
OHPZA proportional error	0.278 (8.96)	0.23 to 0.327
PZA additive error	0.001 FIX
POA additive error	0.001 FIX
POA additive error	0.001 FIX
IIV CL/F (%)	40.5 (18.3)	28.8 to 41.2
IIV Ka (%)	351.1 (51.5)	116.2 to 216.1
IIV F (%)	38.0 (17.4)	31.4 to 44.0
IIV POA CL/F (%)	33.9 (52.1)	10.1 to 41.6
IIV FPOA (%)	27.4 (20.3)	21.6 to 31.1
IIV OHPZA CL/F (%)	16.1 (59.3)	5.3 to 30.9

^aRSE, relative standard error; PZA, pyrazinamide; POA, pyrazinoic acid; OHPZA, 5-hydroxypyrazinamide; CL/F, oral clearance; V/F, oral volume of distribution; K_a, absorption constant; F, bioavailability; F_POA, fraction of pyrazinamide forming pyrazinoic acid; IIV, interindividual variability; FIX, parameter fixed to the indicated value.

Simulations were performed to explore optimized doses with regard to PZA and POA exposure. The simulations indicated that 50-mg/kg doses in males and 35-mg/kg doses in females would result in adequate exposures with regard to a set therapeutic AUC of 363 mg·h/liter (Fig. 2). Furthermore, simulations of POA steady-state concentrations indicated that reducing the dose by 40% in patients with high serum creatinine concentrations (>133 μmol/liter) would result in POA exposure similar to that seen with a standard dose in patients with normal serum creatinine levels (Fig. 3).

FIG 2.

Simulated pyrazinamide area under the plasma concentration-time curve from 0 to 24 h (AUC_0–24) in patients weighting 50 kg coinfected with tuberculosis and HIV simulated by the final model stratified by sex and dose (n = 200). The dashed line shows the clinical therapeutic target (363 mg·h/liter).

FIG 3.

Simulated plasma concentration-time profiles of pyrazinoic acid following repeated administration of pyrazinamide stratified by sex and serum creatinine levels. Solid lines are the geometric means and gray areas are the 5th to the 95th percentiles of the simulated data.

The probability of target attainment (PTA) of pyrazinamide for a typical individual weighting 50 kg could be described as a function of MIC, dose, and patient sex [f(MIC,D,sex)] according to the following equation:

$$\mathrm{PTA}=1-\left(\frac{\mathrm{MI}{\mathrm{C}}^{\mathrm{4}\mathrm{.2}}}{\mathrm{MI}{\mathrm{C}}^{4.2}+{\left\{\mathrm{D}\times \left[0.02611-\left(\mathrm{sex}\times 0.007\right)\right]\right\}}^{4.2}}\right)$$

where sex has a value of 1 for males and 0 for females and D is the total dose (in milligrams) administered. Based on the function, PTA for the mode MIC (25 mg/liter) was calculated to range from 0.73 to 0.41 following administration of standard doses (1,200 mg) of PZA for females and males, respectively. According to our simulations, increasing the doses to 35 mg/kg and 50 mg/kg for males and females would increase the PTA to >0.9 for a MIC of 25 mg/liter. Simulated probabilities of target attainment depending on MIC, dose, and sex, probabilities predicted by the function, and wild-type MIC distributions determined in two other studies are depicted in Fig. 4 (16, 17).

FIG 4.

Probability of target attainment versus MIC (log₂ scale) following administration of pyrazinamide in patients weighting 50 kg coinfected with tuberculosis and HIV stratified by sex and dose (n = 500/group). Dots are simulated probabilities depending on dose and sex. Gray and black lines are probabilities predicted by the function for males and females, respectively. Shaded bars are the distributions of wild-type MICs acquired from two external studies, study 1 (17) and study 2 (16).

DISCUSSION

To the best of our knowledge, this is the first study describing the pharmacokinetics of PZA and its two primary metabolites in patients coinfected with TB and HIV. We evaluated the effects of efavirenz-based antiretroviral therapy, genetic polymorphisms in cytochrome P450 (CYP) and solute carrier organic anion transporter (SLCO), and patient characteristics on PZA, POA, and OHPZA pharmacokinetic parameters. The results indicate that the current regimen results in inadequate PZA exposure with regard to suggested therapeutic targets. Moreover, higher doses may be required in males than females. We also identified serum creatinine as a potential clinical predictor of POA exposure. Based on simulations, patients with high serum creatinine (>133 μmol/liter) should be administered lower doses to avoid potentially toxic accumulation of POA and OHPOA.

The use of a one-compartment model to describe the pharmacokinetics of PZA is in agreement with previous studies (14, 18, 19). Moreover, oral clearances (5.1, 4.5, and 3.4 liters/h, respectively), oral volume of distributions (44.9, 55.9, and 43.2 liters, respectively), and the absorption rate constants (3.6, 3.3, and 3.54 h⁻¹, respectively) estimated by the models are similar to our estimates. Also, the effect of sex on PZA pharmacokinetic parameters has been observed in previous reports (14, 19, 20). The precision of the absorption constant was poor, as judged by the nonparametric bootstrap, despite adequate precision in the covariance step (relative standard error [RSE], 22%). The difference in precision is likely due to lack of data for the absorption phase and high variability in the absorption rate. However, since the population estimate was in line with previous studies and the model predicted the observations well, the poor precision was considered acceptable.

A trend between creatinine clearance and POA clearance was observed in the present study. However, the relationship was not statistically significant when tested in the model. The effect of serum creatinine levels on POA exposure following administration of PZA is in line with two previous studies investigating the effect of renal impairment on PZA and POA exposure (21, 22). Both these studies concluded that a significantly higher exposure of POA was attained in patients with renal impairment than healthy subjects. Our results indicate that serum creatinine may be used for individual dose adaptations.

Although measured in this study, OHPOA concentrations were too low to be included in the analysis. OHPOA has been suggested to be the cause of PZA-induced liver toxicity (23). Since OHPOA is formed from POA, avoiding accumulation of POA and plausibly higher exposure to OHPOA due to lower renal function may result in less toxicity. According to our simulations, reducing the dose by 40% in patients with high serum creatinine could prevent such accumulation.

The clinical normal range for serum creatinine differs between males and females (44 to 133 μmol/liter and 44 to 88 μmol/liter, respectively). However, in the present study there was no significant difference in serum creatinine levels between sexes. Therefore, the normal range for males was used as a reference for simulations. Of note, one patient had considerably low serum creatinine levels (8.8 μmol/liter), which may be due to diet or muscular loss. However, the relationship between serum creatinine and POA oral clearance remained significant when this individual was excluded from the analysis.

An increase in PZA oral clearance from first dose to steady state has been described (19). It was suggested that the observed increase may be due to induction of metabolizing enzymes by rifampin. To the best of our knowledge, this is the first study reporting an effect by concomitant efavirenz-based ART on the disposition of PZA. The effect on distribution volumes of PZA and both metabolites could be due to a correlation with clearance. However, no apparent effect on PZA AUC was found between patients on concomitant ART and patients that were ART naive. Since the effect was relatively small and distribution volume does not influence AUC, we did not account for it during the simulations of optimized doses.

High doses of PZA have been associated with an increased risk of hepatotoxicity. Despite a trend indicative of such increased risk with higher doses, the authors of a meta-analysis concluded that PZA-induced hepatotoxicity is unrelated to dose (24). Nevertheless, a higher frequency of hepatotoxicity has been observed in females than males during TB therapy (25, 26). Our simulations indicated that 35-mg/kg and 50-mg/kg doses in females and males, respectively, would result in adequate exposure in the majority of patients with respect to the suggested therapeutic target. A critical concentration of 100 mg/liter is used for PZA (27). The suggested increase in dose may not be effective at MICs above 50 mg/liter, and an updated PZA susceptibility breakpoint in patients coinfected with HIV could be discussed. Nevertheless, optimization of PZA doses in combination with individualized doses of isoniazid and higher doses of rifampin will likely minimize the risk of treatment failure (28, 29). Such improvement of TB therapy requires further clinical evaluation with regard to hepatotoxicity. Of note, no correlation between PZA, POA, or OHPZA exposure and liver injury was observed in the present study. However, such correlation is challenging to study during first-line TB/HIV therapy, since rifampin-, isoniazid-, or efavirenz-based ART in addition to PZA may cause drug-induced liver injury.

For patients of low weight, standard doses of PZA are lower than the doses used in some studies which led to the reintroduction of PZA as part of the first-line TB therapy (1, 30). Since PZA efficacy is dose dependent in vivo and low PZA exposure has been correlated with poor clinical outcome, doses higher than 25 mg/kg guided by individual patient characteristics may increase efficacy of the first-line TB treatment. Increasing the efficacy could further lower the risk of resistance development. Individualized dosing of PZA should therefore be tested in clinical trials.

The World Health Organization has suggested determination of MICs in each patient as part of the Stop TB strategy (31). PTA functions like the one presented in this study could be used for individual dose calculations based on patient MICs and a desired probability of target attainment (typically 75 to 90%). Such predictions could ensure adequate drug exposure both in patients that would require higher doses than those in standard dosing regimens and in patients in whom lower doses could be used to avoid toxicity. For PZA, however, MIC determination is unreliable, and higher precision in MIC testing would be required if such an approach were to be implemented (27). In addition, the bacterial conversion of PZA to POA varies between patients and depends on local distribution of drug to the site of infection. Relating PZA AUC/MIC to efficacy is therefore intrinsically challenging and will require further confirmation.

Some limitations of the present study include genotypic information regarding the primary metabolizing enzymes of PZA, i.e., deamidase and xanthine oxidase, which was not evaluated on the pharmacokinetic parameters (32). Investigation of polymorphic effects on PZA pharmacokinetics and metabolism could lead to further understanding and optimization of individualized doses. However, the described effects of sex and serum creatinine on PZA and POA exposure are supported by results from previous clinical studies and offer a base for individualized therapy. Second, the modified liquid chromatography-tandem mass spectrometry (LC-MS/MS) method was not adequately sensitive to quantify OHPOA plasma concentrations in the patient population studied. Moreover, two different bioanalysis methods were used to quantify plasma concentrations of PZA, POA, and OHPZA. However, both methods were validated according to acknowledged guidance.

In conclusion, subtherapeutic exposure to PZA with regard to suggested thresholds was observed in the present cohort. Concomitant ART, sex, and serum creatinine levels significantly affected the pharmacokinetics of PZA and POA. The results suggest that serum creatinine may be used as a clinical predictor for exposure of POA. Moreover, simulations indicated that an individualized PZA dosing regimen based on sex and serum creatinine could reduce variability in exposure to PZA and its metabolites in TB/HIV-coinfected patients. Such reduction in variability may lower the risk of treatment failure and resistance development.

MATERIALS AND METHODS

Patients and study design.

In total, 63 Rwandan TB/HIV-coinfected patients were included in the present analysis. All patients were positive for HIV and TB and either were treated for HIV (n = 23) or were HIV treatment naive (n = 40) when TB therapy was initialized. HIV therapy consisted of efavirenz, lamivudine, and tenofovir or zidovudine. Patient demographics are summarized in Table 2.

TABLE 2.

Demographics of adult Rwandan TB/HIV-coinfected patients

Characteristic	Valuea
No. of patients	63
No. on concomitant HIV treatment (no/yes)b	40/23
Age (yrs)	41 (21–57)
Wt (kg)	50 (30–68)
Serum creatinine (μmol/liter)c	71 (9–159)
Creatinine clearance (ml/min)c	83 (30–715)
Aspartate aminotransferase (U/ml)	33 (11–248)
Alanine aminotransferase (U/ml)	33 (5–126)
CD4 cell count (/mm3)	232 (6–716)
Sex (female/male)	26/37
Dose (mg/day)	800 (n = 5); 1,200 (n = 35); 1,600 (n = 23)

^aContinuous data are given as median (range). Categorical data are given as counts.

^bHIV treatment includes efavirenz, lamivudine, and zidovudine or tenofovir.

^cOne patient had a serum creatinine level of 9 μmol/liter and a calculated creatinine clearance of 715 ml/min. The creatinine clearance range was 30 to 155 ml/min when the individual was excluded.

Patients received a total dose of 800, 1,200, or 1,600 mg of PZA in fixed-dose combinations together with rifampin, isoniazid, and ethambutol. Tablets containing 400/75/150/275 mg of PZA, isoniazid, rifampin, and ethambutol (Svizera, Almere, The Netherlands) were administered according to weight band-based standard TB therapy (two tablets for weights of 29 to 37 kg, three tablets for 38 to 54 kg, four tablets for 55 to 70 kg, and five tablets for >71 kg). Blood samples were collected predose and at 1, 2, 3, 4, 6, and 8 h following initiation of TB therapy. Following harvest of plasma, the samples were stored at −30°C in clinics for 1 week before being transferred to −80°C freezers.

Patients were treated in accordance with Rwandan national guidelines on TB/HIV coinfection. The open-label, observational study was conducted according to the principles given in the Helsinki Declaration and International Conference on Harmonization guidance for Good Clinical Practice with the study protocol approved by the National Ethics Committee of the Ministry of Health in Rwanda (33). Patients provided written signed informed consent and were informed that withdrawal from the study was accepted at any time.

Bioanalysis.

Plasma concentrations of PZA, POA, and OHPOA were analyzed using a published LC-MS/MS method with applied modifications as described in the supplemental material (34). Calibration curves ranged between 2.4 and 100 mg/liter for PZA and 0.72 to 30 mg/liter for POA and OHPOA, respectively. Intra- and interday accuracy and precision for PZA, POA, and OHPOA were 89.5 to 106.7% and a <13.2% coefficient of variation (CV), respectively. The extraction recovery varied between 69.0 to 77.7% for PZA and POA and 29.2 to 33.7% for OHPOA and was consistent between samples (<5.7% CV).

Quantification of OHPZA plasma concentrations was achieved by LC-MS/MS (34). In short, the method was validated over a range of 0.06 to 7.5 mg/liter for OHPZA. Accuracy and precision were 91.0 to 105.3% and a <11.7% CV, respectively.

Pharmacokinetic analysis.

Data were analyzed using nonlinear mixed-effects modeling in NONMEM software version 7.4.3 (ICON Development Solutions, Ellicott City, MD, USA) using first-order conditional estimation with interaction. Perl-Speaks-NONMEM version 4.8.1 (Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden) was used for interaction with NONMEM, and R version 3.5.1 (R Foundation for Statistical Computing, Vienna, Austria) was used for diagnostic plots, data handling, and simulations with the final model and to estimate parameters included in the probability of target attainment (PTA) function.

The disposition of PZA was modeled prior to the addition of POA and OHPZA data. One- and two compartment disposition models were applied to PZA plasma concentration-time observations. Different absorption models were tested, including first-order absorption with and without lag time, a transit compartment model with fixed numbers of transit compartments, and a transit compartment estimating the number of transit compartments. Different residual error models were evaluated, including additive, proportional, and combined additive and proportional residual errors. Interindividual variabilities were investigated on all parameters in the structural model. Statistically significant model improvement was based on reduction in objective function value (ΔOFV) where a reduction of 3.84 and 6.63 is equivalent to a model improvement with P values of <0.05 and <0.01, respectively.

One- and two compartment disposition models were investigated for POA and OHPZA. Observations for POA and OHPZA were included simultaneously. PZA was assumed to be fully eliminated via the formation of POA and OHPZA. Distribution volumes for POA and OHPZA were fixed to a previously estimated volume of distribution of POA to ensure model identifiability when estimating the fraction of each metabolite formed by PZA (35). Allometric scaling by body weight was applied to all clearance and volume parameters with exponents of 0.75 and 1, respectively.

Following the development of the structural model, covariates were evaluated on the estimated parameters by stepwise addition of covariates followed by backward elimination. Covariates were added and retained at significance levels of 0.05 and 0.01, respectively. Covariate inclusion was based on drop in OFV, parameter precision, and covariate-parameter relationship plausibility. Continuous covariates were centered on their respective medians and evaluated initially as linear relationships. Exponential and power relationships were evaluated if the covariate significantly improved the model. Covariates tested were alanine aminotransferase, aspartate aminotransferase, age, serum creatinine, creatinine clearance as determined by the Cockcroft and Gault equation (36), CD4 cell count, sex, the presence or absence of HIV drugs (study arm), and cytochrome P450 (CYP) 1A2 (739 T → G, 163 C→A, and 2159 G→A), CYP 2A6 (1436 G→T, 1093 G→A and 48 T→G), CYP 2B6 (516 G→T and 983 T→C), CYP 3A4 (392 A→G), CYP 3A5 (6986 A→G), SLCO 1B1 (463 C→A, 388 A→G, 11187 G→A, rs4149015, 521 T→C, and 1436 G→C), SLCO 1B3 (334 T→G), and CYP 2C19 (*2, *3 and *17) genotypes. Genotyping and distributions of CYP genotypes have been reported previously (37). SLCO and CYP 2C19 genotype distributions will be described elsewhere, since they were not relevant in the present context.

A nonparametric bootstrap (n = 200) and a visual predictive check (n = 1,000) were performed using the final model to estimate parameter precisions and confidence intervals and to visualize model prediction, respectively.

Simulations and PTA.

The final model was used to simulate optimized doses of PZA with regard to exposure of both parent drug and metabolites. An AUC of 363 mg·h/liter was used as a reference for optimal exposure of PZA (8).

PTA was calculated as a percentage of simulated patients (n = 500 per dose arm) with an AUC/MIC ratio above 11.3 following PZA administration (7). MICs were based on wild-type distributions of MIC from two different studies conducted in TB patients (16, 17).

PTA can be approximated as a function of dose (D) and MIC [f(MIC,D)] according to the formula 1 − [MIC^λ/(MIC^λ + PMIC₅₀^λ)], where λ is the slope factor and PMIC₅₀ is the MIC at which the PTA is 0.5. Since AUC is proportional to the dose, assuming linear pharmacokinetics, the probability of reaching a target AUC/MIC at a certain MIC will vary with dose. Hence, a parameter allowing PMIC₅₀ to vary with dose can be implemented: PMIC₅₀ = D − k, where k is the slope describing a linear relationship between PMIC₅₀ and dose. Further, such relationship between dose and PMIC₅₀ can be dependent on covariates affecting the bioavailability (F) and clearance (CL), since those parameters affect AUC: AUC = (F × D)/CL.