Population Pharmacokinetic Modelling and Limited Sampling Strategies for Therapeutic Drug Monitoring of Pyrazinamide in Patients with Tuberculosis

ABSTRACT

Pyrazinamide is one of the first-line antituberculosis drugs. The efficacy of pyrazinamide is associated with the ratio of 24-h area under the concentration–time curve (AUC₂₄) to MIC. The objective of this study was to develop and validate a limited sampling strategy (LSS) based on a population pharmacokinetic (popPK) model to predict AUC₂₄. A popPK model was developed using an iterative two-stage Bayesian procedure and was externally validated. Using data from 20 treatment-naive adult tuberculosis (TB) patients, a one compartment model with transit absorption and first-order elimination best described pyrazinamide pharmacokinetics and fed state was the only significant covariate for absorption rate constant (k_a). External validation, using data from 26 TB patients, showed that the popPK model predicted AUC₂₄ with a slight underestimation of 2.1%. LSS were calculated using Monte Carlo simulation (n = 10,000). External validation showed LSS with time points 0 h, 2 h, and 6 h performed best with RMSE of 9.90% and bias of 0.06%. Food slowed absorption of pyrazinamide, but did not affect bioavailability, which may be advantageous in case of nausea or vomiting in which food can be used to diminish these effects. In this study, we successfully developed and validated a popPK model and LSS, using 0 h, 2 h, and 6 h postdose samples, that could be used to perform therapeutic drug monitoring (TDM) of pyrazinamide in TB patients.

INTRODUCTION

Despite the high efficacy for drug-susceptible tuberculosis (TB) treatment, TB remains one of the top 10 causes of death worldwide. TB is second only to COVID-19 as a leading cause of death from a single infectious agent, ranking above HIV/AIDS. In 2020, there was a global drop on reported TB cases due to the COVID-19 pandemic. Nevertheless, the WHO estimated that 10 million people suffered and 1.5 million died from TB in 2020 (1). First-line TB treatment consists of isoniazid, rifampicin, pyrazinamide, and ethambutol for the first 2 months, continued with isoniazid and rifampicin for another 4 months (2).

Pyrazinamide is a prodrug that is bioactivated to pyrazinoic acid by the pyrazinamidase enzyme inside M. tuberculosis (3). Although its mechanism of action is not clearly understood, pyrazinamide, with its high sterilizing activity, has been an essential component in the treatment of TB for a long time. The addition of pyrazinamide to the rifampicin-based regimen appeared essential to reduce the duration of treatment by 3 months, from 6 to 9 months. Its use was associated with a reduced relapse rate as well, illustrating its sterilizing properties whereby intracellularly located M. tuberculosis persister organisms with low metabolic and low replication rate appear to be killed effectively (3–6).

The efficacy of pyrazinamide is associated with the ratio of 24-h area under the concentration–time curve (AUC₂₄) to MIC (7). Low pyrazinamide exposure may lead to suboptimal treatment, as shown in two independent cohort studies from South Africa and China (8, 9). A pyrazinamide AUC₂₄/MIC ratio > 2.79 was the predominant predictor for 2-months culture conversion in drug-susceptible TB patients treated with first-line anti-TB drugs (8). Pasipanodya et al. showed that poor treatment outcome was associated with AUC₂₄ ≤363 mg*h/L of pyrazinamide in TB patients treated with first-line anti-TB drugs (9). However, patients received a median dose of 36 mg/kg pyrazinamide, which is higher than the WHO advised dosing of 25 mg/kg and 64% of the population were retreatment patients, indicating a selected patient group (9). A recent study showed that the majority of the patients using 20 to 25 mg/kg pyrazinamide (57/72, 79%) did not achieve this therapeutic target AUC₂₄ >363 mg*h/L (10). Variability in pyrazinamide exposure has been explained by factors like sex, body weight, and comorbidities (10–13). To optimize treatment, therapeutic drug monitoring (TDM) has been suggested for selected patients and drugs (14–16). Precision of TDM may improve when dose adjustment is based on AUC_24, that is calculated from a full curve consisting of multiple samples during the day. However, obtaining a full pharmacokinetic (PK) curve to estimate AUC₂₄ is a laborious and expensive procedure and therefore not feasible in clinical practice (17). A sampling strategy using a limited number of appropriately timed blood samples to predict AUC₂₄, may be a solution to overcome this problem (18).

The aim of this study was to develop a population PK (popPK) model of pyrazinamide and a limited sampling strategy (LSS) that can be used to accurately predict AUC₂₄ of pyrazinamide in patients with TB.

RESULTS

The baseline characteristics of both patient cohorts are displayed in Table 1. As can be observed from Table 1, for many patient characteristics, the two cohorts differed significantly (P value <0.05). AUC₂₄ and maximum concentration (Cmax) differed statistically significant between the model and validation patients (Table 2).

TABLE 1.

Patient demographics

Patient parameter	Model cohort (n = 20)	Validation cohort (n = 26)	P a
Male/female, n (%)	12/8 (60/40)	24/2 (92/8)	0.012b
Age, yr	37.0 (24.0 to 49.3)	32.5 (22.0 to 40.0)	0.166
wt, kg	41.5 (38.8 to 47.3)	62.4 (55.3 to 67.9)	<0.001
ht, cm	155 (152 to 161)	175 (166 to 182)	<0.001
Body mass index (BMI), kg/m2	17.0 (16.0 to 18.9)	20.3 (18.9 to 21.4)	<0.001
Underweight (BMI < 18.5 kg/m2), n (%)	14 (70)	3 (11)	<0.001b
Dose, mg	1,200 (1,200 to 1,200)	1,750 (1,500 to 2,000)	<0.001
Dose/wt, mg/kg	28.6 (25.4 to 30.2)	27.8 (26.1 to 29.6)	0.673
Comorbidity, n (%)  HIV  Diabetes, type II  Hepatitis B  Hepatitis C  Endstage renal diseasec	4 (20) 2 (10) 2 (10) 0 0 0	10 (38) 0 2 (8) 8 (31) 1 (4) 1 (4)	0.212b
Serum creatinine concn, μmol/L	75 (64 to 83)	64 (49 to 71)	0.012
Estimated glomerular filtration rated,  mL/min/1.73m2	93 (74 to 119)	133 (112 to 156)	0.002
WHO region, n (%)  South-East Asia  Africa  Europe	20 (100)	1 (4) 14 (54) 11 (42)	<0.001b
Type of TB, n (%)  Pulmonary TB  Extrapulmonary TB  Pulmonary + Extrapulmonary TB	20 (100)	23 (88) 2 (8) 1 (4)	0.164b

^aContinuous data form comparisons of model and validation cohort were tested using the Mann-Whitney U test. Data are presented as median and interquartile range (IQR).

^bChi-square test.

^cEndstage renal disease was defined as glomeral filtration rate < 15 mL/min.

^dEstimated glomerular filtration rate calculated using MDRD formula.

TABLE 2.

Noncompartmental pharmacokinetic parameters of pyrazinamide geometric mean (range)^a

Pharmacokinetic parameters	Model cohort	Validation cohort	P
Cmax (mg/L)	41.7 (29.9 to 61.1)	35.4 (23.6 to 70.3)	0.006
AUC24 (mg*h/L)	474 (284 to 645)	342 (160 to 599)	<0.001
AUC24/dose (h/L)	0.40 (0.20 to 0.60)	0.20 (0.11 to 0.34)	<0.001
Tmax (h), median (IQR)	2.1 (1.7 to 2.8)	1.6 (0.3 to 5.8)	0.185

^aData of model cohort are mean data of the fasted and fed state. Cmax, maximum concentration; AUC₂₄, area under the 24-h concentration–time curve; AUC₂₄/dose, area under the 24-h concentration–time curve divided by pyrazinamide dose in mg; T_max, time to Cmax; IQR: interquartile range. Mann-Whitney U test was used to compare validation with model cohort.

Population pharmacokinetic model.

The initial model resulted in an Akaike information criterion (AIC) value of 4,809 for one compartment with linear elimination. The one-compartment model with mixed order elimination and two-compartment models were not favorable (AIC 4,956 and 5,079, respectively). The final model was a one-compartment model with transit absorption and first-order elimination and was selected based on AIC (2,149) and goodness-of-fit plots (Fig. 1). The estimated parameters for the final popPK model are shown in Table 3.

FIG 1.

Goodness-of-fit plots for the final population pharmacokinetic model of pyrazinamide.

TABLE 3.

Parameter estimates and bootstrap validation of the final population pharmacokinetic model for pyrazinamide^a

Parameters (unit)	Population			Bootstrap
	Mean	IIV (%)	RSE (%)	Median	95% CI
Vd/F (L/43 kg)	30.3	13.3	3.1	30.4	28.4 to 32.2
CL/F (L/h/43kg0.75)	2.54	24.5	5.6	2.54	2.28 to 2.83
ka (1/h)	8.63	104	23.8	8.68	5.50 to 14.3
Effect of fed status on ka	0.36	80.1	18.4	0.36	0.25 to 0.51
F (fixed) Effect of fed status on F	1.00 1.00	6.9	1.6	1.00	0.96 to 1.03
No. of compartments	5.26	107	24.4	5.31	2.96 to 8.61
Proportional error (%)	6.54		3.8	6.53	5.48 to 7.60

^aV_d/F, apparent volume of distribution; CL/F, apparent clearance; k_a, absorption rate constant; F, bioavailability; IIV, Interindividual variability; RSE, relative standard error; 95% CI, 95% confidence interval.

The only covariate incorporated in the model was a factor for the fed state. This covariate impacted absorption rate constant (ka) and bioavailability (F), with 0.33 ± 85.9% and 1.00 ± 6.8%, respectively (Table 3). Allometric scaling was used to incorporate the effect of body weight on clearance (CL) and volume of distribution (V_d) with the fixed exponents of 0.75 and 1, respectively.

Limited sampling strategy.

LSS, using Bayesian fitting, with one time point between 0 h and 6 h showed acceptable bias and precision (mean percentage prediction error [MPPE] ranged from −0.30% to 0.63%, root mean squared error [RMSE] ranged from 6.43% to 7.86%, r² ranged from 0.997 to 0.998). LSSs with two or three time points performed even better. LSS, using multiple linear regression, with one to three time points between 0 h and 6 h showed acceptable bias and precision (MPPE ranged from −3.03% to 2.67%, RMSE ranged from 2.74% to 12.72%, r² ranged from 0.9946 to 0.9996). Again, all LSSs performed within the preset limits of imprecision < 15%, bias < 5%, and r² > 0.95. As all LSSs, irrespective of time points, performed within the preset limits, we chose LSSs with one, two, and three time points using 0 h, 2 h, and 6 h for external validation because of the historical use for TDM of anti-TB drugs and their clinical suitability (Tables 4 and 5) (19, 20).

TABLE 4.

LSSs of pyrazinamide using the Bayesian approach^a

First sampling time point (h)	Second sampling time point (h)	Third sampling time point (h)	RMSE (%)	MPPE (%)	r2
0			7.86	0.48	0.9970
2			6.46	0.63	0.9980
6			7.17	0.12	0.9975
0	2		4.95	–0.57	0.9988
0	6		5.12	–0.13	0.9987
2	6		4.63	–0.65	0.9990
0	2	6	3.84	–0.54	0.9993

^aRMSE, root mean squared error; MPPE, mean percentage prediction error.

TABLE 5.

LSSs of pyrazinamide using the multiple linear regression^a

Sampling time point (h)			AUC0–24, LSS to AUC24, LSS calculation	RMSE (%)	MPPE (%)	r2
1st	2nd	3rd
0			−0.309 + 6.863*C0	12.72	−3.03	0.9946
2			0.046 + 5.945*C2	6.47	0.22	0.9979
6			0.297 + 5.804*C6	8.84	2.21	0.9969
0	2		−0.147 + 2.384*C0 + 3.899*C2	6.14	−1.33	0.9986
0	6		−0.073 + 2.996 *C0+ 3.299*C6	5.42	−0.63	0.9986
2	6		0.082 + 3.344*C2 + 2.560*C6	4.73	0.64	0.9990
0	2	6	−0.057 + 1.653*C0 + 2.333*C2+ 2.159*C6	3.97	−0.47	0.9993

^aAUC_{0–24, LSS} to AUC_{24, LSS}, area under the 24-h concentration–time curve; C, concentration; RMSE, root mean squared error; MPPE, mean percentage prediction error.

Validation.

The external validation of the popPK model using validation cohort data indicated a mean underestimation of 2.1% (standard deviation [SD] 6.1%) of AUC_{24, model} compared with AUC_{24, ref} (Fig. 2A). One patient had a result below the lower line of agreement, the underestimation was 17.4% which could be explained by a low AUC₂₄ (both AUC_{24, ref} and AUC_{24, model} of 160 and 132 mg*h/L, respectively). This indicates that if a patient shows a low AUC₂₄ using the model, the real AUC₂₄ might be higher, but would still be too low. So, a large dose increase, and a subsequent TDM cycle, could be considered. The Passing-Bablok regression (Fig. 2B) showed no constant error (intercept 12.33; 95% CI = −27.35 to 52.29), nor a proportional error (slope 0.95; 95% CI = 0.82 to 1.1). A strong linear relationship was found between AUC_{24, ref} and AUC_{24, model} with a correlation coefficient r² = 0.94.

FIG 2.

External validation of the popPK model (n = 26). Bland-Altman plot of mean of AUC_{24, ref} and AUC_{24, model} (mg*h/L) versus the difference in % of the mean AUC₂₄. The solid line indicates the mean difference. The corresponding limits of agreement (mean difference ± 2 SD difference) are depicted as dashed lines. Passing-Bablok plot.

LSSs with one to three time points using 0 h, 2 h, and 6 h were externally validated with validation patients; however, the acceptance criteria (RMSE < 15%, median absolute percentage prediction error [MAPE] < 15% and bias < 5%) were not met for the majority of the LSSs (Table 6). Although RMSE was considered too high, LSS₀ showed acceptable performance with 81% of the patients with PPE < 15% and was able to discriminate between AUC ≤ or > 363 mg*h/L in 81% of patients. The LSS_0-2-6 showed the best performance in the external validation, with RMSE of 9.90% and bias of 0.06%, and it was the only LSS meeting the preset criteria, so we used it for further evaluation. The Bland-Altman plot of LSS_0-2-6 indicated a mean underestimation of 3.4% (SD 14.0%, Fig. 3). The LSS_0-2-6 did not completely fit the curves of three patients correctly, resulting in an underestimation of 34%, 35% and 44%, respectively. All three patients showed slow drug absorption (with time to maximum concentration T_max ranging from 3.5 h to 5.8 h) that resulted in difficulties in fitting.

TABLE 6.

The external validation of the selected LSSs^a

	Bias and precision				Passing-Bablok
LSS	MPPE (%)	RMSE (%)	MAPE (%)	No. of patients with PPE < 15% (%)	Slope [95%CI]	Intercept [95%CI]	r2 (Pearson correlation)
LSS0	2.78	22.76	6.79	17/21 (81)	0.96 [0.73, 1.27]	33.86 [–68.24, 128.30]	0.90
LSS2	14.93	76.02	25.11	10/26 (38)	0.82 [0.52, 1.55]	119.90 [–166.72, 221.75]	0.46
LSS6	12.38	42.94	13.40	17/26 (65)	0.83 [0.63, 1.00]	97.05 [43.07, 168.79]	0.93
LSS0-2	−2.69	21.83	7.06	18/23 (78)	1.07 [0.86, 1.43]	–28.80 [–142.09, 42.29]	0.75
LSS0-6	3.27	16.38	4.77	21/23 (91)	1.03 [0.79, 1.22]	1.09 [–48.61, 75.71]	0.95
LSS2-6	9.68	37.50	12.27	18/26 (69)	0.78 [0.57, 0.94]	104.60 [45.10, 179.59]	0.77
LSS0-2-6	0.06	9.90	3.07	20/23 (87)	1.03 [0.89, 1.22]	–9.53 [–69.66, 33.49]	0.82

^aMPPE, mean percentage prediction error; RMSE, root mean squared error; MAPE, median absolute percentage prediction error; PPE, percentage prediction error; 95% CI, 95% confidence interval; LSS_x, limited sampling strategy at time point x h.

FIG 3.

Bland-Altman plot of mean of AUC_{24, ref} and AUC_{24, LSS 0–2-6} (mg*h/L) versus the difference in % of the mean AUC₂₄. The solid line indicates the mean difference. The corresponding limits of agreement (mean difference ± 2 SD difference) are depicted as dashed lines.

DISCUSSION

In this study, we developed and validated a one-compartmental model with transit compartment and LSS that accurately predicts AUC₂₄ of pyrazinamide in TB patients. The one-compartmental popPK model is in accordance with the clinical observations, as pyrazinamide distributes rapidly and homogeneously over the body (21).

The pharmacokinetics of pyrazinamide were not affected by sex or age. This is in accordance with some literature (11, 22) and contrary to other (12, 23). We adjusted for the effect of body size and included weight using allometric scaling which may explain this difference. The covariate factor fed state showed a significant effect on the absorption rate (0.33 ± 85.9%), indicating that T_max increases considerably. As a consequence of this, Cmax decreases, which was indeed observed in the original study by Saktiawati et al. (24). The relative effect of the covariate on fixed bioavailability (1.00% ± 6.8%) indicates that bioavailability is not affected by the fed state. This confirms previous studies, reporting that food delayed the absorption rate but not the extent of the absorption (25–27).

Comparing our popPK model, V_d (30.3 L/43 kg) value is in the same range as those reported in literature (median V_d 43 L, range 28 to 62 L) (10–13, 23, 28, 29). Our estimation of CL (2.54 L/h/43°^0.75kg) is somewhat lower than the median reported CL of 4.1 L/h (range 3.3 to 5.1 L/h) (10–13, 22, 23, 28, 29). Partly, this is explained by the fact that we sampled early in treatment and that clearance of pyrazinamide appears to increase over time (13). Indeed the validation cohort, consisting of patients who were on treatment for at least 2 weeks, showed a 42% higher clearance (3.62 L/h/43kg^0.75) than our model cohort. Possibly the overall improving condition of the TB patients on effective drug treatment adds to the increased clearance (29). The absorption rate from our model (8.6 1/h) is high compared with others (median 3.5 1/h, range 1.3 to 3.5 1/h) and shows considerable variability. Our model cohort was sampled extensively in the absorption phase and we included a transit compartment in our model. The transit compartment causes absorption delay through a chain of presystemic compartments, connecting to the central compartment by a first order absorption process.

Our model was developed in a rather homogeneous population that was sampled in both fasted and fed states. The final model was successfully externally validated in a heterogeneous population with unknown fasted and fed states. In addition, the validation patients differed significantly with respect to weight, height, BMI, pyrazinamide dose, duration of treatment and severity of disease, and the model predicted AUC₂₄ with a mean underestimation of only 2.1%. This suggests that the popPK model could be considered in a wider population.

In this study, we developed LSSs with one to three sample time points that are easy and feasible in clinical practice with a maximum time span of 6 h postdose. In the external validation cohort, LSS_0-2-6 was the only LSS with acceptable bias and precision. The other selected LSSs did not meet the preset acceptance criteria of imprecision < 15% and/or bias < 5% in the external validation (Table 6). It is striking that the LSS₂ performed the worst in the external validation. This indicates that a C₂ sample is insufficient to estimate AUC₂₄ of pyrazinamide. This might be explained by the fact that T_max ranged from 1 h to 6 h and C₂ does not always capture Cmax. The LSS_0-2-6 is in accordance with the best performing time point in the multiple linear regression LSS of Magis-Escurra et al. (20). Although, it is more practical than the earlier suggested LSS of 2 h, 4 h, and 8 h by our group, the latest time point of 6 h may still be considered unfeasible in clinical practice as outpatients have to wait only for a blood sample to be taken. If this latest time point is impossible to obtain, clinicians might consider only drawing a through sample, C₀, taking into account the higher imprecision. Besides, as interindividual variability of PK of pyrazinamide is fairly low, one might also consider using any LSS for the combination of first-line drugs (18).

We developed the LSS using multiple linear regression next to the Bayesian approach that can be used to estimate drug exposure with straightforward calculation in a routine clinical setting (30). The LSS using the Bayesian approach provides an estimation of the AUC₂₄ with higher precision and accuracy; however, this approach implicates the use of the modeling software.

There are some limitations for this study. First, one should be cautious using the model and the proposed LSSs in estimating AUC₂₄ in TB patients with impaired renal function, as we were unable to incorporate renal function in our model. Second, we could not combine the two cohorts of patients to develop the popPK model of the mixed population due to the lower number of samples in the validation cohort. Third, the LSS_0-2-6 underestimated AUC₂₄ in a number of patients with delayed absorption. However, delayed absorption can be observed from the data and taken into consideration. Lastly, individual MICs were not available for the included patients. MIC determination for pyrazinamide is notoriously challenging and is dependent on the technique used, pH, and location (31, 32).

Target attainment was calculated as the percentage of the patients that achieved an AUC₂₄/MIC > 2.79 (8), using three MIC distributions (8, 31, 33). As can be observed from Fig. 4, up to an MIC of 64 mg/L (representing 96% of MICs), 100% of the model cohort, and 96% of the validation cohort obtained an AUC₂₄ high enough to achieve an AUC₂₄/MIC of 2.79. From this point of view the case for standard TDM is not strong.

FIG 4.

Target attainment AUC/MIC > 2.79 of model and validation cohort. MIC distributions from references are combined (8, 31, 33).

The majority of the patients (27/46, 59%) achieved a pyrazinamide exposure AUC₂₄ >363 mg*h/L (9); however, this was mainly achieved in the model cohort (18/20, 90%) compared with only 31% (8/26) in the validation cohort. This difference could be caused by selection bias of the validation cohort, being TB patients admitted to a tertiary reference hospital. However, both numbers are higher than the earlier reported 21% and may partly be explained by the lower dose of pyrazinamide (22.7 mg/kg) compared with our study (28.6 mg/kg and 27.8 mg/kg) (10).

The AUC₂₄ in our population ranged from 160 to 688 mg*h/L, a range that is rather similar to Alsultan et al. (10). However, this 4-fold difference between lowest and highest AUC₂₄ is considerably less than the interindividual variability in exposure observed in, for instance, isoniazid (18-fold) and rifampicin (56-fold) at standard doses (34).

It is striking to see that, based on probability of target attainment AUC/MIC > 2.79 for 2 month culture conversion, our population performed very good (98%) and, based on the target AUC₂₄ of > 363 mg*h/L, target attainment was only achieved in 59% of our population. In our view, this indicates that targets are still far from established. One could argue to follow the pharmacodynamic target on culture conversion as it most closely resembles outcome. However, if the difficulties with MIC determination, especially in the case of pyrazinamide, are taken into account, one would maybe prefer the PK target (35). In our view, to attain higher exposure, rather than performing TDM and adjusting doses, upfront higher dosing of pyrazinamide would be preferable. In the earlier days, the WHO recommended 35 mg/kg of pyrazinamide, based on the British Medical Research Council (BMRC) studies. For unknown reasons, the WHO lowered this to 25 mg/kg in 2003 (36–38). Moreover, doses up to 40 mg/kg seem to be tolerated rather well, not causing more hepatotoxicity (37, 39).

In this paper we showed that food slows absorption of pyrazinamide, but does not affect bioavailability, which may be very advantageous in case of nausea or vomiting in which food can be used to diminish these effects (24). Next to that, we identified a large difference in target attainment based on the chosen target, highlighting the need for development for solid targets. After defining this solid target, patient groups at risk for low exposure can be identified and these groups may have an indication for TDM. Until then, we suggest performing TDM of pyrazinamide in cases of suspicion of gastrointestinal abnormalities like malabsorption, poor response, and comorbidities like HIV and diabetes mellitus (14).

In conclusion, we successfully developed and validated a population pharmacokinetic model of pyrazinamide that can be applied for TDM in TB patients. Pyrazinamide exposure can be adequately predicted with LSS 0 h, 2 h, and 6 h in TB patients, both in patient care and future research.

MATERIALS AND METHODS

Patients.

Two data sets were used for this study. The first cohort included participants from a prospective randomized controlled PK study investigating the impact of food on the bioavailability of first-line anti-TB drugs (Fastfood, NCT02121314) (24). Study subjects were newly diagnosed treatment-naive susceptible TB patients of at least 18 years old who received 25 mg/kg pyrazinamide (24). The study was performed on the first 3 days of anti-TB treatment, so patients did not reach steady state of pyrazinamide. Subjects were randomly assigned to either drug administration on day 2 in fasted state and in fed state on day 3, or fed day 2, and fasted day 3. A PK curve was obtained during the first 3 days of treatment. Serial blood samples were taken at 11 time points: 0 h (predose), 0.5 h, 1 h, 1.5 h, 2 h, 2.5 h, 3 h, 4 h, 5 h, 6 h, and 8 h after dosing. Samples were centrifuged and stored at −80^°C until they were analyzed for pyrazinamide using liquid-chromatography-tandem mass spectrometry (LC-MS/MS), as previously described (40).

The second cohort included TB patients aged at least 18 years old, who were treated with pyrazinamide as part of routine treatment and were admitted for a part of the intensive phase at the University Medical Center Groningen, Tuberculosis Center Beatrixoord, Haren, the Netherlands. Patients were eligible if a PK curve for pyrazinamide had been obtained in routine care and if they did not object to the use of their data. Patients were treated with 25 to 30 mg/kg pyrazinamide according to the national guideline (41). Dense PK blood sampling was performed as part of standard clinical care after at least 2 weeks of treatment; samples were taken predose, and three to nine time points between 0.5 h and 8 h postdose. Plasma was separated and stored at −20^°C until analysis. Pyrazinamide concentrations were measured using the validated LC-MS/MS method (40). Demographic and medical data, including age, sex, weight, height, country of origin, ethnicity, type of TB, comorbidities, disease related malnutrition, TB drug regimen, pyrazinamide dose, renal function, liver enzymes, albumin, and presence of side effects, were collected from the electronic medical record system. This study was assessed by the Medical Ethics Review Board of the UMCG and found to be in accordance with the Dutch Law because of its retrospective nature (METc 2020-189).

Cmax was defined as the highest observed concentration, with T_max as the time to reach the Cmax. The reference AUC₂₄, AUC_{24 ref}, was determined by the log-linear trapezoidal rule using the Kinfit module of MWPharm version 3.81 (Mediware, Groningen, the Netherlands). Dose-corrected AUC₂₄ was calculated by dividing AUC₂₄ by pyrazinamide dose in mg. Noncompartmental PK parameters of model and validation population were compared using Mann-Whitney U test.

Population pharmacokinetic model.

The popPK modeling was performed using an iterative two-stage Bayesian (ITSB) of the KinPop module of Edsim++, version 1.98 (Mediware, Prague, Czech Republic). As data from the PK study subjects consisted of two full PK curves with a total 22 concentrations per subject, we decided to use these data to develop the popPK model (model cohort). Data from Beatrixoord patients was used for the external validation (validation cohort).

Various structural models, including one- and two-compartment models, with or without transit absorption and linear or nonlinear elimination were investigated as the base model. First, a simple one-compartment model with linear elimination and Bayesian estimations for clearance (CL), volume of distribution (V_d) and ka was tested. The initial values for CL, V_d, and ka were estimated based on the recent publications (13, 23, 29). Because F of pyrazinamide is almost complete and because it is administered orally only, F was fixed to 1 (42). PK parameters were assumed to be log-normally distributed. Residual errors—additive and proportional—were estimated on 0 mg/L and 0.15, respectively, and assumed to be normal distributed. Second, a one-compartment model with nonlinear elimination using three parameters (V_d, Michaelis-Menten constant, K_m and maximum rate, V_max) was tested. These two initial models were merged into a one-compartment model with combined linear and nonlinear elimination. Pyrazinamide is mainly metabolized in the liver by hydrolysis, only 2% to 14% is renally cleared (42). Therefore, the base model was designed using metabolic clearance only. Thereafter, a separate model with both metabolic and renal clearance was developed, however, the AIC value did not decline (AIC 2,209). Moreover, the renal clearance was overestimated (>24%) and lacking a significant correlation between estimated glomerular filtration rate and pyrazinamide clearance (r² = 0.02 and P = 0.46). Therefore, the model with both metabolic and renal clearance was abandoned.

Furthermore, a model with transit absorption defined using N as the number of transit compartments, was tested. Additionally, a simple two-compartment model with fixed values of central volume of distribution (V_d), peripheral volume of distribution, peripheral clearance, and total clearance from V_d was tested.

The base model was selected using AIC, a measure for goodness of fit using likelihood penalization. An AIC decrease of 3 was considered significantly better (43, 44).

The influence of patient characteristics as possible covariates on PK parameters was investigated with the Mann-Whitney U test, chi-square test, regression, or Kruskal Wallis test. A P value ≤ 0.05 was considered statistically significant. If a statistically significant correlation was observed using Spearman correlation coefficient or Pearson correlations coefficients test, the covariate was added to the base model. Again, the final model was selected based on the AIC and an AIC decrease of 3 was considered significantly better (43, 44).

Limited sampling strategy.

Monte Carlo Simulation was used to create 10,000 virtual pharmacokinetic profiles to represent the pharmacokinetic data. A 42-year-old male with bodyweight of 42 kg, length of 146 cm, body mass index (BMI) of 19.7 kg/m², and serum creatinine 76 μmol/L was selected as a reference patient for Monte Carlo simulation because of a well-fitting and representative pharmacokinetic curve in combination with representative patient characteristics, of the model population. LSS with different combinations of one to three sampling time points with a time resolution of 1 h were evaluated using Bayesian fitting or multiple linear regression. LSS was performed using both Bayesian estimation and multiple linear regression and maximized to a time span of 6 h instead of 24 h postdose because of clinical applicability. LSS was considered acceptable if the RMSE, as a measure of precision, was < 15%. The MPPE, as a measure of bias, was accepted if it was < 5% and the adjusted r² >0.95 (45, 46). The best performing LSSs were validated by comparing the AUC₂₄ predicted with LSS (AUC_{24, LSS}) with the AUC_{24, ref}.

Validation.

The final popPK model was validated using the bootstrap module of Edsim++. To evaluate the performance of the developed popPK model and LSS, external validation using patient data of the Beatrixoord cohort was performed. AUC₂₄ predicted with the popPK model (AUC_{24, model}) or LSS (AUC_{24, LSS}) was compared with AUC_{24, ref}. Correlation between AUC_{24, ref} and AUC_{24, model} or AUC_{24, LSS} was evaluated using Bland-Altman analysis and Passing Bablok regression in SPSS statistics, version 23 (IBM Corp., Armonk, NY, USA) and Analyze-it 4.81 (Analyze-it Software Ltd., Leeds, United Kingdom).

The external validation of the model and best performing LSS was performed according to the method described by Saktiawati et al. (45). In addition to the RMSE, the median absolute percentage prediction error (MAPE, median [100% × I(AUC_{24, LSS} − AUC_{24, ref})I/AUC_{24, ref}]) was calculated as another measure for precision. LSS was considered acceptable if bias and imprecision were smaller than 5% and 15%, respectively. A percentage prediction error (PPE), calculated as [100% × (AUC_{24, LSS} − AUC_{24, ref})/AUC_{24, ref}], was used to show the performance of the model or LSS for each individual. An acceptable PPE was considered smaller than 15%, and the number of patients with a PPE < 15% was calculated for the best performing LSS (45, 47, 48).