A Model-Informed Method for the Purpose of Precision Dosing of Isoniazid in Pulmonary Tuberculosis

The data originated from seven previously conducted studies, including data from both clinical trials and TDM [14, 23‐28]. All studies included patients with pulmonary TB. The study data are presented in Table 1. In total, data of 466 patients from three continents were used to develop the PK model. These PK data consisted of 2546 INH and 2236 acetyl-INH concentrations collected during an interval range of 0–24 h. Of these concentrations, 6.0% of the INH and 10.9% of the acetyl-INH observations were measured as ‘below the limit of quantification’ (BLQ), which ranged from 0 to 27.3% depending on the study.

Four studies involved intensive PK sampling with at least nine samples taken after a dose of INH [14, 24, 26, 27], two studies involved limited sampling with two to three samples taken [23, 28], and one study involved limited sampling with one sample taken for all except nine individuals who were sampled intensively [25]. Five studies only included measurements of a single occasion [14, 24‐27], one study included some measurements of second occasions [28], and one included measurements for second occasions for all individuals [23]. One study included data that were collected during TDM practice [28]. Five studies included PK data on both INH and acetyl-INH [24‐28], while the other two studies included PK data on INH [14, 23].

The analysis of INH and acetyl-INH concentrations was performed in The Netherlands for all studies, using either ultra-performance liquid chromatography with ultraviolet detection or liquid chromatography–tandem mass spectrometry [29]. Both methods were extensively validated in accordance with European Medicines Agency and US Food and Drug Administration guidelines. Accuracy was between 99.4 and 108.8% and between 95.6 and 111.3% and the intra- and inter-assay coefficients of variation (CVs) were less than 12.6% and 10.5% for the ultra-performance liquid chromatography with ultraviolet detection and liquid chromatography–tandem mass spectrometry methods, respectively, dependent on the concentration. The lower limits of quantification for INH and acetyl-INH for the ultra-performance liquid chromatography method were 0.0253 mg/L and 0.162 mg/L, and these were 0.0452 mg/L and 0.0450 mg/L for the liquid chromatography-tandem mass spectrometry method. Performance of the assays was externally evaluated by participation in an international proficiency testing program [30].

R version 3.4.3 was used for data management, statistics, and plotting [31]. Model development was performed using the nonlinear mixed-effects modeling program, NONMEM version 7.4 with Pirana as an interface [32, 33]. The first-order conditional estimation method with interaction was used for estimation. PsN version 4.7 was used as an aid for advanced functionalities [33]. The Xpose4 R package version 4.6.1 was used for graphical visualization of the visual predictive checks (VPCs) [33].

The PK model was developed with a stepwise approach [34]. The INH concentration data were included one study at a time, starting with the studies that had the most informative and dense sampling. After finishing the base INH model, the acetyl-INH data were added to the model. One- and two-compartment disposition models were explored to describe the pharmacokinetics of INH and acetyl-INH. A well-stirred liver model was tested instead of first-order elimination to describe the first-pass effect of INH. The molecular weight of INH and acetyl-INH was used to transform drug concentrations to molar concentrations to model the formation of acetyl-INH from INH. The bioavailability of INH was assumed to be 100% and all estimated PK parameters should be interpreted as apparent oral PK parameters. All volume and clearance parameters were allometrically scaled with total body weight using an exponent of 1 or 0.75, respectively [35]. Allometric scaling based on fat-free mass was not considered because height is not always readily available in TDM practice. NAT2 genotypic data were not determined in the included studies. A mixture model to distinguish between different groups of NAT2 metabolizers in the absence of genotypic data was applied [36]. It is known that the distribution of NAT2 metabolic function is trimodal [8]. The mixture model was tested with two as well as three metabolizer groups as it can be difficult to distinguish the three mixture groups as is seen in other models [4, 17]. In case two, metabolizer groups were used, the fast and intermediate metabolizers were grouped, as metabolization rates of these groups are closer together than those of the slow metabolizers, which have more deviant metabolization rates.

Inter-individual variability in the pharmacokinetics of INH was assumed to be log-normally distributed. Inter-occasion variability was not assessed because the number of individuals who were sampled on multiple occasions was limited. For residual variability, additive, proportional, and combined models were tested for both INH and acetyl-INH. Below the limit of quantification data were handled using the M6 method as described by Beal [37]. The M3 method was tested but did not perform better than the M6 method and increased numerical instability. Using this method, in the elimination phase, the first datapoint BLQ is replaced by the lower limit of quantification/2, and subsequent BLQ points are ignored. In the absorption phase, it is the last datapoint BLQ that is replaced and all previous BLQ points that are ignored. The minimum additive error for data BLQ was fixed to 50% of the lower limit of quantification values.

The number of potential covariates tested was kept low because of the purpose of our model; the covariates available in TDM practice are generally quite limited. It was opted to include only the allometric scaling with total body weight to not hamper a general implementation of the model in routine TDM. Although we did test the impact of formulation differences, but no effect could be identified.

Pharmacokinetic parameter uncertainty was assessed using sampling importance resampling [38, 39]. Sampling importance resampling is a fast method to determine parameter uncertainty which is free of distributional assumptions, a good alternative to the bootstrap. The initial estimates for the SIR were based on a successful covariance step and inflated by factor 1.5. The samples per iteration were 1000, 1000, 1000, 2000, and 2000, the re-samples per iteration were 200, 400, 500, 1000, and 1000. Parameter precision was presented using the calculated 95% confidence intervals (CIs). The predictive performance of the final model was assessed using VPCs and goodness-of-fit plots. The VPCs were prediction corrected and the PsN mixture option was used [40, 41].

The performance of three LSSs was tested. These LSSs had sampling times at 2 h, 2 and 4 h, and 2, 4, and 6 h after dosing. These LSSs were chosen considering that sampling at 2 and 6 h, introduced by Peloquin et al., is common for TB drugs, and we have added a 4-h sampling point in our TDM service [2, 42]. In addition, samples with these sampling times were available within most of the datasets. Sampling at 2 and 6 h was not included as it does not offer any benefit over sampling at 2 and 4 h, which is more feasible to perform in clinical practice. For each LSS, the performance of AUC₂₄ and C_max prediction was determined using the patients who had a full PK curve including samples at 2, 4, and 6 h after dosing (169 patients from five studies) [14, 24‐27]. The performance of the LSSs was also compared to the performance of the model without any sampling to assess the added value of sampling in TDM. The most suitable LSS was selected based on predictive performance and clinical practicality. The performance of predicting the AUC₂₄ was regarded as more important than that of the C_max. In these assessments, the mean error (ME) and root mean square error (RMSE) and their 95% CIs of the prediction of AUC₂₄ and C_max were calculated as measures of bias and precision [43, 44]. The ME and RMSE were expressed as a percentage of the mean of the corresponding model-estimated parameter using the full PK curve.

The most suitable LSS was used to perform a fit-for-purpose analysis, meaning that it was investigated how well the pharmacokinetics of INH could be predicted from a previous measurement [45]. The patients including data of a second occasion and the sampling times for the selected LSS were used for this. Apart from the most suitable LSS, ‘no sampling’ was tested as well to evaluate the amount of variability explained by the most suitable LSS. Suitable data for this analysis were available from 13 patients from only one study [28]. The performance of predicting the AUC₂₄ for the second occasion was determined using the ME and RMSE.

The added value of both the acetyl-INH metabolite data and inclusion of a mixture model accounting for the polymorphic NAT2 clearance was assessed for the most suitable LSS. The selected LSS was used to provide AUC₂₄ predictions using only the INH data. These predictions were compared to model predictions using the full dataset, including the acetyl-INH data. To determine the added benefit of a mixture model to the performance of predicting the AUC₂₄, the mixture component was removed, and model parameters were re-estimated. The performance was again compared using the ME and RMSE.

The final model is depicted in Fig. 1. It included four transit absorption compartments going into a well-stirred liver model [46]. The pharmacokinetics of INH was best described by a two-compartment disposition model. Acetyl-INH pharmacokinetics was characterized using a single compartment and first-order elimination. Metabolization in the liver compartment could either clear INH or transform it into acetyl-INH. It was not possible to estimate INH clearance as a trimodal distribution using a mixture model and thus a bimodal mixture model was included. The volume of the liver compartment and hepatic plasma flow were fixed to 1 L and 49.5 L/h, respectively, and allometrically scaled on total body weight like other volume and clearance parameters.

The final model parameter estimates and their uncertainty are shown in Table 2. Uncertainty in the parameter estimates was generally low (relative standard error, RSE < 12%CV), except for the IIV of the central volume of acetyl-INH (RSE = 40%CV) and the correlation between the IIV of the clearances (RSE = 71%CV). The absorption processes were variable between individuals with an IIV estimated at 83.2%CV (95% CI 78.1–91.7). The proportion of fast NAT2 acetylators in the studies was estimated at 43.4% (95% CI 38.4–48.9). Slow acetylators typically had 13% of the intrinsic NAT2 clearance of fast acetylators. The second clearance pathway, not through NAT2, typically made up 74% of the total clearance for slow acetylators and 27% of the clearance for fast acetylators. A correlation was found between the clearance through acetylation and through other pathways, but the uncertainty of this correlation was quite high (0.143, 95% CI − 0.0620, 0.325). Additionally, a correlation between the proportional residual errors of INH and acetyl-INH was found.

The VPCs, shown in Fig. 2, generally describe the model well. Some limitations of the model can be discerned from this figure. The model does not describe the median observed peak perfectly. Furthermore, the model simulates concentrations that are slightly too high on the upper end of the concentration range for acetyl-INH at timepoints after 8 h. The VPCs of the model were deemed satisfactory for TDM using the AUC₂₄. The performance of the model for TDM using the C_max should be explored further. Other goodness-of-fit plots are shown in Fig. 3 and do not show any obvious misspecifications. The full code of the final model is included in the Electronic Supplementary Material (ESM).

The AUC₂₄ and C_max predicted by the LSSs were compared to the AUC₂₄ and C_max predicted by the model based on full PK curves. Scatterplots of this are shown in ESM 1. The bias and precision of these strategies are shown in Table 3. The LSS using only one sample performed substantially worse in both bias and precision than the strategies with two or three sampling points. The strategies employing sampling at 2 and 4, and 2, 4, and 6 hours after dosing have a similar performance. Based on bias, precision, clinical practicality, and conformity with a previously developed strategy for rifampicin [28], the strategy using sampling at 2 and 4 hours after dosing was selected as the most suitable.

To assess if the model and LSS is fit for purpose, the AUC₂₄ of a second sampling occasion was predicted using data from a first sampling occasion. The fit-for-purpose analysis of the model using the 2- and 4-h sampling strategy resulted in an ME of 25.7% and an RMSE of 37.2%. Without sampling in the first occasion, the ME was 82.7% and the RMSE 117.9%.

The final model using the 2- and 4-h LSS without the acetyl-INH data had an ME of − 1.8% and an RMSE of 28.9% for estimating the AUC₂₄. For estimation of the C_max, the ME was 0.1% and the RMSE 23.5%. Comparison to data in Table 3 shows that the prediction of the model without acetyl-INH data is less precise compared to the predictions including acetyl-INH for the 2- and 4-h sampling strategy. For the 2-, 4-, and 6-h strategy without acetyl-INH data, the estimation of the AUC₂₄ had an ME of 1.7% and an RMSE of 20.9%. For estimation of the C_max, the ME was 1.2% and the RMSE 23.8%. This is comparable to the performances of the 2-, 4-, and 6-h and 2- and 4-h strategies including acetyl-INH data. ESM 2a shows the effect of removing the acetyl-INH data on the performance of predicting the AUC₂₄ for the 2- and 4-h sampling strategy.

The re-estimated model without a mixture component using the 2- and 4-hour LSS had an ME of − 1.1% and RMSE of 24.6% for AUC₂₄ estimation, and an ME of 7.7% and RMSE of 23.3% for estimation of the C_max, meaning that the mixture component was not essential for the predictive performance of the model. The estimated PK parameters for the model without a mixture component were similar to those of the final model, except for the clearance representing both metabolization groups and their IIV. The new clearance has a value of 9.12 L/h and lies in between the clearances of the slow and fast metabolizers as estimated by the final model. The estimated IIV of this clearance has increased drastically by more than two-fold to 115.8%CV. ESM 2b shows the effect of removing the mixture model on the performance of predicting the AUC₂₄.