Chapter 6: A semi-mechanistic model of the bactericidal activity of high-dose isoniazid
6.8 Supplemental Results
6.8.1 Pharmacokinetic model
The final model describing isoniazid's pharmacokinetics was a two-compartment PK model with first-order absorption, transit compartment absorption, and first-order elimination using a well-stirred liver model. The well-stirred liver model's use to capture the effect of first-pass metabolism significantly improved the model fit (ΔAIC = -6.13). Allometric scaling was applied to all the clearance and volume parameters (including the liver), to account for the effect of
143 body size, and it improved the fit explaining part of the between-subject variability. Fat-free mass was found to be a more suitable descriptor of body weight for allometric scaling of all disposition parameters. The clearance of isoniazid was significantly affected by NAT2 genotype (p ≪0.001), as CLint varied greatly between rapid (46.3 L/h), intermediate (23.9 L/h), and slow acetylators (9.25 L/h). Parameter estimates of the PK of isoniazid are displayed in Table E6.1. Model evaluation through VPC (Figure E6.2) shows that the model described the data well since the percentiles of the raw data (summarised as solid and dashed lines) fell within or near their respective model-predicted confidence intervals for all time points.
Table E6.1: Final PK parameter estimates for isoniazid.
Parameter Typical value (95% CIa) Variability b, %CV (95% CIa)
CLintc (L/h) NAT2 Rapid 46.3 (36.6 – 59.1)
35.9 (31.7 – 39.6)*
CLintc (L/h) NAT2 Intermediate 23.9 (20.4 – 28.1) CLintc (L/h) NAT2 Slow 9.25 (8.01 – 10.74)
Vc d (L) 30.9 (28.0 – 34.2)
Q/F c (L/h) 8.15 (7.35 – 8.82)
Vpd (L) 15.3 (13.0 – 17.7)
ka (1/h) 3.28 (2.48 – 4.62) 72.2 (54.6 – 88.4)#
MTT (h) 0.112 (0.0648 – 0.170) 112 (82.6 - 149)#
NN () 2.32 (1.64 – 3.27)
QHc (L/h) 90 FIXED
fu (%) 95FIXED
Prehepatic relative bioavailability 1FIXED 23.1(18.6 – 29.9)#
Proportional error (%) 12.7 (11.2 – 14.8)
Additive error (mg/L) 0.021e FIXED
Abbreviations: CLint clearance intrinsic; Vc apparent central volume of distribution for INH; VP apparent peripheral volume of distribution for INH; Q/F apparent intercompartmental clearance for INH; ka first-order rate constant of INH absorption;
MTT absorption mean transit time; NN Number of absorption transit compartment; QH blood liver flow (Yang et al., 2007);
fu unbound fraction of isoniazid in plasma (Alghamdi et al., 2018).
a 95% confidence intervals (CIs) were obtained with the SIR procedure
b Variability was modelled with log-normal distribution and is presented as an approximate percentage CV.
c Clearance parameters are allometrically scaled based on fat-free mass (typical value reported for 44 kg, which was the median fat-free mass weight of the study population).
d Volume pf distribution parameters are scaled based on weight (typical value reported for 51 kg, which was the median weight of the study population).
e Additive error was fixed to 20% of the LLOQ.
* Between subject variability.
# Between occasion variability
144 Figure E6.2: Visual predictive check of the isoniazid model, stratified by dose and NAT2 genotype. The solid and dashed lines are the 5th, 50th, and 95th percentiles of the observations, while the shaded areas represent the 95% model-predicted confidence intervals for the same percentiles
145 6.8.2 Pharmacokinetics/pharmacodynamic model
The empirical model with an exponential decline of bacterial load could roughly describe the decrease in M.tb in the sputum, but it did not explain the delay in the onset of killing for the inhA arms. The introduction of a delay in the onset of drug action or a bi-exponential decline provided a slight improvement of the model fit but made the parameter estimates unstable and unreliable. When assessing the effect of isoniazid PK on bacterial decline within this empirical model, which assumes time-invariant rates of decline, we could only test a “static”
metric of drug exposure, so we used AUC24. The inclusion of AUC significantly improved the fit and was a better explanatory variable than dose level (i.e., study arm). Interestingly, replacing AUC24 with AUC24/MIC led to worsening of the model fit and an increase in the unexplained variability.
Switching to a compartmental model with time-varying kill rate provided much more flexibility in fitting the data compared to the empirical exponential model. The effect of isoniazid on the first-order killing of M.tb was best described by using an effect compartment, which could satisfactorily describe the delayed onset of killing action against inhA-mutated M.tb. We used an Emax function to characterize the relationship between effective concentration (in the effect compartment) and kill rate and we estimated significantly different values of EC50 for drug-sensitive and InhA-mutated M.tb (p ≪0.001), reflecting that isoniazid is much more potent against sensitive strains. After including the categorization drug-sensitive vs. inhA-mutated, we found limited additional explanatory value of the individual values of MIC on EC50 (p=0.035). Testing the effect of MIC only within the inhA- mutated subpopulation also did not reach the stipulated statistical significance threshold (p=0.0425).
146 While the lack of explanatory value of MIC after the differentiation between drug-sensitive and inhA-mutated (which was based on the result of the molecular test) could be due to large proportion of missing values, we used a methodology known to minimise the impact of missingness. Even in the patients with available MIC values, these did not meaningfully explain variability in the model. This is in line with the large variability associated with the determination of MIC (Xuesong Wen et al., 2016); minor variations in the incubation period, the storage of samples, lab techniques, may all play a role in the observed value. Moreover, MIC values depend on the dilution series (generally by a factor of 2) and are actually interval- censored data, thus potentially carrying an uncertainty of up to 50%.
The stochastic simulations and estimations investigating the estimation property of the model revealed a relative bias <15% and relative standard error <30% for the typical values of all PD parameters. The sensitivity analysis confirmed that a change in the sputum sampling time within the 16-hours sampling window did not substantially impact the model parameters characterizing the drug effect.
147