Table 4.

Final parameter estimates of the time‐to‐event model describing the time to death from TBM

Parameter	NONMEM estimates (%RSE)	SIR median (95%CI)
Using isoniazid Cmax linked to hazard of death
μ	3.42 (18.1)	3.48 (2.37–4.54)
σ	1.18 (16.4)	1.22 (0.86–1.64)
Glasgow coma scale on μ (%)	9.07 (14.9)	8.83 (6.36–12.68)
HIV coinfection on μ (%)	–27.7 (35.3)	–27.4 (−54.5 to −11.1)
IC50 (mg/L)	1.37 (34.3)	1.43 (0.54–2.44)
γ	2.79 (30.3)	2.77 (1.28–5.81)
Using isoniazid AUC linked to hazard of death
μ	3.29 (18.4)	3.33 (2.20–4.47)
σ	1.12 (16.2)	1.14 (0.79–1.57)
Glasgow coma scale on μ (%)	9.39 (13.6)	9.34 (6.34–13.03)
HIV coinfection on μ (%)	–33.5 (29.6)	–33.6 (−50.9 to −14.9)
IC50 (hour·mg/L)	7.03 (45.1)	6.99 (2.34–14.34)
γ	1.74 (28.1)	1.70 (0.87–3.08)

The hazard function can be described by the equations below.

$h\left(t\right)=h_0\left(t\right)\times \left(1-\frac{C_{\text{max,INH}}^{\mathrm{\gamma }}}{C_{\text{max,INH}}^{\gamma }+I{C}_{50,\text{INH}}^{\gamma }}\right)$, $h_0(t)=\frac{{(\mathrm{\sigma }t\sqrt{2\mathrm{\pi }})}^{-1}{e}^{\left(-\frac{1}{2}{Z}^2\right)}}{1-\mathrm{\Phi }(Z)}$,$Z=\frac{\ln \left(t\right)-\mu }{\sigma }$

where t represents the survival time, h(t) is the hazard function. h ₀(t) is the baseline hazard followed lognormal distribution, where μ and σ are the median and standard deviation of the distribution. IC₅₀ is 50% inhibitory C_max or AUC. γ is the slope‐factor for the drug effect. Glasgow coma scale (GCS) was included on parameter μ using a linear model, and HIV coinfection was implemented on μ using a proportional model $(\mathrm{\mu }={\mathrm{\mu }}_{\text{TV}}·\left(1+{\mathrm{\theta }}_{\text{GCS}}·\left(\text{GCS}-14\right)\right)·\left(1+{\mathrm{\theta }}_{\text{HIV}}·\text{HIV}\right))$, where ${\mathrm{\mu }}_{\text{TV}}$ was the typical value of the parameter. The isoniazid exposure was included on the hazard.

AUC, area under the concentration‐time curve; C_max, peak concentration; RSE, relative standard errors; SIR, sampling importance resampling.