Table 2.

Estimated population pharmacokinetic parameters of tacrolimus and bootstrap validation

	Population modeling		Bootstrap (n=1000)
Parameter - Symbol	Estimates	RSE (%)	Median	95% CI	Biasa (%)
CL/F (L.hr−1) − ${\theta }_{CL/F}$	19.7	6.30	19.6	17.5 – 22.1	−0.10
CYP3A5*3*6*7 on CL/F
CIMCYP3A5 − ${\theta }_2$	1.45	9.90	1.46	1.20 – 1.78	0.01
CEMCYP3A5 − ${\theta }_3$	2.25	13.6	2.28	1.64 – 3.01	0.03
V/F (L) − ${\theta }_{V/F}$	234	10.2	231	190 – 276	−3.00
CLp/F (L.hr−1) − ${\theta }_{C{L}_p/F}$	52.6	9.50	53.2	44.1 – 63.6	0.60
Vp/F (L) − ${\theta }_{V_p/F}$	403	20.1	404	275 – 572	1.00
ka (hr−1) − ${\theta }_{k_a}$	4.21	20.3	4.14	2.77 – 5.74	−0.07
Lag time (hr) − ${\theta }_{\mathit{lag}}$	0.828	3.80	0.830	0.740 – 0.873	0.002
Between-subject variability
BSV CL/F (CV%) − ${\eta }_1$	37.0	6.20	36.1	30.9 – 40.7	−0.9
BSV V/F (CV%) − ${\eta }_2$	76.7	12.1	76.0	56.0 – 93.5	−0.7
BSV CLp/F (CV%) − ${\eta }_3$	48.6	16.5	47.8	29.4 – 64.9	−0.8
BSV ka (CV%) − ${\eta }_4$	69.4	16.5	68.6	48.3 – 93.9	−0.8
Residual variability
Proportional error − ${\epsilon }_1$	9.00	5.60	8.90	8.04 – 9.83	−0.1

RSE (%) Percent relative standard error of the estimate; 95% CI 95^th Confidence interval: 2.5 and 97.5^th percentiles, BSV Between-subject variability expressed as percent coefficient of variation (CV%); CL/F =Apparent elimination clearance; CL_p/F Apparent distribution clearance; V/F Apparent central volume of distribution; V_p/F Apparent peripheral volume of distribution; k_a Absorption rate.

^aThe bias of each parameter was calculated by computing the difference between the median value derived from the bootstrap and the final parameter estimate.

99% of the bootstraps runs minimized successfully (990/1000).

Final pharmacokinetic model (typical individual values):

$CL/F_i={\theta }_{CL/F}\times {\theta }_2^{H1}\times {\theta }_3^{H2}$ and $V/F_i={\theta }_{V1/F}\times \left(\frac{\mathit{TBW}}{85.9}\right)$

where H1 = 1 for CYP3A5 intermediate metabolizers (cIM_CYP3A5) and H2 = 1 for CYP3A5 extensive metabolizers (cEM_CYP3A5). TBW Total body weight (kg)