Table 2.
Parameter estimates for the basic model with and without time-dependent (td) CL, the final model and the bootstrap procedure and their coefficients of variation (CV)
| Parameter | Basic model without tdCL | Basic model with tdCL Estimate (CV%) | Final model | 500 Bootstrap replicates of the final model Mean estimate (CV%) |
|---|---|---|---|---|
| Minimum OFV | 454.9 | 163.5 | −505.5 | |
| PK parameters | ||||
| ka (h–1) | 4.4 (6%) | 3.6 (5%) | 4.0 (7%) | 4.0 (8%) |
| V1 (l) | 131 (8%) | 111 (10%) | 69 (6%) | 70 (4%) |
| CL (l h–1) | 27 (4%) | – | 23 (2%) | 23 (3%) |
| V2 (l) | 449 (10%) | 388 (9%) | 298 (8%) | 299 (8%) |
| Q (l h–1) | 64 (11%) | 49 (10%) | 34 (7%) | 35 (9%) |
| tlag (h) | 0.21 (2%) | 0.24 (1%) | 0.24 (1%) | 0.23 (5%) |
| Time-dependent parameters | ||||
| CLss (l h–1) | – | 20 (3%) | – | – |
| CLΔ (l h–1) | – | 14 (6%) | – | – |
| θrate (h–1) | – | 8.8 × 10−4 (12%) | – | – |
| Between-patient variability | ||||
| ka (%) | 156 (13%) | 112 (15%) | 101 (14%) | 109 (12%) |
| V1 (%) | 148 (13%) | 113 (17%) | 90 (16%) | 94 (9%) |
| CL (%) | 44 (9%) | 38 (9%) | 36 (9%) | 36 (5%) |
| Q (%) | 104 (25%) | 78 (22%) | 60 (21%) | 61 (12%) |
| Covariance (r) in estimates for between-patient variability | ||||
| rka–V1 | 0.74 (15%) | – | 0.45 (28%) | 0.49 (18%) |
| rka–CL | 0.14 (67%) | – | −0.13 (67%) | −0.13 (66%) |
| rka–Q | 0.54 (29%) | – | 0.21 (72%) | 0.23 (66%) |
| rV1–CL | 0.40 (21%) | 0.44 (19%) | 0.45 (17%) | 0.43 (16%) |
| rV1–Q | 0.46 (27%) | 0.55 (24%) | 0.33 (30%) | 0.31 (34%) |
| rCL–Q | 0.50 (19%) | 0.56 (17%) | 0.54 (18%) | 0.51 (19%) |
| Within-patient variability | ||||
| ka (%) | 137 (12%) | 124 (14%) | 116 (10%) | 117 (6%) |
| V1 (%) | 89 (11%) | 80 (13%) | 71 (12%) | 71 (6%) |
| CL (%) | 34 (7%) | 24 (10%) | 21 (10%) | 21 (5%) |
| Q (%) | 77 (23%) | 74 (22%) | 41 (39%) | 41 (21%) |
| Residual variability | ||||
| Additive error (mg l–1)* | 0.42 (2%) | 0.44 (2%) | 0.44 (2%) | 0.43 (2%) |
| Covariate effects | ||||
| CsA dose on ka | – | – | 9.8 × 10−4 (20%) | 9.4 × 10−4 (20%) |
| Factor for missing data | 0.99 (12%) | 0.98 (14%) | ||
| Albm on V1 | – | – | −1.2 (17%) | −1.2 (17%) |
| Factor for missing data | – | – | 1.0 (6%) | 1.1 (6%) |
| CLCR on V1 | – | – | −0.49 (10%) | −0.48 (10%) |
| Antacids on V1 | – | – | 1.4 (8%) | 1.4 (8%) |
| CsA predose concentration on CL | – | – | 4.8 × 10−4 (16%) | 4.8 × 10−4 (16%) |
| Factor for missing data | – | – | 0.96 (5%) | 0.96 (5%) |
| Albm on CL | – | – | −0.72 (13%) | −0.71 (13%) |
| Factor for missing data | – | – | 1.1 (3%) | 1.1 (3%) |
| CLCR on CL | – | – | −0.22 (7%) | −0.22 (8%) |
| Hb on CL | – | – | −0.48 (16%) | −0.48 (16%) |
| Between-patient variability in covariate effects | ||||
| CLCR on CL (%) | – | – | 66 (29%) | 67 (15%) |
| Albm on CL (%) | – | – | 112 (44%) | 115 (23%) |
Residual variability is on a natural logarithmic-scale as data were logarithmically transformed.tdCL = time-dependent CL, OFV = objective function, ka = first order absorption rate constant, V1 = central distribution volume, CL = clearance, V2 = peripheral distribution volume, Q = intercompartment clearance, tlag = lag time, CLss = steady-state value of CL, CLΔ = change of MPA CL from its steady-state value, θrate = first order rate constant determining the rate with which CL changes over time, r = correlation coefficient, CLCR = creatinine clearance, Albm = plasma albumin concentration, Hb = haemoglobin, CsA = cyclosporin. Typical ka, V1 and CL values can be calculated as follows:
ka = 4.0 × (1 + 9.8 × 10−4 × (CsA dose-325) × FLAG3ij) × 0.991–FLAG3ij
V1 = 69 × (CLCR/50)−0.49 × (Albm/38)–1.18 ×FLAG1ij × 1. 01–FLAG1ij × 1.4antacids
CL = 23 × (CLCR/50)CR−0.22 ×exp(ηCL) × (Albm/38)Albm−0.72 ×exp(η) ×FLAG1ij × 1.11–FLAG1ij × (1 + 4.8 × 10−4 × (CsA predose−200) × FLAG2ij) × 0.961–FLAG2ij × (Hb/11)−0.48
where FLAG1ij, FLAG2ij and FLAG3ij are 1 when Albm, CsA predose concentration and, respectively, CsA dose data are present and 0 when covariate data are missing.