Table IV.
Published simulation studies evaluating the performances of tests on discrete covariate effect for differents designs using nonlinear mixed effects models. ANOVA, Student and Wilcoxon tests are based on empirical Bayes estimates of the individual parameters
| First author (reference) | Year | Algorithm | Software | Number of PK parameters | Design | Test | Covariate | Type I error | |
|---|---|---|---|---|---|---|---|---|---|
| Distribution (%) | Effect | ||||||||
| Bertrand (present study) | 2009 | SAEM | MONOLIX | 3 | N={40,200}/n=4 N=80/n=2 N=100/n=4,1 |
ANOVA Wald LRT |
24:48:28 | 1:1.2:1.6 | No inflation for ANOVA Slight inflation for Wald and LRT when N={40,80,100} corrected on N=200 |
| Panhard1 (28) | 2009 | SAEM | MONOLIX | 3 | N={40,24}/n=10 | Wald LRT |
50:50 | - | No inflation |
| Bertrand (8) | 2008 | FO FOCE-I |
NONMEM | 3 | N={40,200}/n=4 | ANOVA Wald LRT |
24:48:28 | 1:1.2:1.6 | No inflation for ANOVA Strong inflation for Wald and LRT with FO when N={40,200} Slight inflation for Wald and LRT when N=40 corrected on N=200 with FOCE-I |
| Samson (17) | 2007 | SAEM | MONOLIX | 4 | N={40,80,200}/n=6 | Wald LRT |
50:50 | 1:{1.3,1.5} | No inflation |
| Panhard1 (36, 33) | 2007/2005 | FOCE-I | R (nlme) | 3 | N=12/n=10 N=24/n=5 N=40/n=3 N={24,40,60}/n=10 |
Student Wilcoxon Wald LRT |
50:50 | 1:{0.8,0.875, 0.9,1.1, 1.125,1.25} | Inflation for Student and Wilcoxon when n=3, but not for n={5,10} Inflation for Wald and LRT when N={24,12}, but not for N=40 No inflation for Wald and LRT when modelling IOV |
| Bonate (31) | 2005 | FOCE | NONMEM | 2 | All combinations of N={50,100,150,200}/n={2,4,6} | ANOVA LRT |
50:50 | 1:1.25 | No inflation for ANOVA Inflation for LRT when n={4,6} |
| Zhang (45) | 2003 | FOCE-I | NONMEM | 4 | N=30/n=5 | LRT | 50:50 | - | No inflation |
| Gobburu (30) | 2002 | FO FOCE FOCE-I |
NONMEM | 3 | N=30/{n=5,2,(5,2)} | LRT | Continuous | - | Strong inflation with FO Sligh inflation with FOCE when n={5,(5,2)} No inflation with FOCE-I |
| Comets (32) | 2001 | FOCE FOCE-I |
NONMEM | 3 | N=20/n=7 | Wilcoxon LRT |
50:50 | 1:1.2 | No inflation for Wilcoxon (individual fits) Inflation for LRT with FOCE No inflation for LRT with FOCE-I |
| Lee (40) | 2001 | FOCE-I | R (nlme) | 3 | N=200/n=2 N=100/n={2,3,(5,2)} |
Student LRT |
90:10 80:20 70:30 60:40 50:50 |
1:1.3 | Inflation for Student when n=5,2 Inflation for LRT when n={2,(5,2)} Inflation increases when the proportion of the subpopulation increases |
| Wählby (29) | 2001 | FO FOCE FOCE-I Laplacian Laplacian-I |
NONMEM | 2 | All combinations of N={10,25,50,250,1000}/n={2,4,19} | LRT | 98:2 90:10 75:25 33:33:33 |
- | Strong inflation with FOCE and Laplacian, when n={4,19} and when N={10,25,50}/n=2 with addition of N={250}/n=2 for FO Slight inflation with-I method, when N={10,25} No impact of the covariate distribution, when N=50/n=2 |
| White (39) | 1992 | FO | NONMEM | 2 | All combinations of N={60,75,100}2/n={10,2} | Wald LRT |
85:154 70:30 50:50 |
1:{0.9,0.8, 0.7,0.6} | Inflation for both Wald and LRT on all designs Inflation increases when n and/or the proportion of the subpopulation increases |
1
Cross-over trials
2
The size of the control group remains 50, only the size of the comparison group varies