Power difference in a χ2 test vs generalized linear mixed model in the presence of missing data – a simulation study

Table 5 Summary of empirical Type I error rates (%) derived from χ² method and GLMM test with compound symmetric variance-covariance matrix from 1000 simulations with a total sample size N = 398 (p_i1 = 0.1) and N = 776 (p_i1 = 0.5)

	p_i1 = 0.1, ρ = 0.3^c	p_i1 = 0.1, ρ = 0.7^c	p_i1 = 0.5, ρ = 0.3^c	p_i1 = 0.5, ρ = 0.7^c
Complete
χ^{2 a}	6.2	6.6	5.1	4.5
GLMM^b	4.0	3.2	3.4	2.8
MCAR
Equal drop out (30% drop out in each arm)
χ^{2 a}	6.2	5.8	4.7	4.8
GLMM^b	3.3	3.0	2.9	2.7
Unequal dropouts 1 (20% drop out in control, 40% drop out in treatment)
χ^{2 a}	6.0	5.3	4.6	5.0
GLMM^b	3.7	2.4	3.5	1.7
Unequal dropouts 2 (40% drop out in control, 20% drop out in treatment)
χ^{2 a}	4.5	6.0	4.7	3.7
GLMM^b	3.8	2.5	3.1	2.1
MAR1 (observations more likely to be deleted if prior observation was positive)
Equal drop out (30% drop out in each arm)
χ^{2 a}	4.8	4.7	5.1	4.6
GLMM^b	3.0	2.2	2.7	2.5
Unequal dropouts 1 (20% drop out in control, 40% drop out in treatment)
χ^{2 a}	4.7	6.7	6.7	19.4
GLMM^b	2.7	1.8	2.6	2.3
Unequal dropouts 2 (40% drop out in control, 20% drop out in treatment)
χ^{2 a}	5.3	8.3	9.5	27.6
GLMM^b	2.9	2.5	2.7	3.0
MAR2 (observations less likely to be deleted if prior observation was positive)
Equal drop out (30% drop out in each arm)
χ^{2 a}	4.6	5.5	5.0	5.3
GLMM^b	3.6	2.8	3.1	2.9
Unequal dropouts 1 (20% drop out in control, 40% drop out in treatment)
χ^{2 a}	6.3	10.1	9.6	27.3
GLMM^b	3.8	3.3	2.3	3.1
Unequal dropouts 2 (40% drop out in control, 20% drop out in treatment)
χ^{2 a}	5.9	8.3	7.5	19.5
GLMM^b	3.6	4.1	2.9	2.5

^aIndependent two-sample χ2 test for test of treatment effect at time point 3
^bGeneralized linear mixed model with compound symmetric variance-covariance matrix, contrast used to estimate treatment effect at time point 3
^cRange of Monte Carlo SE for Type I error rate: (0.005–0.008); (0.004–0.010); (0.005–0.010); (0.004–0.014)

ISSN: 1471-2288