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Table 3 Summary of empirical estimates of log-OR and relative bias (%), power (%) and MC standard error, coverage (%), model standard error and empirical standard error derived from χ2 method and GLMM test with compound symmetric variance-covariance matrix from 1000 simulations with a total sample size N = 776

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

 

pi1 = 0.5, ρ = 0.3

Log-odds (% bias)

Power (%)c

Coverage (%)c

Model SEc

Empirical SEc

Complete

χ2 a

0.396 (0)

78.1

93.6

0.145

0.144

 GLMMb

0.507 (0)

75.6

97.5

0.199

0.171

MCAR

Equal drop out (30% drop out in each arm)

χ2

0.392 (−1.0)

61.6

95.0

0.174

0.175

  GLMM

0.508 (0.3)

61.7

97.3

0.223

0.198

Unequal dropouts 1 (20% drop out in control, 40% drop out in treatment)

χ2

0.404 (2.0)

61.5

95.3

0.176

0.176

  GLMM

0.516 (1.8)

63.9

97.1

0.224

0.197

Unequal dropouts 2 (40% drop out in control, 20% drop out in treatment)

χ2

0.394 (−0.3)

63.0

96.3

0.175

0.170

  GLMM

0.510 (0.6)

65.4

98.0

0.224

0.193

MAR1 (observations more likely to be deleted if prior observation was positive)

Equal drop out (30% drop out in each arm)

χ2

0.405 (2.3)

63.6

95.9

0.173

0.172

  GLMM

0.510 (0.7)

64.7

97.7

0.223

0.193

Unequal dropouts 1 (20% drop out in control, 40% drop out in treatment)

χ2

0.314 (−20.6)

43.9

93.2

0.145

0.174

  GLMM

0.529 (4.3)

66.6

97.8

0.223

0.194

Unequal dropouts 2 (40% drop out in control, 20% drop out in treatment)

χ2

0.495 (25.2)

80.2

91.0

0.175

0.174

  GLMM

0.495 (−2.4)

60.6

97.4

0.224

0.194

MAR2 (observations less likely to be deleted if prior observation was positive)

Equal drop out (30% drop out in each arm)

χ2

0.406 (2.7)

63.9

94.5

0.176

0.177

  GLMM

0.514 (1.4)

65.8

97.8

0.224

0.198

Unequal dropouts 1 (20% drop out in control, 40% drop out in treatment)

χ2

0.496 (25.4)

79.7

91.4

0.179

0.176

  GLMM

0.494 (−2.6)

60.0

97.7

0.225

0.197

Unequal dropouts 2 (40% drop out in control, 20% drop out in treatment)

χ2

0.311 (−21.3)

41.4

93.2

0.177

0.177

  GLMM

0.530 (4.5)

66.9

97.6

0.224

0.196

  1. aIndependent two-sample χ2 test for test of treatment effect at time point 3
  2. bGeneralized linear mixed model with compound symmetric variance-covariance matrix, contrast used to estimate treatment effect at time point 3
  3. cRange of Monte Carlo SE: Power (0.013–0.016); Coverage (0.004–0.009); Model SE (< 0.0001–0.001); Empirical SE (0.003–0.004)