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Table 1 Results for the simulation 1: fully efficient one-step approach and the two-step marginal multivariate meta-analysis approach were compared

From: Efficient two-step multivariate random effects meta-analysis of individual participant data for longitudinal clinical trials using mixed effects models

  N = 5 N = 10 N = 15 N = 20
One-step Two-step One-step Two-step One-step Two-step One-step Two-step
μ2 = 0.14
 Mean 0.135 0.135 0.146 0.146 0.135 0.136 0.130 0.130
 SE 0.866 0.867 0.612 0.613 0.495 0.496 0.434 0.435
\( \widehat{\mathrm{SE}} \) 0.867 0.866 0.608 0.606 0.495 0.494 0.428 0.427
 Coverage Rate 0.949 0.950 0.948 0.947 0.949 0.947 0.950 0.948
 Power 0.052 0.053 0.056 0.058 0.058 0.059 0.071 0.070
μ4 = 0.83
 Mean 0.827 0.826 0.836 0.836 0.828 0.829 0.825 0.824
 SE 0.415 0.416 0.287 0.287 0.236 0.236 0.206 0.205
\( \widehat{\mathrm{SE}} \) 0.410 0.410 0.287 0.287 0.234 0.234 0.202 0.202
 Coverage Rate 0.950 0.950 0.951 0.951 0.948 0.947 0.939 0.941
 Power 0.533 0.533 0.825 0.825 0.936 0.937 0.978 0.978
μ5 = −0.46
 Mean −0.461 −0.461 −0.460 −0.460 −0.460 −0.460 −0.461 −0.461
 SE 0.032 0.032 0.023 0.023 0.018 0.018 0.016 0.016
\( \widehat{\mathrm{SE}} \) 0.032 0.032 0.022 0.022 0.018 0.018 0.016 0.016
 Coverage Rate 0.949 0.948 0.949 0.947 0.953 0.955 0.951 0.949
 Power 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
μ7 = 0.14
 Mean 0.139 0.139 0.141 0.141 0.143 0.143 0.144 0.144
 SE 0.178 0.178 0.122 0.122 0.100 0.100 0.088 0.088
\( \widehat{\mathrm{SE}} \) 0.176 0.176 0.123 0.123 0.100 0.100 0.087 0.087
 Coverage Rate 0.948 0.947 0.949 0.949 0.949 0.949 0.940 0.942
 Power 0.127 0.128 0.211 0.215 0.295 0.297 0.382 0.381
μ9 = 0.05
 Mean 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050
 SE 0.020 0.020 0.014 0.014 0.011 0.011 0.010 0.010
\( \widehat{\mathrm{SE}} \) 0.020 0.020 0.014 0.014 0.011 0.011 0.010 0.010
 Coverage Rate 0.947 0.947 0.951 0.951 0.949 0.952 0.941 0.940
 Power 0.734 0.735 0.947 0.947 0.995 0.995 0.999 0.999
μ10 = −0.06
 Mean −0.060 −0.060 −0.060 −0.060 −0.060 −0.060 −0.059 −0.059
 SE 0.042 0.042 0.030 0.030 0.024 0.024 0.021 0.021
\( \widehat{\mathrm{SE}} \) 0.042 0.042 0.029 0.029 0.024 0.024 0.021 0.021
 Coverage Rate 0.949 0.949 0.948 0.947 0.949 0.950 0.946 0.945
 Power 0.301 0.302 0.540 0.543 0.700 0.701 0.811 0.811