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Table 5 Simulation results for scenario A, n = 500, 25%missing

From: Comparison of methods for handling covariate missingness in propensity score estimation with a binary exposure

Missingness MechanismMethodTrue confoundersLeave ×1 outAdd ×5Leave ×1 out + Add ×5
Bias (SD)SERMSEBias (SD)SERMSEBias (SD)SERMSEBias (SD)SERMSE
 complete−0.001 (0.041)0.0680.0410.036 (0.043)0.0670.056−0.001 (0.043)0.0700.0430.042 (0.043)0.0680.060
comGBM0.029 (0.042)0.0670.050
MCARSI + pe + pu0.000 (0.049)0.0680.0410.036 (0.049)0.0670.0610.000 (0.051)0.0700.0510.042 (0.050)0.0680.065
SI + pe−0.003 (0.049)0.0680.0410.035 (0.048)0.0670.059−0.002 (0.050)0.0700.0500.041 (0.049)0.0680.064
TMI0.105 (0.065)0.0720.1130.131 (0.064)0.0710.1460.109 (0.066)0.0740.1270.138 (0.066)0.0720.153
MI−0.001 (0.045)0.0680.0410.036 (0.046)0.0670.058−0.001 (0.047)0.0700.0470.042 (0.047)0.0680.063
MIMP−0.001 (0.045)0.0690.0410.035 (0.046)0.0670.058−0.001 (0.047)0.0700.0470.042 (0.047)0.0680.063
GBM0.067 (0.050)0.0660.079
GBM + SI + pe0.035 (0.047)0.0670.054
MAR1SI + pe + pu0.000 (0.048)0.0680.0410.036 (0.048)0.0670.0600.000 (0.050)0.0700.0500.042 (0.049)0.0680.065
SI + pe0.000 (0.048)0.0680.0410.036 (0.047)0.0670.0590.000 (0.050)0.0700.0500.042 (0.048)0.0680.064
TMI0.102 (0.060)0.0700.1100.129 (0.060)0.0690.1420.109 (0.062)0.0710.1250.136 (0.062)0.0700.149
MI0.000 (0.044)0.0680.0410.036 (0.045)0.0670.0580.000 (0.046)0.0700.0460.042 (0.046)0.0680.062
MIMP0.000 (0.045)0.0690.0410.037 (0.045)0.0670.0580.000 (0.046)0.0700.0460.043 (0.046)0.0680.063
GBM0.066 (0.048)0.0660.078
GBM + SI + pe0.036 (0.046)0.0670.055
MAR2SI + pe + pu0.000 (0.049)0.0680.0410.036 (0.049)0.0670.0610.001 (0.051)0.0700.0510.043 (0.049)0.0680.065
SI + pe−0.001 (0.048)0.0680.0410.035 (0.048)0.0670.059−0.001 (0.050)0.0700.0500.042 (0.049)0.0680.065
TMI0.104 (0.068)0.0730.1120.129 (0.068)0.0720.1460.111 (0.071)0.0750.1320.137 (0.069)0.0730.153
MI0.000 (0.045)0.0680.0410.037 (0.046)0.0670.0590.001 (0.047)0.0700.0470.043 (0.047)0.0680.064
MIMP0.002 (0.045)0.0690.0410.038 (0.045)0.0670.0590.001 (0.047)0.0700.0470.043 (0.046)0.0680.063
GBM0.069 (0.050)0.0670.080
GBM + SI + pe0.037 (0.046)0.0670.055
MAR SinisterSI + pe + pu0.003 (0.048)0.0680.0410.037 (0.048)0.0660.0610.004 (0.049)0.0690.0490.043 (0.048)0.0670.064
SI + pe−0.002 (0.049)0.0680.0410.035 (0.049)0.0670.060−0.002 (0.050)0.0700.0500.041 (0.050)0.0680.065
TMI0.118 (0.062)0.0710.1250.144 (0.062)0.0700.1570.122 (0.064)0.0730.1380.151 (0.064)0.0710.164
MI0.003 (0.045)0.0680.0410.040 (0.045)0.0670.0600.003 (0.046)0.0700.0460.046 (0.046)0.0680.065
MIMP0.003 (0.045)0.0680.0410.040 (0.046)0.0670.0610.003 (0.046)0.0700.0460.046 (0.046)0.0680.065
GBM0.074 (0.049)0.0660.085
GBM + SI + pe0.036 (0.047)0.0670.055
  1. Note. Complete: logistic regression with complete data before introducing missingness; comGBM GBM with complete data before introducing missingness; SI + pe + pu single imputation + prediction error + parameter uncertainty; SI + pe single imputation + prediction error; TMI treatment mean imputation; MI multiple imputation (m = 20); MIMP multiple imputation missingness pattern (m = 20); GBM GBM with incomplete data; GBM + SI + pe GBM after single imputation + prediction error; SD standard deviation; SE standard error; RMSE root mean squared error