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

Coffman, Donna L.; Zhou, Jiangxiu; Cai, Xizhen

doi:10.1186/s12874-020-01053-4

BMC Medical Research Methodology

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 Mechanism	Method	True confounders			Leave ×1 out			Add ×5			Leave ×1 out + Add ×5
Missingness Mechanism	Method	Bias (SD)	SE	RMSE	Bias (SD)	SE	RMSE	Bias (SD)	SE	RMSE	Bias (SD)	SE	RMSE
	complete	−0.001 (0.041)	0.068	0.041	0.036 (0.043)	0.067	0.056	−0.001 (0.043)	0.070	0.043	0.042 (0.043)	0.068	0.060
	comGBM	0.029 (0.042)	0.067	0.050	–	–	–	–	–	–	–	–	–
MCAR	SI + pe + pu	0.000 (0.049)	0.068	0.041	0.036 (0.049)	0.067	0.061	0.000 (0.051)	0.070	0.051	0.042 (0.050)	0.068	0.065
	SI + pe	−0.003 (0.049)	0.068	0.041	0.035 (0.048)	0.067	0.059	−0.002 (0.050)	0.070	0.050	0.041 (0.049)	0.068	0.064
	TMI	0.105 (0.065)	0.072	0.113	0.131 (0.064)	0.071	0.146	0.109 (0.066)	0.074	0.127	0.138 (0.066)	0.072	0.153
	MI	−0.001 (0.045)	0.068	0.041	0.036 (0.046)	0.067	0.058	−0.001 (0.047)	0.070	0.047	0.042 (0.047)	0.068	0.063
	MIMP	−0.001 (0.045)	0.069	0.041	0.035 (0.046)	0.067	0.058	−0.001 (0.047)	0.070	0.047	0.042 (0.047)	0.068	0.063
	GBM	0.067 (0.050)	0.066	0.079	–	–	–	–	–	–	–	–	–
	GBM + SI + pe	0.035 (0.047)	0.067	0.054	–	–	–	–	–	–	–	–	–
MAR1	SI + pe + pu	0.000 (0.048)	0.068	0.041	0.036 (0.048)	0.067	0.060	0.000 (0.050)	0.070	0.050	0.042 (0.049)	0.068	0.065
	SI + pe	0.000 (0.048)	0.068	0.041	0.036 (0.047)	0.067	0.059	0.000 (0.050)	0.070	0.050	0.042 (0.048)	0.068	0.064
	TMI	0.102 (0.060)	0.070	0.110	0.129 (0.060)	0.069	0.142	0.109 (0.062)	0.071	0.125	0.136 (0.062)	0.070	0.149
	MI	0.000 (0.044)	0.068	0.041	0.036 (0.045)	0.067	0.058	0.000 (0.046)	0.070	0.046	0.042 (0.046)	0.068	0.062
	MIMP	0.000 (0.045)	0.069	0.041	0.037 (0.045)	0.067	0.058	0.000 (0.046)	0.070	0.046	0.043 (0.046)	0.068	0.063
	GBM	0.066 (0.048)	0.066	0.078	–	–	–	–	–	–	–	–	–
	GBM + SI + pe	0.036 (0.046)	0.067	0.055	–	–	–	–	–	–	–	–	–
MAR2	SI + pe + pu	0.000 (0.049)	0.068	0.041	0.036 (0.049)	0.067	0.061	0.001 (0.051)	0.070	0.051	0.043 (0.049)	0.068	0.065
	SI + pe	−0.001 (0.048)	0.068	0.041	0.035 (0.048)	0.067	0.059	−0.001 (0.050)	0.070	0.050	0.042 (0.049)	0.068	0.065
	TMI	0.104 (0.068)	0.073	0.112	0.129 (0.068)	0.072	0.146	0.111 (0.071)	0.075	0.132	0.137 (0.069)	0.073	0.153
	MI	0.000 (0.045)	0.068	0.041	0.037 (0.046)	0.067	0.059	0.001 (0.047)	0.070	0.047	0.043 (0.047)	0.068	0.064
	MIMP	0.002 (0.045)	0.069	0.041	0.038 (0.045)	0.067	0.059	0.001 (0.047)	0.070	0.047	0.043 (0.046)	0.068	0.063
	GBM	0.069 (0.050)	0.067	0.080	–	–	–	–	–	–	–	–	–
	GBM + SI + pe	0.037 (0.046)	0.067	0.055	–	–	–	–	–	–	–	–	–
MAR Sinister	SI + pe + pu	0.003 (0.048)	0.068	0.041	0.037 (0.048)	0.066	0.061	0.004 (0.049)	0.069	0.049	0.043 (0.048)	0.067	0.064
	SI + pe	−0.002 (0.049)	0.068	0.041	0.035 (0.049)	0.067	0.060	−0.002 (0.050)	0.070	0.050	0.041 (0.050)	0.068	0.065
	TMI	0.118 (0.062)	0.071	0.125	0.144 (0.062)	0.070	0.157	0.122 (0.064)	0.073	0.138	0.151 (0.064)	0.071	0.164
	MI	0.003 (0.045)	0.068	0.041	0.040 (0.045)	0.067	0.060	0.003 (0.046)	0.070	0.046	0.046 (0.046)	0.068	0.065
	MIMP	0.003 (0.045)	0.068	0.041	0.040 (0.046)	0.067	0.061	0.003 (0.046)	0.070	0.046	0.046 (0.046)	0.068	0.065
	GBM	0.074 (0.049)	0.066	0.085	–	–	–	–	–	–	–	–	–
	GBM + SI + pe	0.036 (0.047)	0.067	0.055	–	–	–	–	–	–	–	–	–

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

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ISSN: 1471-2288

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