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 6 Simulation results for scenario G, 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	−0.014 (0.044)	0.071	0.046	0.037 (0.043)	0.068	0.057	−0.016 (0.045)	0.073	0.048	0.040 (0.043)	0.069	0.059
	comGBM	0.029 (0.044)	0.067	0.053	–	–	–	–	–	–	–	–	–
MCAR	SI + pe + pu	−0.011 (0.052)	0.071	0.053	0.040 (0.049)	0.068	0.063	−0.012 (0.054)	0.072	0.055	0.043 (0.050)	0.068	0.066
	SI + pe	−0.013 (0.051)	0.071	0.053	0.039 (0.049)	0.068	0.063	−0.014 (0.053)	0.072	0.055	0.042 (0.049)	0.068	0.065
	TMI	0.096 (0.064)	0.076	0.115	0.131 (0.061)	0.073	0.145	0.096 (0.067)	0.078	0.117	0.134 (0.063)	0.074	0.148
	MI	−0.011 (0.048)	0.071	0.049	0.039 (0.046)	0.068	0.060	−0.013 (0.050)	0.073	0.052	0.042 (0.047)	0.069	0.063
	MIMP	−0.011 (0.048)	0.072	0.049	0.039 (0.046)	0.068	0.060	−0.013 (0.050)	0.073	0.052	0.042 (0.047)	0.069	0.063
	GBM	0.060 (0.051)	0.067	0.079	–	–	–	–	–	–	–	–	–
	GBM + SI + pe	0.033 (0.049)	0.067	0.059	–	–	–	–	–	–	–	–	–
MAR1	SI + pe + pu	0.000 (0.051)	0.070	0.051	0.048 (0.048)	0.067	0.068	−0.002 (0.053)	0.072	0.053	0.052 (0.049)	0.068	0.071
	SI + pe	−0.001 (0.050)	0.070	0.050	0.048 (0.047)	0.067	0.067	−0.003 (0.052)	0.072	0.052	0.051 (0.048)	0.068	0.070
	TMI	0.113 (0.057)	0.073	0.127	0.148 (0.055)	0.070	0.158	0.116 (0.059)	0.074	0.130	0.152 (0.056)	0.071	0.162
	MI	−0.001 (0.047)	0.071	0.047	0.048 (0.045)	0.068	0.066	−0.002 (0.048)	0.072	0.048	0.051 (0.046)	0.068	0.069
	MIMP	−0.001 (0.047)	0.071	0.047	0.048 (0.045)	0.068	0.066	−0.002 (0.048)	0.072	0.048	0.052 (0.046)	0.069	0.069
	GBM	0.066 (0.050)	0.067	0.083	–	–	–	–	–	–	–	–	–
	GBM + SI + pe	0.039 (0.047)	0.067	0.061	–	–	–	–	–	–	–	–	–
MAR2	SI + pe + pu	− 0.009 (0.051)	0.070	0.052	0.040 (0.050)	0.068	0.064	−0.011 (0.053)	0.072	0.054	0.043 (0.050)	0.068	0.066
	SI + pe	−0.009 (0.051)	0.070	0.052	0.041 (0.049)	0.068	0.064	−0.010 (0.053)	0.072	0.054	0.045 (0.050)	0.068	0.067
	TMI	0.090 (0.069)	0.078	0.113	0.125 (0.066)	0.074	0.141	0.093 (0.071)	0.080	0.117	0.128 (0.067)	0.076	0.144
	MI	−0.008 (0.046)	0.071	0.047	0.041 (0.046)	0.068	0.062	−0.010 (0.048)	0.073	0.049	0.044 (0.046)	0.069	0.064
	MIMP	−0.008 (0.047)	0.072	0.048	0.042 (0.046)	0.068	0.062	−0.010 (0.049)	0.073	0.050	0.045 (0.047)	0.069	0.065
	GBM	0.058 (0.051)	0.067	0.077	–	–	–	–	–	–	–	–	–
	GBM + SI + pe	0.036 (0.048)	0.067	0.060	–	–	–	–	–	–	–	–	–
MAR Sinister	SI + pe + pu	−0.006 (0.050)	0.070	0.050	0.040 (0.048)	0.067	0.062	−0.007 (0.052)	0.071	0.052	0.042 (0.048)	0.068	0.064
	SI + pe	−0.012 (0.051)	0.071	0.052	0.039 (0.049)	0.068	0.063	−0.014 (0.053)	0.072	0.055	0.042 (0.050)	0.069	0.065
	TMI	0.113 (0.060)	0.075	0.128	0.147 (0.057)	0.072	0.158	0.113 (0.062)	0.077	0.129	0.151 (0.059)	0.073	0.162
	MI	− 0.007 (0.047)	0.071	0.048	0.043 (0.045)	0.068	0.062	−0.009 (0.048)	0.072	0.049	0.046 (0.046)	0.069	0.065
	MIMP	−0.007 (0.047)	0.071	0.048	0.043 (0.046)	0.068	0.063	−0.009 (0.049)	0.073	0.050	0.046 (0.046)	0.069	0.065
	GBM	0.068 (0.050)	0.067	0.084	–	–	–	–	–	–	–	–	–
	GBM + SI + pe	0.035 (0.048)	0.067	0.059	–	–	–	–	–	–	–	–	–

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

Back to article page

ISSN: 1471-2288

Contact us

General enquiries: journalsubmissions@springernature.com