Table 4.

Results of Simulation setting 2 where the multiple imputation by chained equations (MICE) with Bayesian linear regression is used  for a sensitivity analysis

	Heterogeneous treatment effect
	Propensity matching				Propensity weighting
	Coefficient		Bias	MSE	Coefficient		MSE
	Mean	SD			Mean	SD
No adjustment	1.730	0.158	1.410	2.012	1.730	0.158	3.019
After adjustment	0.321	0.096	0.000	0.009	− 0.017	0.156	0.025
No interaction term
Multiple imputation
With Y	0.304	0.095	− 0.017	0.009	− 0.041	0.170	0.031
Without Y	0.536	0.101	0.215	0.056	0.292	0.142	0.105
Combined method
With Y	0.303	0.095	− 0.018	0.009	− 0.042	0.172	0.031
Without Y	0.537	0.104	0.216	0.058	0.294	0.143	0.107
Interaction terms
Multiple imputation	0.315	0.094	− 0.006	0.009	− 0.014	0.169	0.029
Combined method	0.315	0.096	− 0.006	0.009	− 0.015	0.171	0.029
No interaction term
Multiple imputation
With Y	0.220	0.103	− 0.101	0.021	− 0.116	0.192	0.050
Without Y	0.568	0.110	0.247	0.073	0.264	0.158	0.095
Combined method
With Y	0.220	0.101		0.010	− 0.116	0.190	0.049
Without Y	0.568	0.111	0.248	0.074	0.264	0.157	0.094
Interaction terms
Multiple imputation	0.330	0.101	0.009	0.010	0.002	0.199	0.040
Combined method	0.331	0.103	0.010	0.011	0.001	0.198	0.039
No interaction term
Multiple imputation
With Y	0.102	0.110	− 0.219	0.060	− 0.269	0.213	0.118
Without Y	0.570	0.110	0.249	0.074	0.325	0.153	0.129
Combined method
With Y	0.095	0.103	− 0.225	0.061	− 0.275	0.211	0.120
Without Y	0.537	0.105	0.216	0.058	0.233	0.149	0.076
Interaction terms
Multiple imputation	0.173	0.101	− 0.147	0.032	− 0.197	0.220	0.087
Combined method	0.169	0.103	− 0.151	0.034	− 0.206	0.215	0.089