Estimation of average treatment effect based on a multi-index propensity score

Table 3 Estimation results for multi-index propensity score estimator incorporating extra incorrect models based on 1000 replications

	n = 300					n = 1000
Estimator	BIAS(%)	RMSE	MC-SE	BS-SE	CI-Cov(%)	BIAS(%)	RMSE	MC-SE	BS-SE	CI-Cov(%)
Under 25% treated
Kernel regression-based MiPS estimator
MiPS-1111-2PS	-11.969	0.207	0.202	0.212	96.4	-9.355	0.123	0.118	0.115	93.4
MiPS-1111-2OR	-11.959	0.208	0.203	0.212	96.6	-9.304	0.123	0.117	0.115	94.2
MiPS-1111-2PS2OR	-12.417	0.213	0.207	0.217	96.4	-9.966	0.127	0.121	0.119	93.8
Artificial neural network-based MiPS estimator
MiPS-1111-2PS	-0.391	0.170	0.170	0.217	98.8	-0.842	0.084	0.084	0.092	96
MiPS-1111-2OR	-0.262	0.169	0.169	0.218	98.8	-0.645	0.085	0.085	0.092	96
MiPS-1111-2PS2OR	-0.687	0.173	0.174	0.222	99.2	-0.827	0.084	0.084	0.093	96
Under 50% treated
Kernel regression-based MiPS estimator
MiPS-1111-2PS	-10.967	0.189	0.184	0.186	94.4	-9.795	0.113	0.106	0.101	91.8
MiPS-1111-2OR	-10.971	0.189	0.184	0.186	94.8	-9.907	0.113	0.106	0.101	92.6
MiPS-1111-2PS2OR	-11.444	0.194	0.189	0.191	94.4	-10.583	0.118	0.110	0.104	92.6
Artificial neural network-based MiPS estimator
MiPS-1111-2PS	-0.376	0.128	0.129	0.146	97.0	1.034	0.070	0.070	0.068	94
MiPS-1111-2OR	-0.781	0.127	0.127	0.146	97.8	0.993	0.071	0.071	0.069	94.2
MiPS-1111-2PS2OR	-0.480	0.129	0.129	0.147	97.2	0.988	0.070	0.070	0.069	94.4

MiPS-1111-2PS indicates the estimator with two additional incorrect propensity score models on the basis of MiPS-1111 estimator
MiPS-1111-2OR indicates the estimator with two additional incorrect outcome regression models on the basis of MiPS-1111 estimator
MiPS-1111-2PS2OR indicates the estimator with two additional two incorrect propensity score and 2 incorrect outcome regression models on the basis of MiPS-1111 estimator
BIAS bias, RMSE root mean square error, MC-SE Monte Carlo standard error, BS-SE bootstrapping standard error, CI-Cov coverage rate of 95% Wald confidence interval, MiPS multi-index propensity score

ISSN: 1471-2288