Evaluation of the Propensity score methods for estimating marginal odds ratios in case of small sample size

Pirracchio, Romain; Resche-Rigon, Matthieu; Chevret, Sylvie

doi:10.1186/1471-2288-12-70

BMC Medical Research Methodology

Table 2 Bias and variance of the estimated treatment effect for the different selected PS models and according to the method used (PS matching or IPTW)

From: Evaluation of the Propensity score methods for estimating marginal odds ratios in case of small sample size

		Model 1		Model 2		Model 3		Model 4		Model 5		Model 6		Model 7		Model 8
N		X2		X3		X4		X2,X3		X2,X4		X3,X4		X2,X3,X4		X1,X2,X3,X4
		PSm	IPTW	PSm	IPTW	PSm	IPTW	PSm	IPTW	PSm	IPTW	PSm	IPTW	PSm	IPTW	PSm	IPTW
40	Type I error	0.062	0.041	0.059	0.051	0.058	0.040	0.060	0.047	0.053	0.036	0.048	0.045	0.053	0.044	0.052	0.047
	Bias	0.273	0.235	0.265	0.251	0.086	0.06	0.259	0.25	0.075	0.061	0.064	0.071	0.075	0.074	0.048	0.079
	Relative bias	32.6	28.1	31.7	30	10.3	7.2	31	29.9	9	7.3	7.6	8.5	9	8.8	5.7	9.4
	Variance	0.809	0.508	0.872	0.566	0.862	0.551	0.874	0.573	0.843	0.56	0.907	0.634	0.904	0.644	0.903	0.683
	MSE	0.884	0.563	0.942	0.629	0.869	0.555	0.941	0.635	0.848	0.563	0.911	0.639	0.909	0.649	0.905	0.69
60	Type I error	0.055	0.050	0.058	0.057	0.045	0.038	0.052	0.053	0.043	0.037	0.049	0.042	0.044	0.041	0.044	0.039
	Bias	0.239	0.203	0.235	0.217	0.041	0.02	0.245	0.219	0.047	0.022	0.051	0.028	0.059	0.03	0.05	0.033
	Relative bias	28.6	24.3	28.1	25.9	4.9	2.4	29.3	26.2	5.6	2.6	6.1	3.3	7.1	3.6	6	3.9
	Variance	0.466	0.317	0.52	0.354	0.494	0.339	0.532	0.348	0.477	0.333	0.524	0.379	0.514	0.375	0.516	0.388
	MSE	0.523	0.359	0.575	0.401	0.495	0.339	0.592	0.396	0.479	0.334	0.527	0.38	0.517	0.376	0.519	0.389
100	Type I error	0.062	0.057	0.065	0.066	0.052	0.039	0.057	0.062	0.042	0.034	0.046	0.041	0.044	0.037	0.04	0.036
	Bias	0.209	0.193	0.212	0.203	0.029	0.013	0.215	0.203	0.029	0.013	0.028	0.016	0.028	0.016	0.025	0.016
	Relative bias	25	23.1	25.3	24.3	3.5	1.6	25.7	24.3	3.5	1.6	3.3	1.9	3.3	1.9	2.9	1.9
	Variance	0.239	0.175	0.254	0.194	0.242	0.186	0.256	0.188	0.239	0.18	0.259	0.205	0.253	0.199	0.261	0.204
	MSE	0.282	0.212	0.299	0.235	0.243	0.186	0.302	0.23	0.24	0.18	0.259	0.205	0.254	0.2	0.262	0.204
500	Type I error	0.148	0.155	0.150	0.162	0.051	0.045	0.146	0.157	0.046	0.040	0.046	0.042	0.045	0.037	0.042	0.037
	Bias	0.187	0.182	0.192	0.191	0.014	0.005	0.193	0.191	0.015	0.005	0.014	0.005	0.014	0.005	0.013	0.005
	Relative bias	22.3	21.8	22.9	22.8	1.7	0.6	23.1	22.8	1.8	0.6	1.7	0.6	1.7	0.6	1.5	0.6
	Variance	0.037	0.032	0.042	0.036	0.04	0.034	0.041	0.034	0.039	0.033	0.044	0.037	0.042	0.035	0.042	0.035
	MSE	0.072	0.066	0.079	0.072	0.04	0.034	0.078	0.071	0.039	0.033	0.044	0.037	0.042	0.035	0.042	0.035

This table specially details the sample sizes ranging from 40 to 500. Prevalence of the treatment set at 0.5, treatment effect.

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