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

Table 1 Type I errors, Bias and Mean Square Error (MSE) for non parsimonious PS model according to the method used (PS matching (PSm) or IPTW) and to the strength of the association between baseline covariates, treatment/outcome

N		OR(a) = 1.5, OR(b) = 1.5		OR(a) = 2.5, OR(b) =1.5		OR(a) = 1.5, OR(b) = 2.5		OR(a) = 2.5, OR(b) = 2.5
		PSm	IPTW	PSm	IPTW	PSm	IPTW	PSm	IPTW
40	Type I error	0.055	0.048	0.053	0.056	0.052	0.039	0.052	0.047
	Bias	0.05	0.057	0.049	0.07	0.059	0.055	0.048	0.079
	%	5.6	6.5	5.4	7.8	7.1	6.6	5.7	9.4
	Variance	0.875	0.593	0.918	0.694	0.873	0.576	0.903	0.683
	MSE	0.878	0.597	0.92	0.699	0.876	0.579	0.905	0.690
60	Type I error	0.045	0.046	0.047	0.046	0.044	0.039	0.044	0.039
	Bias	0.058	0.036	0.058	0.049	0.048	0.022	0.05	0.033
	%	6.4	4	6.4	5.4	5.7	2.6	6	3.9
	Variance	0.511	0.36	0.553	0.414	0.484	0.329	0.516	0.388
	MSE	0.514	0.362	0.556	0.416	0.486	0.33	0.519	0.389
100	Type I error	0.049	0.046	0.047	0.046	0.047	0.034	0.04	0.036
	Bias	0.023	0.018	0.02	0.022	0.021	0.015	0.025	0.016
	%	2.6	2	2.2	2.5	2.5	1.8	2.9	1.9
	Variance	0.254	0.194	0.282	0.223	0.242	0.177	0.261	0.204
	MSE	0.255	0.194	0.283	0.223	0.243	0.177	0.262	0.204
500	Type I error	0.049	0.046	0.05	0.048	0.041	0.038	0.042	0.037
	Bias	0.01	0.007	0.012	0.008	0.01	0.005	0.013	0.005
	%	1.1	0.8	1.3	0.9	1.2	0.6	1.5	0.6
	Variance	0.04	0.034	0.045	0.038	0.037	0.032	0.042	0.035
	MSE	0.04	0.034	0.045	0.038	0.037	0.032	0.042	0.035

This table specially details the sample sizes ranging from 40 to 500. Prevalence of the treatment was set at 0.5. Conditional treatment effect was set at log(2.5) except for Type I errors estimations (log(1)). (N: number of subjects; PS: propensity score; IPTW: inverse probability of treatment weighting, OR(a) and OR(b): strengths of the association between baseline covariates and treatment or outcome respectively, as defined on an odds ratio scale).

ISSN: 1471-2288