Quasi-rerandomization for observational studies

Zhang, Hengtao; Su, Wen; Yin, Guosheng

doi:10.1186/s12874-023-01977-7

BMC Medical Research Methodology

Table 4 The bias and RMSE for \(\tau _{\textrm{PATE}}\) under quasi-rerandomization (QReR) and other balancing methods under different combinations of the covariate scenarios, response surfaces and ratios (\(r=N_0/N_1\)). The average Monte Carlo standard errors (MCSEs) of bias are 0.02, 0.03 and 0.40 and those of RMSE are 0.02, 0.02 and 0.77 for Linear, NonLinear (Interaction) and NonLinear (Polynomial) models, respectively

From: Quasi-rerandomization for observational studies

r	Response	Method	Scenario 1		Scenario 2		Scenario 3
			\(\textrm{Bias}\)	RMSE	\(\textrm{Bias}\)	RMSE	\(\textrm{Bias}\)	RMSE
1	Linear	IPW	0.040	0.42	0.217	0.55	0.179	0.50
		PSM	0.162	0.42	0.247	0.57	0.365	0.67
		FM	0.156	0.40	0.280	0.57	0.378	0.66
		EBAL	-0.002	0.11	-0.003	0.11	-0.005	0.11
		SBW	-0.003	0.10	-0.004	0.11	-0.005	0.11
		EBCW	-0.002	0.11	-0.003	0.11	-0.004	0.11
		\(\textrm{QReR}_{\textrm{M}}\)	-0.022	0.12	-0.031	0.12	-0.029	0.12
	Nonlinear	IPW	0.077	0.58	0.290	0.72	0.245	0.64
	(Interaction)	PSM	0.245	0.61	0.241	0.81	0.423	0.95
		FM	0.235	0.59	0.292	0.80	0.440	0.93
		EBAL	0.012	0.19	-0.029	0.22	-0.041	0.21
		SBW	0.011	0.19	-0.042	0.22	-0.056	0.22
		EBCW	0.012	0.19	-0.029	0.22	-0.040	0.21
		\(\textrm{QReR}_{\textrm{M}}\)	-0.033	0.19	-0.123	0.24	-0.133	0.26
	Nonlinear	IPW	0.247	3.56	5.333	11.91	-10.193	14.00
	(Polynomial)	PSM	0.097	3.54	5.217	9.40	-8.803	10.90
		FM	0.124	3.53	5.134	9.29	-8.872	11.00
		EBAL	0.092	2.72	4.925	8.51	-8.850	10.62
		SBW	0.119	2.55	5.419	8.54	-7.836	9.52
		EBCW	0.092	2.72	4.925	8.51	-8.850	10.62
		\(\textrm{QReR}_{\textrm{M}}\)	0.025	2.04	4.875	7.01	-6.112	7.56
2	Linear	IPW	0.024	0.35	-0.565	0.96	-1.154	1.42
		PSM	0.085	0.41	-0.032	0.49	-0.311	0.58
		FM	0.088	0.40	-0.035	0.48	-0.302	0.56
		EBAL	0.002	0.09	0.002	0.09	0.001	0.09
		SBW	0.001	0.09	0.001	0.09	0.000	0.09
		EBCW	0.002	0.09	0.002	0.09	0.001	0.09
		\(\textrm{QReR}_{\textrm{M}}\)	-0.017	0.10	-0.017	0.10	-0.013	0.10
	Nonlinear	IPW	0.049	0.46	-0.766	1.23	-1.611	1.91
	(Interaction)	PSM	0.130	0.56	-0.174	0.68	-0.603	0.91
		FM	0.132	0.54	-0.179	0.67	-0.595	0.88
		EBAL	0.006	0.17	-0.023	0.20	-0.032	0.20
		SBW	-0.052	0.17	-0.104	0.22	-0.121	0.23
		EBCW	0.006	0.17	-0.023	0.20	-0.032	0.20
		\(\textrm{QReR}_{\textrm{M}}\)	-0.080	0.18	-0.142	0.23	-0.145	0.25
	Nonlinear	IPW	0.060	3.22	4.734	14.91	-12.453	18.48
	(Polynomial)	PSM	-0.105	2.72	5.280	9.50	-8.156	10.14
		FM	-0.064	2.66	5.230	9.45	-8.279	10.20
		EBAL	-0.056	2.20	5.098	8.74	-8.151	10.08
		SBW	-0.069	2.09	5.678	8.83	-6.955	8.77
		EBCW	-0.056	2.20	5.098	8.74	-8.152	10.08
		\(\textrm{QReR}_{\textrm{M}}\)	-0.261	1.63	4.810	6.81	-4.825	6.26

IPW: inverse probability weighting using propensity scores; PSM: propensity score matching; FM: optimal full matching; EBAL: entropy balancing; SBW: stable balancing weights; EBCW: empirical balancing calibration weighting; and \(\textrm{QReR}_{\textrm{M}}\): quasi-rerandomization using average weight vector with acceptance probability \(p_a=0.1\)

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