Simulation example: comparing AIPW and SES

In this vignette, we will compare the performances of the AIPW-adjusted approach and the SES approach based on RT data (Yang et al., (2022), Section S4.1). The data generating mechanism is the same as in here except that we now consider different propensity score distributions.

(weak separation of propensity score distributions by treatment group) \(\alpha = (-2,-1,-1)\).
(median separation of propensity score distributions by treatment group) \(\alpha = (-2,-2,-2)\).
(strong separation of propensity score distributions by treatment group) \(\alpha = (-2,-3,-3)\).

The following figure shows the propensity score distributions by treatment group and demonstrates the degrees of separation in the three scenarios.

The simulation results (Yang et al., (2022), Table S2) for comparing RT.AIPW and RT.SES are the following:

Case 1: weak separation
	AIPW.2	AIPW.3	RT.2	RT.3
bias	-1.4	-2.3	-0.5	-0.9
S.D.	241.8	248.2	180.1	185.6
root-MSE	242.2	249.3	180.2	185.8
Coverage rate	94.4	91.8	95.4	93.2
width	955.1	941.7	709.3	709.9

Case 2: median separation
	AIPW.2	AIPW.3	RT.2	RT.3
bias	1.3	-0.7	0.4	-1.2
S.D.	364.8	380.5	259.6	249.3
root-MSE	365.0	380.6	259.6	249.6
Coverage rate	92.8	93.2	94.6	94.6
width	1389.5	1420.0	974.1	970.7

Case 3: strong separation
	AIPW.2	AIPW.3	RT.2	RT.3
bias	2.7	0.5	-1.5	-2.0
S.D.	622.2	554.9	393.9	396.7
root-MSE	622.7	554.9	394.2	397.2
Coverage rate	91.0	92.0	93.2	91.6
width	14568.9	5076.9	1448.0	1447.9