Table 4.

Performance of Q-learning adjustment methods under the confounding by counterfactuals simulations: bias, Monte Carlo variance (MC var), mean squared error (MSE), and coverage of 95% bootstrap confidence intervals.

	Randomized treatment				Confounded treatment
Adjustment method	Bias	MC var	MSE	Cover	Bias	MC var	MSE	Cover
n = 250
None	0.0020	0.0082	0.0082	94.0	0.2293	0.0080	0.0605	26.4
Linear	0.0011	0.0032	0.0032	95.1	0.0051	0.0039	0.0039	93.8
PS (linear)	0.0010	0.0052	0.0052	96.2	0.0548	0.0060	0.0090	89.4
PS (quintiles)	0.0008	0.0056	0.0056	96.1	0.0779	0.0061	0.0121	83.2
IPW	0.0004	0.0046	0.0046	93.9	0.0108	0.0075	0.0076	92.8
n = 1000
None	−0.0012	0.0022	0.0022	93.4	0.2246	0.0021	0.0525	0.5
Linear	0.0001	0.0009	0.0009	93.5	0.0037	0.0010	0.0010	93.5
PS (linear)	−0.0002	0.0014	0.0014	95.5	0.0446	0.0015	0.0035	77.0
PS (quintiles)	−0.0004	0.0015	0.0015	95.7	0.0699	0.0015	0.0064	55.0
IPW	−0.0008	0.0012	0.0012	93.6	0.0018	0.0018	0.0018	93.6