Table 1.

Comparison of three estimators of the marginal proximal treatment effect, β̂₁, when an important moderator is omitted.

	Weighted and Centered				GEE-IND				GEE-AR(1)
${\beta }_{11}^{\ast }$	Mean	SD	RMSE	CP	Mean	SD	RMSE	CP	Mean	SD	RMSE	CP
0.2	−0.20	0.08	0.08	0.96	−0.17	0.07	0.07	0.94	−0.16	0.04	0.06	0.86
0.5	−0.20	0.08	0.08	0.95	−0.14	0.07	0.09	0.88	−0.13	0.05	0.09	0.70
0.8	−0.20	0.08	0.08	0.95	−0.10	0.07	0.12	0.78	−0.10	0.05	0.12	0.57

RMSE, root mean squared error and SD, standard deviation of β̂₁; CP, 95% confidence interval coverage probability for ${\beta }_1^{\ast }=-0.2$. Results are based on 1000 replicates with n = T = 30. Boldface indicates whether Mean or CP are significantly different, at the 5% level, from −0.2 or 0.95, respectively. GEE-IND is the same as the proposed method but with W_t = 1 and no centering. In GEE-AR(1) includes an AR(1) working correlation matrix.