Table 1. Marginal Treatment Effect Analysis: Parameter estimates, sandwich standard errors, and bootstrap standard error.

Std: unaugmented GEE, Aug: augmented GEE. Ind: independence, Exch: exchangeable correlation with single parameter, Exch-TS: exchangeable with treatment-specific correlation parameters. SE₁: unadjusted sandwich SE, SE₂: sandwich with nuisance parameter adjustment, SE₃: sandwich with small-sample adjustment, SE₄: sandwich with small-sample and nuisance adjustments. Exch: Exchangeable correlation with single parameter, Exch-TS: Exchangeable with treatment-specific correlation parameters. ARE: square of the sandwich SE of the Std(Exch) estimator divided by the square of the sandwich SE of the indicated estimator. ARE boot: square of the bootstrap SE of the Std(Exch) estimator divided by the square of the bootstrap SE of the indicated estimator. ARE and Confidence intervals(CIs) are based on SE₃ and SE₄ for unaugmented and augmented estimators, respectively.

	Estimate	Sandwich Standard Error with Adjustments						Bootstrap SE
	${\widehat{\beta }}_1$	SE1	SE2	SE3	SE4	95% CI	ARE	SE boot	ARE boot
Std (Exch)	0.354	0.082	-	0.088	-	(0.182,0.526)	1.000	0.081	1.000
Std (Exch-TS)	0.355	0.082	-	0.086	-	(0.186,0.525)	1.034	0.085	0.910
Aug (Ind)	0.360	0.066	0.060	0.071	0.064	(0.236,0.485)	1.528	0.062	1.681
Aug (Exch)	0.364	0.063	0.057	0.067	0.060	(0.245,0.482)	1.730	0.064	1.582
Aug (Exch-TS)	0.360	0.063	0.061	0.066	0.064	(0.234,0.485)	1.769	0.082	0.966