Table 4.

Sample size effect and correlation magnitude effects for data generation mechanism given in Equation 5 with β^O = (1,1,1, 1,1) and β^M = (−3, 1/2, 1/2, 1/2, 1/2). Statistics for 1000 replicates are the bias compared to $M_E^{\ast }$, the empirical standard errors over the replicates, the mean asymptotic nuisance-adjusted standard errors and the coverage for the GEE, the IPW, the AUG and the DR with independence (−I) and exchangeable (−E) working correlation matrix.

	$M_E^{\ast }$	Bias		Standard Error (SE)						Coverage
				Empirical		Robust		Fay’s		Robust		Fay’s
		−I	−E	−I	−E	−I	−E	−I	−E	−I	−E	−I	−E
Small sample M = 10, ni = (10, 20, 30) with probability 1/3 each, Low correlation
GEE	2.0	−1.7473	−1.7479	0.4351	0.4360	0.3963	0.3256	0.4559	0.4603	0.8	2.3	3.9	4.9
IPW	2.0	−1.0130	−1.0130	0.6793	0.6842	0.5538	0.5591	0.6735	0.6766	49.0	49.2	59.8	59.9
AUG	2.0	−1.8099	−1.8111	0.3371	0.3269	0.8362	0.8353	0.8834	0.8817	29.7	29.1	40.1	39.2
DR	2.0	0.0008	0.0006	0.1552	0.1586	0.1127	0.1140	0.1190	0.1201	84.8	83.8	86.0	86.2
Large sample M = 100, ni = (90,100,110) with probability 1/3 each, Low correlation
GEE	2.0	−1.7335	−1.7321	0.1015	0.1013	0.0985	0.0727	0.0994	0.0994	0.0	0.0	0.0	0.0
IPW	2.0	−0.9955	−0.9952	0.1514	0.1517	0.1559	0.1563	0.1588	0.1592	0.2	0.2	0.2	0.2
AUG	2.0	−1.8019	−1.8022	0.0695	0.0664	0.2556	0.2550	0.2569	0.2563	0.0	0.0	0.0	0.0
DR	2.0	0.0016	0.0017	0.0265	0.0265	0.0262	0.0263	0.0264	0.0264	95.1	95.0	95.1	95.2
Small sample M = 10, ni = (10, 20, 30) with probability 1/3 each, High correlation
GEE	2.0	−0.0086	−0.0086	0.5265	0.5314	0.4701	0.4721	0.5651	0.5657	88.5	88.4	92.9	92.7
IPW	2.0	−1.0221	−1.0229	0.7026	0.7083	0.5776	0.5829	0.7015	0.7044	52.4	52.2	62.2	61.5
AUG	2.0	−1.7985	−1.7987	0.5058	0.5084	0.8748	0.8727	0.9243	0.9209	35.8	35.8	45.1	45.5
DR	2.0	0.0098	0.0062	0.4328	0.4407	0.2469	0.2480	0.2607	0.2614	77.4	77.7	79.7	79.6
Large sample M = 100, ni = (90, 100, 110) with probability 1/3 each, High correlation
GEE	2.0	−1.7325	−1.7312	0.1145	0.1141	0.1121	0.0753	0.1132	0.1132	0.0	0.0	0.0	0.0
IPW	2.0	−0.9945	−0.9940	0.1618	0.1620	0.1652	0.1656	0.1682	0.1686	0.2	0.2	0.2	0.2
AUG	2.0	−1.8014	−1.8017	0.0787	0.0761	0.2587	0.2581	0.2600	0.2594	0.0	0.0	0.0	0.0
DR	2.0	0.0029	0.0032	0.0609	0.0610	0.0590	0.0590	0.0593	0.0593	94.7	94.6	94.7	94.6

Marginal model for the GEE:

$${\mu }_{\mathit{ij}}(\mathit{\beta },A_i)={\beta }_0+{\beta }_A{A}_i$$

OM in AUG and DR is fitted for each treatment group A_i = a using a stepwise regression:

$$B_{\mathit{ij}}({\mathit{X}}_i,A_i=a)=\text{stepwise}(X_{\mathit{ij}}^1,X_{\mathit{ij}}^2,X_{\mathit{ij}}^3,{\overline{X^1}}_{i.},{\overline{X^2}}_{i.},{\overline{X^3}}_{i.})$$

PS in DR and IPW is fitted for the whole dataset using a stepwise regression:

$$\mathit{logit}({\pi }_{\mathit{ij}}({\mathit{X}}_{i,}{A}_i))=\text{stepwise}({\mathit{A}}_i,X_{\mathit{ij}}^1,X_{\mathit{ij}}^2,X_{\mathit{ij}}^3,{\overline{X^1}}_{i.},{\overline{X^2}}_{i.},{\overline{X^3}}_{i.})$$