Table 5.

Simulation of the scenario described in Equation 6 mimicking the SAM study data. Statistics for 1000 replicates are the bias compared to $M_E^{\ast }$, the empirical standard errors over replicates, the mean asymptotic nuisance-adjusted standard error, and the coverage for the GEE, the IPW, the AUG and the DR with independence (−I) and exchangeable (−E) working correlation matrix.

	$M_E^{\ast }$			Standard Error (SE)						Coverage
		Bias		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
GEE	5.73	2.214	2.213	1.330	1.329	1.829	1.848	1.359	1.363	89.4	88.7	59.4	59.7
IPW	5.73	0.536	0.537	1.333	1.333	1.214	1.214	1.470	1.471	86.5	86.4	92.1	92.1
AUG	5.73	0.173	0.173	0.973	0.973	0.878	0.878	0.925	0.925	88.6	88.6	89.9	89.9
DR	5.73	−0.104	−0.104	1.102	1.101	0.932	0.931	0.982	0.982	90.3	90.3	92.0	92.0
SAM-like sample M = 50, ni = (20, 30, 30) with probability 1/3 each
GEE	5.73	2.347	2.343	0.308	0.308	0.532	0.466	0.308	0.309	0.0	0.0	0.0	0.0
IPW	5.73	0.622	0.623	0.303	0.303	0.317	0.317	0.323	0.323	50.7	50.7	52.1	52.1
AUG	5.73	0.215	0.215	0.222	0.222	0.230	0.230	0.232	0.232	85.1	85.1	85.2	85.2
DR	5.73	0.037	0.026	0.259	0.260	0.252	0.253	0.254	0.255	94.6	95.3	94.6	95.4

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 using a stepwise regression:

$$B_{\mathit{ij}}({\mathit{X}}_i,A_i=a)=\text{stepwise}({\text{EMP}}_{\mathit{ij}},{\text{MARI}}_{\mathit{ij}},{\text{AGE}}_{\mathit{ij}},{\text{REL}}_{\mathit{ij}},{\text{CAGE}}_{\mathit{ij}},{\text{HIV}}_{\mathit{ij}},{\text{CDM}}_{\mathit{ij}},{\mathrm{X}}^1{ }_{\mathit{ij}},{\mathrm{X}}^2{ }_{\mathit{ij}},{\mathrm{X}}^3{ }_{\mathit{ij}})$$

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

$$\mathit{logit}({\pi }_{\mathit{ij}}({\mathit{X}}_i,A_i))=\text{stepwise}(A_i,{\text{EMP}}_{\mathit{ij}},{\text{MARI}}_{\mathit{ij}},{\text{AGE}}_{\mathit{ij}},{\text{REL}}_{\mathit{ij}},{\text{CAGE}}_{\mathit{ij}},{\text{HIV}}_{\mathit{ij}},{\text{CDM}}_{\mathit{ij}},{\mathrm{X}}^1{ }_{\mathit{ij}},{\mathrm{X}}^2{ }_{\mathit{ij}},{\mathrm{X}}^3{ }_{\mathit{ij}})$$