Alternating logistic regressions with improved finite sample properties

Alternating logistic regressions is an estimating equations procedure used to model marginal means of correlated binary outcomes while simultaneously specifying a within-cluster association model for log odds ratios of outcome pairs. A recent generalization of alternating logistic regressions, known as orthogonalized residuals, is extended to incorporate finite sample adjustments in the estimation of the log odds ratio model parameters for when there is a moderately small number of clusters. Bias adjustments are made both in the sandwich variance estimators and in the estimating equations for the association parameters. The proposed methods are demonstrated in a repeated cross-sectional cluster trial to reduce underage drinking in the United States, and in an analysis of dental caries incidence in a cluster randomized trial of 30 aboriginal communities in the Northern Territory of Australia. A simulation study demonstrates improved performance with respect to bias and coverage of their estimators relative to those based on the uncorrected orthogonalized residuals procedure.