Adaptive Logistic Regression Modeling of Multivariate Dichotomous and Polytomous Outcomes

Abstract

This chapter formulates and demonstrates adaptive fractional polynomial modeling of means and dispersions for repeatedly measured dichotomous and polytomous outcomes with two or more values. Marginal modeling extends from the multivariate normal outcome context to the multivariate dichotomous and polytomous outcome context. However, due to the complexity in general of computing likelihoods and quasi-likelihoods (as needed to account for non-unit dispersions) for general multivariate marginal modeling, generalized estimating equations (GEE) techniques are often used instead, thereby avoiding computation of likelihoods and quasi-likelihoods. This complicates the extension of adaptive modeling to the GEE context since it is based on cross-validation (CV) scores computed from likelihoods or likelihood-like functions, but a readily computed extended likelihood is formulated for use in adaptive GEE-based modeling of multivariate dichotomous and polytomous outcomes. Conditional modeling also extends to the multivariate dichotomous and polytomous outcome context, both transition modeling and general conditional modeling. In contrast to marginal GEE-based modeling, conditional modeling of means for multivariate dichotomous and polytomous outcomes with unit dispersions is based on pseudolikelihoods that can be used to compute pseudolikelihood CV (PLCV) scores on which to base adaptive transition and general conditional modeling of multivariate dichotomous and polytomous outcomes. These marginal and conditional models can be extended to model dispersions as well as means. Example analyses of these kinds are presented of post-baseline respiratory status over time for patients with respiratory disorder in terms of the baseline respiratory status, time, and being on an active as opposed to a placebo treatment.