Improved generalized estimating equations for incomplete longitudinal binary data, covariance estimation in small samples, and ordinal data

The focus of this research is to improve existing methods for the marginal modeling of associated categorical outcomes. Generalized estimating equations, based on quasilikelihood, is in wide use to make inference on marginal mean parameters, especially for categorical data. In the case that response data are not all observed, generalized estimating equations give inconsistent parameter estimates when missingness depends on observed or unobserved outcomes. Inverse-probability weighted generalized estimating equations give valid results if missingness depends only on observed outcomes, and a missingness model is correctly specified. For our first topic we propose specific forms of semi-parametric efficient estimators in marginal models when dropouts for longitudinal binary data are missing at random. The efficiency of inverse-probability weighted generalized estimating equations is also explored in this setting.;The other specific topics of concern in this research are related to extensions of generalized estimating equations that allow for modeling associations between categorical outcomes. Although associations are often considered nuisances, it is not uncommon that they are scientifically relevant. It may be of interest in this case to model associations on covariates defined by characteristics of clusters or outcome pairs. Alternating logistic regressions model marginal means of correlated binary outcomes while simultaneously allowing for an association model that parameterizes the odds ratio for outcome pairs. Our second topic concerns point and variance estimation of association parameters for finite samples. Bias adjustments in estimating outcome variance have recently been introduced for small samples in generalized estimating equations. We propose an extension of these adjustments to odds ratio parameters in alternating logistic regressions.;The remaining topic of our research concerns generalized estimating equations for ordinal data, for which alternating logistic regressions has recently been adapted. An alternate formulation of alternating logistic regressions based on orthogonalized residuals has been introduced for binary data resolving some problems in the existing procedure, including lack of invariance of the variance estimator to observation order. In our final topic we define this alternate formulation of alternating logistic regressions for correlated ordinal data, and examine its efficiency with regards to estimating within-cluster association parameters.