Biomedical research studies frequently involve repeated measurements. For example, in longitudinal studies a group of individuals is followed over time and repeated measurements are made at several points in time, in two-period cross-over experiments subjects are first administered one treatment and then """"""""crossed-over"""""""" to a second treatment, and in many (observational and experimental) studies there is more than one endpoint of interest. Flexible methodology based on modelling the mean vector and the covariance matrix of the multivariate Gaussian distribution is available for analyzing such data when the measurements are continuous. There is comparatively little methodology available for the analysis of repeated categorical measurements. This is particularly true for likelihood based methodology. The present proposal is to develop likelihood based methodology for the analysis of (a) longitudinal studies having a binary outcome, (b) binary cross-over experiments, (c) longitudinal studies having an ordinal outcome, and (d) studies having multiple categorical endpoints. Models for the analysis of the latter will allow for any combination of binary, nominal, and ordinal outcomes. The goal is to develop models which facilitate making inferences for the marginal effects of covariates on outcomes, as well as for making inferences regarding the association between outcomes. Computer software will be developed to fit these models by the method of maximum likelihood. The importance of model specification for three-way and higher-way associations will be evaluated, and comparisons will be made with non-maximum likelihood methodologies to determine when and how they might be used in place of maximum likelihood. Methods for computing estimated standard errors and for constructing confidence intervals will also be evaluated.
