Variables in health-related sciences are often categorical. Tables displaying such data are often sparse, having few observations in come categories, because (1) the study may have a small number of subjects, or (2) repeated measurement of responses may produce many cells for the table. The proposed research focuses on development of statistical methods for sparse categorical data. Small-sample methods are useful for comparing medical treatments when the sample size is insufficient for large-sample approximations. Models for repeated measurement data are useful for allowing subject heterogeneity, for instance in comparing treatments in cross-over studies, assessing inter-rater agreement about a medical condition, modeling matched-pairs responses in opthalmalogic research, and assessing population size in public health applications with capture-recapture models. Repeated categorical measurement data: Methods will be developed to describe clustered categorical data. A common theme of this research will be application of generalized linear mixed models containing random effects. Specific topics include studying the extent to which one can use a distribution-free approach for the random effects in regression models for multivariate categorical responses, developing a parametric model based on a multivariate binomial-logit normal distribution, describing heterogeneity of ordinal odds ratios, and using mixed models for applications such as capture-recapture estimation. Small-sample analyses: Small-sample methods for making inferences about parameters in models for categorical data will be further developed and evaluated. Topics to be considered include approximate confidence intervals for binomial and Poisson parameters and measures comparing such parameters, improved exact confidence intervals for the trend parameters in linear logit models, order-restricted methods for small-sample inference that assume only monotone orderings on parameters rather than a fully parametric model, and treatment of sampling zeroes in multi-center clinical trails.
