Variables measured in health-related sciences are often categorical. Contingency tables displaying such data are often sparse, having few observations in some categories, because (1) the study may have relatively few subjects, or (2) repeated measurement and other forms of clustering of responses produces many cells for the table. The proposed research focuses on development of statistical methods for sparse categorical data. Small-sample statistical methods are useful for comparing medical treatments when the sample size is insufficient to use standard large-sample methods. Models for clustered data enable handling of subject heterogeneity and consequent within-subject correlation in studies with repeated measurement of subjects, for instance in comparing treatments in cross-over studies. Repeated categorical measurement data: Methods will be developed and evaluated for analyzing clustered categorical data, focusing on applications with repeated measurement. A common theme is application and study of properties of generalized linear mixed models containing random effects. Specific topics include studying the effects on efficiency and bias of distribution-free and parametric approaches for the random effects, modeling binary and ordinal responses to describe heterogeneity in applications such as multi-center clinical trials, developing measures for descriptive and inferential comparison of non-nested models, and modeling clustered data when the response is a continuous proportion. Small-sample analyses: Small-sample inferential methods for parameters of relevance with categorical data will be further developed and evaluated. Topics include improved 'exact' confidence intervals (i.e. confidence level guaranteed to be at least the nominal level) for the difference of proportions, odds ratio, and relative risk, and improved approximate confidence intervals for these measures. The two types of improved intervals will be compared (In some cases, approximate may be better because of the inherent conservativeness of exact methods for discrete data), and extensions will be developed for stratified data.
