Many variables in health-related sciences are measured on ordered categorical scales. Contingency tables that display such data are often sparse, having few observations in many cells of the table. Two common reasons for this are (1) constraints of a study necessitate a small sample size, or (2) repeated measurement of responses for subjects at several occasions results in a multidimensional table with a large number of cells. The proposed research focuses on developing statistical methodology for these two situations. Exact methods will be developed for making inferences about the association between treatment and response, adjusting for relevant covariates. Small-sample analyses: Exact statistical tests for an ordered categorical response will be developed for the hypotheses of conditional independence and no three-factor interaction. Non-null inferences, such as exact confidence intervals for ordinal odd ratios, will also be developed. The methods will be connected to recently developed loglinear and logit models for ordinal data. Repeated categorical measurement analyses: Two types of analyses will be considered. One type models how marginal distributions of the response vary across occasions and according to values of covariates. The other type models the dependence among repeated responses. Special attention will be given to modeling inter-rater agreement, an important problem when several physicians make subjective evaluations on a categorical scale, using the same sample. For both types of analyses, semi-parametric methods will be developed to handle cases in which traditional maximum likelihood approaches are awkward or infeasible.
