This is a Phase II SBIR proposal for a major extension to Cytel's flagship software, StatXact, to perform small sample exact inference for correlated categorical data. Such data are common in biomedical research, especially in areas such as genetics, ophthalmology, and developmental toxicology. In this Phase II effort, we will develop correlated data analogues for most of the existing small sample procedures for independent data currently provided in the StatXact software. Specifically the resulting module will implement correlated data extensions of: 1) Exact tests of independence in unordered and ordered R x C contingency table. 2) Tests for differences in the distributions of 2 ordered multinomial populations. 3) Exact Mantel-Haenszel-type tests for assessing homogeneity of relative odds for stratified 2x2 tables, 4) Exact correlated data methods for situations in which independent factors vary across observations within a cluster. This extension will expand the applicability of such methods to a wider range of longitudinal and multiple outcome settings. Because implementing the above procedures can be computationally complex, a final goal of the proposal is the development of new algorithms to make these tools practical for general use. These include new efficient network-based algorithms and Monte Carlo simulation strategies for model fitting. The final product of this effort will be a toolbox of exact procedures will enable users to avoid relying on potentially poor large sample approximations when analyzing small sample correlated categorical data. This advantage will ultimately lead to more reliable analyses of such data. There is currently no software for such methods other than a limited prototype developed in Phase I of this proposal.
