Nonparametric statistical methods are commonly used to plan studies and analyze biomedical data. A key feature of these methods is the use of asymptotic theory to derive the approximate permutation distribution of the relevant test statistic. Inference based on such asymptotic approximations is not always satisfactory. Therefore, over the past decade, fast recursive algorithms have been developed for exact nonparameric inference. At present, these algorithms are capable of handling one, two, and K-sample problems, IxJ contingency tables, and stratified 2xC contingency tables. However, with the availability of these algorithms, the demand for more exact inference has also grown. The big challenge is to provide the capability for exact inference concerning the parameters of discrete regression models like the logistic, polytomous and Poisson regression models. A second major challenge is to extend exact inference from IxJ, to IxJxK contingency tables. The current numerical algorithms are simply not equal to the task. The investigator proposes to develop powerful new algorithms using ideas from integer programming, Monte Carlo sampling with variance reduction, and Monte Carlo sampling from Markov chains. This new generation of algorithms will have the power to perform exact inference for discrete regression models and for three-way contingency tables. A secondary objective is to conduct an empirical investigation of exact and asymptotic confidence intervals for the ratio of two binomial parameters. This ratio is more important for cohort studies than the odds ratio.
