Non-parametric 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 permutational distribution of the relevant test statistic. Inference based on such asymptotic approximations in not always satisfactory. Many data sets do not satisfy the large sample criteria that are needed for the asymptotic results to hold. It is thus desirable to have the option to base inference on the exact permutational distribution of the test statistic. In the past, this has not been a practical option because of the formidable computational difficulties inherent in such an approach. Recent spectacular advances in computer technology, combined with the availability of efficient numerical algorithms for exact permutational inference, can change the situation. The main goal of this research project is to develop such numerical algorithms for five commonly encountered biomedical problems; loglinear models for categorical data, regression, multivariate models, power and sample size computations, and empirical assessments of exact conditional inference. An interdisciplinary approach will be taken. Powerful techniques of network optimization, recursion, Monte-Carlo sampling with variance reduction, and hashing, from the fields of operations research and computer science, are to play a prominent role in all the algorithms. The investigator states that many new areas for methodological research will be stimulated by the development of these algorithm and the results will be useful to practicing statisticians for planning and analyzing cancer clinical trials, to applied epidemiologists conducting case-control studies, and to theoretical statisticians needing exact bench-marks against which to compare their asymptotic results.
