Cytel Corporation is the innovator of several software programs for analyzing data using exact methods. Their product list includes StatXact for exact tests, LogXact for exact logistic regression (especially useful for unbalanced data), EaSt for planning/monitoring group sequential clinical trials, and the Egret software package for design/analysis of epidemiological analysis. A new version of their software program for analyzing logistic regression with exact methods was released this year. Version 4.1 of LogXact is written for the Microsoft Windows environment. It will run on Windows 3.1 or higher. This package was originally intended for small sample logistic regression. The previous releases of LogXact produced estimates implementing a method described by Cox (1970). The unique feature of this special-purpose package is the support for exact small sample p values and confidence intervals in addition to the commonly available approximations based on chi-squared and normal distributions. The software will perform unconditional or conditional maximum likelihood inference and conditional exact inference. In addition, the present release adds Monte Carlo methods such that one can use the software's exact methods in analyzing larger datasets. Finally, version 4.1 also includes exact inference for Poisson regression. Using the Cox method for determining estimates based on permutation distributions limited the inital releases of the software to small datasets. The new version of LogXact 4.1 adds a Monte Carlo simulation method to the logistic regression collection of tools. This new tool allows the same capabilities for handling ill-conditioned predictors without the need to completely enumerate the permutation set. Instead, one can specify the number of permutations (selected via Monte Carlo) to consider in applying the estimation methods. The maturity of this special-purpose data analysis package allows application to a larger number of datasets and should now interest those users who have heretofore considered the package unable to support their larger (dataset) analysis needs. The exact method is based on permutation distributions of the sufficient statistics and is an alternative to maximum likelihood that produces results when maximum likelihood cannot. A common example in logistic regression is the presence of a perfect predictor; for example, when we have a binary predictor for which the outcome is always positive (or negative) in the presence of the predictor. Maximum likelihood methods will either drive the coefficient to infinity or recognize the ill-conditioned problem and drop the predictor from consideration. An example will illustrate the utility of the methods. Consider the synthetic data with 16 observations where frequency is the number of observations with the associated covariate pattern and result.
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James W. Hardin (2000) studied this question.