Exact Logistic Regression Model

With the increase in the computer’s capacity to do tedious calculations, the use of exact logistic regression models has become increasingly popular in healthcare, banking, and other industries. Traditional methods (which are based on asymptotic theory) when used for analyzing small, skewed, or sparse datasets are not usually reliable. When sample sizes are small or the data are sparse or skewed, exact conditional inference is necessary and applicable (Derr, 2000). Exact methods of inferences are based on enumerating the exact distributions of certain statistics to estimate the parameters of interest in a logistic regression model, conditional on the remaining parameters. This is a method of testing and estimation that uses conditional methods to obtain exact tests of parameters in binary and nominal logistic models. Exact methods are appropriate for small sample or sparse data situations that often result in the failure (nonconvergence or separation) of the usual unconditional maximum likelihood estimation method. However, exact methods can take a great deal of time and memory as sample or model sizes increase. For sample sizes too large for the default exact method, a Monte Carlo method is provided. The chapter uses EXACT statement in PROC LOGISTIC or PROC GENMOD, and we also fit models in SAS, C+, and R. Our methods are based on Troxler, S., Lalonde, T. L., and Wilson J. R. (2011). Exact logistic models for nested binary data. Statistics in Medicine, 30(8).