Computing Distributions for Exact Logistic Regression

TLDR: In this paper, an efficient recursive algorithm was proposed to generate the joint and conditional distributions of the sufficient statistics for logistic regression with binary response variables, and the algorithm was shown to be computationally feasible except in a few special situations.

Abstract: Logistic regression is a commonly used technique for the analysis of retrospective and prospective epidemiological and clinical studies with binary response variables. Usually this analysis is performed using large sample approximations. When the sample size is small or the data structure sparse, the accuracy of the asymptotic approximations is in question. On other occasions, singularity of the covariance matrix of parameter estimates precludes asymptotic analysis. Under these circumstances, use of exact inferential procedures would seem to be a prudent alternative. Cox (1970) showed that exact inference on the parameters of a logistic model with binary response requires consideration of the distribution of sufficient statistics for these parameters. To date, however, resorting to the exact method has not been computationally feasible except in a few special situations. This article presents an efficient recursive algorithm that generates the joint and conditional distributions of the sufficient...