Improved Conditional Logistic Regression using Information in Concordant Pairs with Software

Abstract: We develop an improvement to conditional logistic regression (CLR) in the setting where the parameter of interest is the additive effect of binary treatment effect on log-odds of the positive level in the binary response. Our improvement is simply to use information learned above the nuisance control covariates found in the concordant response pairs' observations (which is usually discarded) to create an informative prior on their coefficients. This prior is then used in the CLR which is run on the discordant pairs. Our power improvements over CLR are most notable in small sample sizes and in nonlinear log-odds-of-positive-response models. Our methods are released in an optimized R package called bclogit.