Improved Conditional Logistic Regression using Information in Concordant Pairs with Software

TL;DR

Conditional logistic regression (CLR) faces efficiency and calibration issues when nuisance intercepts must be estimated under matched-pair designs. The authors propose a two-step Bayesian CLR (BCLR) that first uses concordant-pair data to form informative priors on nuisance coefficients, then performs CLR on discordant pairs to estimate the treatment effect $\beta_w$. They develop four prior families (naive, mixture of g's, probability-matching, and a hybrid) and implement 12 flavors across three concordant-pair models in the R package $\texttt{bclogit}$, enabling Hamiltonian MCMC posterior sampling. Through simulations and a Framingham Heart Study analysis, BCLR yields higher power and better calibration than CLR, particularly in nonlinear logit settings, providing a practical, open-source tool for matched-pair analyses.

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.