Exact inference for conditional logistic regression using stochastic approximation Monte Carlo importance sampling

초록

Exact inference in conditional logistic regression is often attempted with Markov chain Monte Carlo (MCMC) but performs poorly in small or sparse samples and near-separation because valid datasets are rare, causing poor mixing and unreliable results. We propose SIS-CLR (stochastic approximation Monte Carlo importance sampling for conditional logistic regression), which integrates the stochastic approximation Monte Carlo framework with adaptive importance sampling. SIS-CLR draws from an enlarged reference set that also includes auxiliary datasets violating the sufficient-statistic constraints for nuisance parameters. This design improves the mixing efficiency of the Markov chain, accelerates convergence, and ensures a desired proportion of valid samples. The method remains reliable in difficult inferential settings, such as near-boundary data or perfect separation, where likelihood-based or asymptotic approaches often fail. Simulations and real-data analyses show that SIS-CLR yields more accurate and stable p-value estimates than existing methods while substantially reducing computation. Together, these results position SIS-CLR as a practical and theoretically grounded tool for exact conditional inference in challenging logistic regression problems.

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