Conditional logistic regression in cluster-specific 1: m matched treatment–control designs

ABSTRACT

Conditional logistic regression is a popular method for estimating a treatment effect while eliminating cluster-specific nuisance parameters when they are not of interest. Under a cluster-specific 1: m matched treatment–control study design, we present a new closed-form relationship between the conditional logistic regression estimator and the ordinary logistic regression estimator. In addition, we prove an equivalence between the ordinary logistic regression and the conditional logistic regression estimators, when the clusters are replicated infinitely often, which indicates that potential bias concerns when applying conditional logistic regression to complex survey samples.

KEYWORDS:

• Binary outcomes
• cluster-specific
• conditional logistic regression
• matched treatment–control studies.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J15
• 62F12

Acknowledgments

The author would like to thank Dr. Nicholas P. Jewell for his helpful and constructive comments that greatly contributed to the improvement of the paper.