Combining case-control studies for identifiability and efficiency improvement in logistic regression

TL;DR

This paper demonstrates that combining multiple case-control studies using logistic regression can improve parameter estimation accuracy, achieve intercept identifiability, and attain semiparametric efficiency, even when studies are unrelated.

Contribution

It introduces a method for integrating separate case-control studies in logistic regression, ensuring parameter identifiability and optimal statistical efficiency.

Findings

Combined studies yield more accurate slope estimates.

Intercepts become identifiable in combined analysis.

Estimates are consistent and asymptotically normal.

Abstract

Can two separate case-control studies, one about Hepatitis disease and the other about Fibrosis, for example, be combined together? It would be hugely beneficial if two or more separately conducted case-control studies, even for entirely irrelevant purposes, can be merged together with a unified analysis that produces better statistical properties, e.g., more accurate estimation of parameters. In this paper, we show that, when using the popular logistic regression model, the combined/integrative analysis produces a more accurate estimation of the slope parameters than the single case-control study. It is known that, in a single logistic case-control study, the intercept is not identifiable, contrary to prospective studies. In combined case-control studies, however, the intercepts are proved to be identifiable under mild conditions. The resulting maximum likelihood estimates of the intercepts and slopes are proved to be consistent and asymptotically normal, with asymptotic variances achieving the semiparametric efficiency lower bound.