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

arXiv: https://arxiv.org/abs/2106.00939 · HTML: https://mlsanity.com/paper/2106.00939/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2021.

## Built on by (most cited first, 3 of 3)

- [Efficient semi-supervised inference for logistic regression under case-control studies](https://mlsanity.com/paper/2402.15365/) (2024)
- [Statistical inference for case-control logistic regression via integrating external summary data](https://mlsanity.com/paper/2405.20655/) (2024)
- [Deep non-parametric logistic model with case-control data and external summary information](https://mlsanity.com/paper/2409.01829/) (2024)

## Abstract (arXiv)

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.