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Can two separate case-control studies, one about Hepatitis disease and theother about Fibrosis, for example, be combined together? It would be hugelybeneficial if two or more separately conducted case-control studies, even forentirely irrelevant purposes, can be merged together with a unified analysisthat produces better statistical properties, e.g., more accurate estimation ofparameters. In this paper, we show that, when using the popular logisticregression model, the combined/integrative analysis produces a more accurateestimation of the slope parameters than the single case-control study. It isknown that, in a single logistic case-control study, the intercept is notidentifiable, contrary to prospective studies. In combined case-controlstudies, however, the intercepts are proved to be identifiable under mildconditions. The resulting maximum likelihood estimates of the intercepts andslopes are proved to be consistent and asymptotically normal, with asymptoticvariances achieving the semiparametric efficiency lower bound.

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