It is often challenging to share detailed individual-level data among studies due to various informatics and privacy constraints. However, it is relatively easy to pool together aggregated summary level data, such as the ones required for standard meta-analyses. Focusing on data generated from case-control studies, we present a flexible inference procedure that integrates individual-level data collected from an "internal" study with summary data borrowed from "external" studies. This procedure is built on a retrospective empirical likelihood framework to account for the sampling bias in case-control studies. It can incorporate summary statistics extracted from various working models adopted by multiple independent or overlapping external studies. It also allows for external studies to be conducted in a population that is different from the internal study population. We show both theoretically and numerically its efficiency advantage over several competing alternatives.
Keywords: Lagrange multiplier; case-control studies; empirical likelihood; estimating equations; meta-analysis; retrospective likelihood.
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