Optimal utilization of heterogeneous external information via model averaging

It is increasingly feasible to obtain external information from multiple prior studies, and appropriately leveraging such information can assist the analysis of internal individual-level data. However, external information from multiple sources is often heterogeneous, and not all sources are informative for a given internal study. In this paper, we propose a model averaging procedure that optimally utilizes heterogeneous summary information from external studies to improve prediction performance. The procedure incorporates informative external information and downweights uninformative sources through data-driven weight assignments. Notably, our framework does not require the internal model to be correctly specified. We establish weight convergence and asymptotic optimality under correctly specified and misspecified internal models, respectively, and we compare the risk of the proposed model averaging procedure with that of simple equal-weight averaging. Numerical simulations demonstrate superior predictive performance, which we further illustrate using a Beijing housing rental dataset and a skin cutaneous melanoma dataset.