Data Integration with Oracle Use of External Information from Heterogeneous Populations

It is common to have access to summary information from external studies. Such information can be useful for an internal study of interest to improve parameter estimation efficiency when incorporated. However, external studies may target populations different from the internal study, in which case an incorporation of the corresponding information may introduce estimation bias. We develop a penalized constrained maximum likelihood (PCML) method that simultaneously (a) selects the external studies whose information is useful for internal model fitting and (b) incorporates the corresponding information into internal estimation. The PCML estimator has the same efficiency as an oracle estimator that fully incorporates the useful external information alone. We establish estimation consistency, parametric rate of convergence, external information selection consistency, asymptotic normality, and oracle efficiency. An algorithm for implementation is provided, together with a data-adaptive tuning parameter selection. Supplemental materials are available online containing some details referred to throughout the article.