021 - Unified Oracle Approach to Synthesizing External Aggregate Information

It is well recognized that incorporating summary information from external sources may improve the efficiency of the analysis of a study of interest, whereas failure to recognize inconsistency or properly account for the discrepancy between the external sources and the internal study may introduce bias. Even in absence of these concerns, failure to properly account for uncertainty in the external information may also lead to invalid inference. Addressing all three potential sources of invalid inference, we propose a penalized combined likelihood approach that simultaneously selects and incorporate consistent external information in the internal study analysis, while properly accounting for uncertainty in the selected information. The proposed approach does not assume the homogeneity of the target population between the internal study and the external sources nor require a reference dataset to address the discrepancies. The proposed estimator is as efficient as an oracle estimator that incorporates only consist external information. For implementation, we develop an alternative optimization strategy in which each step is a convex optimization. Simulation studies show that our approach consistently selects the correct external information, and has a smaller mean square error than the maximum likelihood method that only analyzes the internal study. We illustrate our approach by an application of gestational weight gain study.

Meta-analysis

Population heterogeneity

Model selection

Empirical likelihood

Regularization