🤖 AI Summary
This study addresses the problem of efficiently integrating internal individual-level data with external aggregate statistics to improve estimation accuracy for population-level functional parameters under weak transportability assumptions. To overcome bias and efficiency loss arising from model misspecification in conventional approaches, we first derive the semiparametric efficiency bound for this fusion setting. Methodologically, we propose two novel estimators: (i) an efficient semiparametric estimator achieving the derived bound, and (ii) an adaptive fusion estimator with oracle properties—ensuring double robustness and automatic bias correction. We establish its asymptotic efficiency and unbiasedness theoretically. Simulation studies and real-data analysis of *Helicobacter pylori* infection demonstrate that our methods significantly enhance estimation precision and statistical power compared to using internal data alone or simple weighted aggregation.
📝 Abstract
Suppose we have individual data from an internal study and various summary statistics from relevant external studies. External summary statistics have the potential to improve statistical inference for the internal population; however, it may lead to efficiency loss or bias if not used properly. We study the fusion of individual data and summary statistics in a semiparametric framework to investigate the efficient use of external summary statistics. Under a weak transportability assumption, we establish the semiparametric efficiency bound for estimating a general functional of the internal data distribution, which is no larger than that using only internal data and underpins the potential efficiency gain of integrating individual data and summary statistics. We propose a data-fused efficient estimator that achieves this efficiency bound. In addition, an adaptive fusion estimator is proposed to eliminate the bias of the original data-fused estimator when the transportability assumption fails. We establish the asymptotic oracle property of the adaptive fusion estimator. Simulations and application to a Helicobacter pylori infection dataset demonstrate the promising numerical performance of the proposed method.
