Treatment Effect Estimation with Efficient Data Aggregation

Abstract

Data aggregation, also known as meta analysis, is widely used to synthesize knowledge on parameters shared in common (e.g., average treatment effect) between multiple studies. We introduce in this paper an attractive data aggregation protocol based on summary statistics from existing studies, to inform the design of a (new) validation study and estimate shared parameters by combining all the studies. In particular, we focus on the scenario where each existing study relies on an 1 -regularized regression analysis to select a parsimonious model from a set of high dimensional covariates. We derive an estimator for the shared parameter by aggregating summary statistics from each study through a novel technique called data carving. Our estimator (a) aims to make the fullest possible use of data from the existing studies without the bias from data re-use in model selection and parameter estimation, and (b) provides the added benefit of individual data privacy, because full data from these studies need not be shared for efficient estimation.

Selective Inference with Distributed Data

“…We take a different approach in the distributed setup by casting the problem into a randomized framework, and provide an asymptotic likelihood function for the selected GLM. A randomized framework for selective inference has been considered for better power in [39,27], for a more efficient use of data in [33,31], and for stability in [45].…”