Empirical Bayes Double Shrinkage for Combining Biased and Unbiased Causal Estimates

TL;DR

This paper introduces a new class of double-shrinkage estimators that combine biased and unbiased causal estimates, providing a hyperparameter-free, data-driven approach for multidimensional causal inference with valid confidence intervals.

Contribution

It develops novel Empirical Bayes double-shrinkage estimators for integrating biased and unbiased causal estimates without hyperparameter tuning, applicable to multidimensional causal effects.

Findings

Demonstrates improved estimation accuracy in simulations.

Provides valid Empirical Bayes confidence intervals.

Shows utility on Women's Health Initiative data.

Abstract

Motivated by the proliferation of observational datasets and the need to integrate non-randomized evidence with randomized controlled trials, causal inference researchers have recently proposed several new methodologies for combining biased and unbiased estimators. We contribute to this growing literature by developing a new class of estimators for the data-combination problem: double-shrinkage estimators. Double-shrinkers first compute a data-driven convex combination of the the biased and unbiased estimators, and then apply a final, Stein-like shrinkage toward zero. Such estimators do not require hyperparameter tuning, and are targeted at multidimensional causal estimands, such as vectors of conditional average treatment effects (CATEs). We derive several workable versions of double-shrinkage estimators and propose a method for constructing valid Empirical Bayes confidence intervals. We also demonstrate the utility of our estimators using simulations on data from the Women's Health Initiative.