Meta-Analysis of Randomized Experiments with Applications to Heavy-Tailed Response Data

TL;DR

This paper introduces a novel cross-validation-like method for evaluating treatment effect estimators in randomized trials, especially effective in heavy-tailed data, by leveraging unbiased difference-of-means estimates and aggregating results across many RCTs.

Contribution

It proposes a new methodology combining unbiased difference estimates with aggregation across multiple RCTs to assess estimator performance in heavy-tailed response data.

Findings

Downweighting or truncating large values improves estimation accuracy in heavy-tailed data.

The methodology is validated on 699 Amazon supply chain RCTs.

Procedures that bias slightly can reduce variance and enhance effect estimation.

Abstract

A central obstacle in the objective assessment of treatment effect (TE) estimators in randomized control trials (RCTs) is the lack of ground truth (or validation set) to test their performance. In this paper, we propose a novel cross-validation-like methodology to address this challenge. The key insight of our procedure is that the noisy (but unbiased) difference-of-means estimate can be used as a ground truth ``label" on a portion of the RCT, to test the performance of an estimator trained on the other portion. We combine this insight with an aggregation scheme, which borrows statistical strength across a large collection of RCTs, to present an end-to-end methodology for judging an estimator's ability to recover the underlying treatment effect as well as produce an optimal treatment "roll out" policy. We evaluate our methodology across 699 RCTs implemented in the Amazon supply chain. In this heavy-tailed setting, our methodology suggests that procedures that aggressively downweight or truncate large values, while introducing bias, lower the variance enough to ensure that the treatment effect is more accurately estimated.