Sharpening randomization-based causal inference for $2^2$ factorial designs with binary outcomes

TL;DR

This paper improves causal inference in $2^2$ factorial designs with binary outcomes by deriving a sharp variance lower bound, leading to more accurate variance estimation and better insights from clinical trial data.

Contribution

It introduces a novel variance estimator based on a sharp lower bound, enhancing the existing randomization-based causal inference framework for binary outcomes.

Findings

New variance estimator reduces over-estimation in finite populations

Simulation studies demonstrate improved accuracy of variance estimates

Application to clinical trial data yields new scientific insights

Abstract

In medical research, a scenario often entertained is randomized controlled $2^2$ factorial design with a binary outcome. By utilizing the concept of potential outcomes, Dasgupta et al. (2015) proposed a randomization-based causal inference framework, allowing flexible and simultaneous estimations and inferences of the factorial effects. However, a fundamental challenge that Dasgupta et al. (2015)'s proposed methodology faces is that the sampling variance of the randomization-based factorial effect estimator is unidentifiable, rendering the corresponding classic "Neymanian" variance estimator suffering from over-estimation. To address this issue, for randomized controlled $2^2$ factorial designs with binary outcomes, we derive the sharp lower bound of the sampling variance of the factorial effect estimator, which leads to a new variance estimator that sharpens the finite-population Neymanian causal inference. We demonstrate the advantages of the new variance estimator through a series of simulation studies, and apply our newly proposed methodology to two real-life datasets from randomized clinical trials, where we gain new insights.