The covariate-adjusted residual estimator and its use in both randomized trials and observational settings

TL;DR

This paper evaluates the covariate-adjusted residuals estimator for causal effect estimation, introduces a new unbiased estimator with inverse probability weighting applicable to both randomized and observational studies, and demonstrates its efficiency through simulations and real data.

Contribution

It develops a new estimator combining covariate adjustment and inverse probability weighting, valid in both randomized and observational settings, with improved efficiency.

Findings

The covariate-adjusted residuals estimator is unbiased and efficient in randomized trials.

The new estimator is unbiased in both randomized and observational studies.

Simulation and real data support the estimator's improved performance.

Abstract

We often seek to estimate the causal effect of an exposure on a particular outcome in both randomized and observational settings. One such estimation method is the covariate-adjusted residuals estimator, which was designed for individually or cluster randomized trials. In this manuscript, we study the properties of this estimator and develop a new estimator that utilizes both covariate adjustment and inverse probability weighting We support our theoretical results with a simulation study and an application in an infectious disease setting. The covariate-adjusted residuals estimator is an efficient and unbiased estimator of the average treatment effect in randomized trials; however, it is not guaranteed to be unbiased in observational studies. Our novel estimator, the covariate-adjusted residuals estimator with inverse probability weighting, is unbiased in randomized and observational settings, under a reasonable set of assumptions. Furthermore, when these assumptions hold, it provides efficiency gains over inverse probability weighting in observational studies. The covariate-adjusted residuals estimator is valid for use in randomized trials, but should not be used in observational studies. The covariate-adjusted residuals estimator with inverse probability weighting provides an efficient alternative for use in randomized and observational settings.