A Rule of Thumb for the Power Gain due to Covariate Adjustment in Randomized Controlled Trials with Continuous Outcomes

TL;DR

This paper presents a simple rule of thumb for estimating the power gain from covariate adjustment in RCTs with continuous outcomes, showing it depends on the correlation between covariates and outcomes.

Contribution

It derives a straightforward approximation formula for the power increase due to covariate adjustment in randomized trials.

Findings

Power ratio approximately equals 1 + 0.5 * R^2 for covariate adjustment

Adjustment can significantly increase power when covariates are highly correlated with outcomes

Provides a practical rule of thumb for trial design and analysis

Abstract

Randomized Controlled Trials (RCTs) often adjust for baseline covariates in order to increase power. This technical note provides a short derivation of a simple rule of thumb for approximating the ratio of the power of an adjusted analysis to that of an unadjusted analysis. Specifically, if the unadjusted analysis is powered to approximately 80\%, then the ratio of the power of the adjusted analysis to the power of the unadjusted analysis is approximately $1 + \frac{1}{2} R^2$, where $R$ is the correlation between the baseline covariate and the outcome.