Designing efficient randomized trials: power and sample size calculation when using semiparametric efficient estimators

TL;DR

This paper presents a simple formula for calculating the power and sample size of two-arm trials using semiparametric efficient estimators, enabling more efficient and smaller trials without sacrificing power.

Contribution

It introduces a straightforward method for sample size calculation in trials with semiparametric efficient estimators, improving efficiency over traditional unadjusted methods.

Findings

Simulation confirms large-sample properties match nominal values.

Fewer subjects needed when accounting for efficient estimators.

Method applied to real clinical trial data.

Abstract

Trials enroll a large number of subjects in order to attain power, making them expensive and time-consuming. Sample size calculations are often performed with the assumption of an unadjusted analysis, even if the trial analysis plan specifies a more efficient estimator (e.g. ANCOVA). This leads to conservative estimates of required sample sizes and an opportunity for savings. Here we show that a relatively simple formula can be used to estimate the power of any two-arm, single-timepoint trial analyzed with a semiparametric efficient estimator, regardless of the domain of the outcome or kind of treatment effect (e.g. odds ratio, mean difference). Since an efficient estimator attains the minimum possible asymptotic variance, this allows for the design of trials that are as small as possible while still attaining design power and control of type I error. The required sample size calculation is parsimonious and requires the analyst to provide only a small number of population parameters. We verify in simulation that the large-sample properties of trials designed this way attain their nominal values. Lastly, we demonstrate how to use this formula in the "design" (and subsequent reanalysis) of a real clinical trial and show that fewer subjects are required to attain the same design power when a semiparametric efficient estimator is accounted for at the design stage.