Power Calculations for Replication Studies

TL;DR

This paper advocates for using Bayesian predictive power instead of traditional conditional power in designing replication studies, improving decision-making and accounting for uncertainty in original effect estimates.

Contribution

It introduces Bayesian predictive power into replication study design and discusses its advantages over conditional power, including interim analysis applications.

Findings

Predictive power better accounts for uncertainty in effect estimates.

Bayesian methods improve decision-making in replication studies.

Application to social sciences data demonstrates practical benefits.

Abstract

The reproducibility crisis has led to an increasing number of replication studies being conducted. Sample sizes for replication studies are often calculated using conditional power based on the effect estimate from the original study. However, this approach is not well suited as it ignores the uncertainty of the original result. Bayesian methods are used in clinical trials to incorporate prior information into power calculations. We propose to adapt this methodology to the replication framework and promote the use of predictive instead of conditional power in the design of replication studies. Moreover, we describe how extensions of the methodology to sequential clinical trials can be tailored to replication studies. Conditional and predictive power calculated at an interim analysis are compared and we argue that predictive power is a useful tool to decide whether to stop a replication study prematurely. A recent project on the replicability of social sciences is used to illustrate the properties of the different methods.