Sample-size formula for clustered survival data using weighted log-rank statistics

Abstract

We present a simple sample‐size formula for weighted log‐rank statistics applied to clustered survival data with variable cluster sizes and arbitrary treatment assignments within clusters. This formula is based on the asymptotic normality of weighted log‐rank statistics under certain local alternatives in the clustered data context. We also provide consistent variance estimators. The derived sample‐size formula reduces to Schoenfeld's (1983) formula for cases of no clustering or independence within clusters. Simulation results verify control of the Type I error and accuracy of the sample‐size formula. Use of the sample‐size formula in an event‐driven clinical trial design is illustrated using data from the Early Treatment Diabetic Retinopathy Study.