Sample size calculation for the weighted rank statistics with paired survival data

Abstract

This paper introduces a sample size calculation method for the weighted rank test statistics with paired two-sample survival data. Our sample size formula requires specification of joint survival and censoring distributions. For modelling the distribution of paired survival variables, we may use a paired exponential survival distribution that is specified by the marginal hazard rates and a measure of dependency. Also, in most trials randomizing paired subjects, the subjects of each pair are accrued and censored at the same time over an accrual period and an additional follow-up period, so that the paired subjects have a common censoring time. Under these practical settings, the design parameters include type I and type II error probabilities, marginal hazard rates under the alternative hypothesis, correlation coefficient, accrual period (or accrual rate) and follow-up period. If pilot data are available, we may estimate the survival distributions from them, but we specify the censoring distribution based on the specified accrual trend and the follow-up period planned for the new study. Through simulations, the formula is shown to provide accurate sample sizes under practical settings. Real studies are taken to demonstrate the proposed method.