A Menu-Driven Facility for Sample-Size Calculation in Novel Multiarm, Multistage Randomized Controlled Trials with a Time-to-Event Outcome

Abstract

We present menu- and command-driven Stata programs for the calculation of sample size, number of events, and trial duration for a novel type of clinical trial design with a time-to-event outcome and two or more experimental arms. The approach is based on terminating accrual of patients to inferior experimental treatment arms at an early stage in the trial, allowing through to the next stage only treatments that show a predefined degree of advantage against the control treatment. The first stage of testing uses an intermediate outcome measure for the definitive (primary) outcome rather than with the primary outcome itself. The experimental arms are compared pairwise with the control arm according to the intermediate outcome measure. Arms that survive the comparison enter the next stage of patient accrual, culminating in comparisons against control on the primary outcome measure. The features supported include unequal patient allocation, target hazard ratios that may differ from 1 under the null hypothesis, and the ability to stop patient recruitment at a specified time after trial initiation. The computations of sample size and power are based on the asymptotic mean and variance of the log hazard-ratio under the null and alternative hypotheses. The overall operating characteristics are computed from the intermediate and final stage significance levels and power, and the correlation between the log hazard-ratios on the intermediate and primary outcome measures at the different stages. We illustrate the approach with the design of a United Kingdom Medical Research Council six-arm trial in prostate cancer in which the intermediate outcome is failure-free survival and the primary outcome is overall survival.