Sample size calculation for the one‐sample log‐rank test

Abstract

An improved method of sample size calculation for the one-sample log-rank test is provided. The one-sample log-rank test may be the method of choice if the survival curve of a single treatment group is to be compared with that of a historic control. Such settings arise, for example, in clinical phase-II trials if the response to a new treatment is measured by a survival endpoint. Present sample size formulas for the one-sample log-rank test are based on the number of events to be observed, that is, in order to achieve approximately a desired power for allocated significance level and effect the trial is stopped as soon as a certain critical number of events are reached. We propose a new stopping criterion to be followed. Both approaches are shown to be asymptotically equivalent. For small sample size, though, a simulation study indicates that the new criterion might be preferred when planning a corresponding trial. In our simulations, the trial is usually underpowered, and the aspired significance level is not exploited if the traditional stopping criterion based on the number of events is used, whereas a trial based on the new stopping criterion maintains power with the type-I error rate still controlled.

Taxon Richness of “Megaviridae” Exceeds those of Bacteria and Archaea in the Ocean

“…, 70%, 80%, and 90%). The significance of differences between richness curves was assessed using a Log-rank test ( 70 ).…”

Survival analysis: Part I — analysis of time-to-event

“…Survival analysis is an analysis method that analyzes the time to an event of interest. In the log-rank test or Cox proportional hazards regression model, the hazard ratio is used for sample size calculation [ 22 ]. Just as a normal distribution and an effect size, e.g., Cohen’s h, are presupposed in other statistical methods for checking the statistical power or calculating the required sample size, the underlying survival model and effect size must be defined prior to calculating the sample size for survival analysis.…”

Two‐stage phase II survival trial design

“…The OSLRT was first introduced by Breslow, and its applications to the single‐arm phase II trial designs were discussed by Sun et al, Kwak and Jung, Wu, Schmidt et al, and Belin et al The study design based on the OSLRT requires each patient to be followed until an event occurs or until the end of study. In real practice, however, the full follow‐up information for a phase II trial is often difficult to obtain in the late period of trial, particularly when the accrual duration is long; obtaining the status of each patient within a restricted period is more realistic …”

“…Furthermore, none of these designs are fully efficient. Finkelstein et al, Sun et al, Wu, and Schmidt et al proposed single‐stage designs by using the one‐sample log‐rank test (OSLRT) which evaluates the treatment effect based on the entire survival distribution. Kwak and Jung and Belin et al developed an optimal two‐stage design without and with restricted follow‐up, respectively.…”