Sample size calculations for single-arm survival studies using transformations of the Kaplan-Meier estimator

TL;DR

This paper introduces new sample size calculation methods for single-arm survival studies that improve accuracy in small samples by using alternative transformations of the Kaplan-Meier estimator.

Contribution

It proposes alternative transformations for the Kaplan-Meier estimator to enhance sample size calculations in small-sample single-arm survival trials.

Findings

Proposed methods yield more accurate sample size estimates.

The arcsine square-root transformation improves empirical power.

Methods validated with clinical trial data.

Abstract

In single-arm clinical trials with survival outcomes, the Kaplan-Meier estimator and its confidence interval are widely used to assess survival probability and median survival time. Since the asymptotic normality of the Kaplan-Meier estimator is a common result, the sample size calculation methods have not been studied in depth. An existing sample size calculation method is founded on the asymptotic normality of the Kaplan-Meier estimator using the log transformation. However, the small sample properties of the log transformed estimator are quite poor in small sample sizes (which are typical situations in single-arm trials), and the existing method uses an inappropriate standard normal approximation to calculate sample sizes. These issues can seriously influence the accuracy of results. In this paper, we propose alternative methods to determine sample sizes based on a valid standard normal approximation with several transformations that may give an accurate normal approximation even with small sample sizes. In numerical evaluations via simulations, some of the proposed methods provided more accurate results, and the empirical power of the proposed method with the arcsine square-root transformation tended to be closer to a prescribed power than the other transformations. These results were supported when methods were applied to data from three clinical trials.