Testing for sufficient follow-up in censored survival data by using extremes

TL;DR

This paper introduces a new statistical test for assessing whether follow-up time in censored survival data is sufficient, especially for light-tailed distributions, using a bootstrap approach and applied to cancer datasets.

Contribution

It develops a novel, simple test for checking sufficient follow-up in survival analysis with cure fractions, addressing a gap in existing methods.

Findings

The test performs well in finite samples based on simulations.

It effectively distinguishes sufficient from insufficient follow-up in practical datasets.

Applications to leukemia and breast cancer data demonstrate its utility.

Abstract

In survival analysis, it often happens that some individuals, referred to as cured individuals, never experience the event of interest. When analyzing time-to-event data with a cure fraction, it is crucial to check the assumption of `sufficient follow-up', which means that the right extreme of the censoring time distribution is larger than that of the survival time distribution for the non-cured individuals. However, the available methods to test this assumption are limited in the literature. In this article, we study the problem of testing whether follow-up is sufficient for light-tailed distributions and develop a simple novel test. The proposed test statistic compares an estimator of the non-cure proportion under sufficient follow-up to one without the assumption of sufficient follow-up. A bootstrap procedure is employed to approximate the critical values of the test. We also carry out extensive simulations to evaluate the finite sample performance of the test and illustrate the practical use with applications to leukemia and breast cancer datasets.