Testing for sufficient follow-up in cure models with categorical covariates

TL;DR

This paper extends tests for sufficient follow-up in cure models to include categorical covariates, proposing a new method that improves power by focusing on a key covariate value, with validation through simulations and real data.

Contribution

It introduces a novel test procedure for assessing sufficient follow-up in cure models with categorical covariates, enhancing power over existing methods.

Findings

The proposed test maintains asymptotic level α.

Simulation studies show improved power of the new test.

Application to melanoma data demonstrates practical utility.

Abstract

In survival analysis, estimating the fraction of 'immune' or 'cured' subjects who will never experience the event of interest, requires a sufficiently long follow-up period. A few statistical tests have been proposed to test the assumption of sufficient follow-up, i.e. whether the right extreme of the censoring distribution exceeds that of the survival time of the uncured subjects. However, in practice the problem remains challenging. To address this, a relaxed notion of 'practically' sufficient follow-up has been introduced recently, suggesting that the follow-up would be considered sufficiently long if the probability for the event occurring after the end of the study is very small. All these existing tests do not incorporate covariate information, which might affect the cure rate and the survival times. We extend the test for 'practically' sufficient follow-up to settings with categorical covariates. While a straightforward intersection-union type test could reject the null hypothesis of insufficient follow-up only if such hypothesis is rejected for all covariate values, in practice this approach is overly conservative and lacks power. To improve upon this, we propose a novel test procedure that relies on the test decision for one properly chosen covariate value. Our approach relies on the assumption that the conditional density of the uncured survival time is a non-increasing function of time in the tail region. We show that both methods yield tests of asymptotically level $\alpha$ and investigate their finite sample performance through simulations. The practical application of the methods is illustrated using a skin melanoma dataset.