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

2025-05-19

AI Summary

In survival analysis, assessing whether follow-up duration is “practically sufficient” to reliably estimate the cure fraction requires accounting for covariate effects. Existing methods omit categorical covariates and rely on overly conservative intersection–union tests. This paper extends the “practically sufficient follow-up” test to cure models with categorical covariates—its first such generalization. We propose a novel asymptotic α-level testing procedure based on representative covariate levels and introduce a tail non-increasing density assumption to balance statistical power and type-I error control. We rigorously establish that the method achieves the nominal asymptotic significance level. Monte Carlo simulations demonstrate substantially higher power than conventional approaches. An application to leukemia data confirms the method’s practical utility and robustness.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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 leukemia dataset.

Problem

• Testing sufficient follow-up in cure models with categorical covariates
• Extending follow-up tests to include covariate information effects
• Proposing a novel test for practical sufficient follow-up criteria

Innovation

• Extends follow-up test with categorical covariates
• Proposes novel test using chosen covariate value
• Assumes non-increasing survival time density tail