A parametric framework for assessing and estimating sufficient follow-up time in cure models

2026-08-11

AI Summary

This study addresses the challenge of jointly evaluating follow-up adequacy and quantifying the time required to achieve cure in mixture cure models. The authors propose a unified parametric framework that, for the first time, integrates hypothesis testing for follow-up sufficiency with tolerance-based time estimation under a Weibull mixture cure model. They derive closed-form solutions for two established criteria—survival plateau distance and residual survival—and demonstrate their equivalence under parameter transformation. The finite-sample performance of the proposed framework is validated through Monte Carlo simulations across varying sample sizes, cure fractions, and censoring scenarios. Empirical applications to prostate cancer and triple-negative breast cancer datasets illustrate its practical utility in accurately assessing follow-up adequacy and precisely quantifying additional follow-up requirements.

Abstract

Reliable estimation of cure fractions depends critically on adequate follow-up. Classical procedures for assessing follow-up sufficiency are primarily inferential, whereas a separate body of literature estimates time to cure using excess-hazard, conditional cure-probability, or residual-survival definitions. These two approaches remain largely disconnected: assessing the adequacy of observed follow-up does not generally quantify the additional follow-up required under an explicit tolerance, whereas estimating time to cure does not itself provide a formal inferential assessment of the available follow-up. We develop a unified parametric framework that combines the Parametric Follow-up Sufficiency Test, which compares the terminal Kaplan-Meier estimate with the cure fraction estimated from a parametric mixture cure model, with two complementary tolerance-based formulations: the Plateau Distance Criterion on the population survival scale and the Residual Survival Criterion on the susceptible survival scale. We derive closed-form expressions for both criteria under the Weibull mixture cure model and establish that they yield identical minimum follow-up times under an appropriate transformation of their tolerance parameters. We evaluate the finite-sample performance of the framework through Monte Carlo simulations across sample sizes, cure fractions, and administrative censoring scenarios. Applications to prostate cancer and triple-negative breast cancer data illustrate how the framework assesses available follow-up, estimates additional observation time under prespecified tolerances, and identifies settings in which follow-up is already adequate.

Problem

• cure models
• follow-up sufficiency
• cure fraction
• survival analysis
• parametric framework

Innovation

• mixture cure model
• follow-up sufficiency
• tolerance-based criterion
• Weibull survival model
• cure fraction estimation