A parametric mixture cure rate model with competing risks
Abstract
The well-known standard mixture cure model is widely used to model long-term survivors by distinguishing cured from non-cured individuals in the study population. Since its seminal introduction by Berkson and Gage, numerous extensions have been proposed to enhance its flexibility and applicability across diverse clinical settings. However, most existing extensions focus on a single cause of failure among non-cured individuals, often treating events from alternative causes as censored observations. This limitation may inadequately represent the complexity of survival data in which individuals are exposed to multiple competing causes of failure. In particular, treating competing events as non-informative censoring when estimating the probability of a specific cause of failure may lead to biased estimates of cumulative incidence and potentially misleading clinical interpretations. These limitations motivate the development of flexible survival models that jointly account for long-term survivors and multiple competing causes of failure. In this study, we propose an extension of the standard mixture cure model that incorporates a cure fraction and multiple competing risks within a unified framework. Model parameters are estimated by maximum likelihood using augmented data. The finite-sample performance of the proposed estimators is evaluated through extensive simulation studies, which yield satisfactory results across the scenarios considered. Finally, the proposed methodology is illustrated using melanoma patient data from the Surveillance, Epidemiology, and End Results (SEER) database, which include long-term survivors and multiple competing causes of death.
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BibTeX
@misc{brito2026parametric,
title = {{A parametric mixture cure rate model with competing risks}},
author = {Carolyne Soares de Brito and Frederico Machado Almeida},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26934},
eprint = {2610.26934},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26934},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A parametric mixture cure rate model with competing risks
AU - Carolyne Soares de Brito
AU - Frederico Machado Almeida
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.26934
UR - https://arxiv.org/abs/2610.26934
AB - The well-known standard mixture cure model is widely used to model long-term survivors by distinguishing cured from non-cured individuals in the study population. Since its seminal introduction by Berkson and Gage, numerous extensions have been proposed to enhance its flexibility and applicability across diverse clinical settings. However, most existing extensions focus on a single cause of failure among non-cured individuals, often treating events from alternative causes as censored observations. This limitation may inadequately represent the complexity of survival data in which individuals are exposed to multiple competing causes of failure. In particular, treating competing events as non-informative censoring when estimating the probability of a specific cause of failure may lead to biased estimates of cumulative incidence and potentially misleading clinical interpretations. These limitations motivate the development of flexible survival models that jointly account for long-term survivors and multiple competing causes of failure. In this study, we propose an extension of the standard mixture cure model that incorporates a cure fraction and multiple competing risks within a unified framework. Model parameters are estimated by maximum likelihood using augmented data. The finite-sample performance of the proposed estimators is evaluated through extensive simulation studies, which yield satisfactory results across the scenarios considered. Finally, the proposed methodology is illustrated using melanoma patient data from the Surveillance, Epidemiology, and End Results (SEER) database, which include long-term survivors and multiple competing causes of death.
ER -