Modeling cure fractions in interval-censored competing risks data: An AFT mixture approach

Yijun Wang; Bing Zhou; Chenghui Fu; Xuan Xu; Yijun Wang; Bing Zhou; Chenghui Fu; Xuan Xu

doi:10.3934/era.2026288

Electronic Research Archive

2026, Volume 34, Issue 9: 6573-6613. doi: 10.3934/era.2026288

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Research article

Modeling cure fractions in interval-censored competing risks data: An AFT mixture approach

1.
School of Statistics and Data Science, Zhejiang Gongshang University, Hangzhou 310018, China
2.
Collaborative Innovation Center of Statistical Data Engineering, Technology & Application, Zhejiang Gongshang University, Hangzhou 310018, China
3.
Laboratory for Statistical Monitoring and Intelligent Governance of Common Prosperity, Zhejiang Gongshang University, Hangzhou 310018, China
4.
Asset and Laboratory Management Office, Zhejiang University of Finance and Economics, Hangzhou 310018, China

Received: 02 July 2026 Revised: 24 July 2026 Accepted: 27 July 2026 Published: 03 August 2026

This paper proposes a parametric mixture cure model within the accelerated failure time (AFT) framework for interval-censored data with competing risks. The model integrates multinomial logistic regression for the incidence of various event types (including cure) and AFT models for the latency among susceptible individuals. We consider three lifetime distributions (Weibull, lognormal, loglogistic) and develop an expectation-maximization (EM) algorithm for estimation. The large-sample properties of the proposed estimators are established and validated through comprehensive simulations, which show minimal bias, well-aligned standard errors, and coverage probabilities reaching the nominal level. In an empirical application to Lending Club personal loan data, our model, which accounts for default and prepayment as competing risks, reveals distinct covariate mechanisms overlooked by models ignoring competition: Annual income symmetrically "delays default while accelerating prepayment", while loan amount consistently accelerates only prepayment. Model comparison based on Akaike information criterion (AIC) selects the Weibull distribution as optimal.
- mixture cure model,
- interval censoring data,
- competing risks,
- accelerated failure time,
- EM algorithm
Citation: Yijun Wang, Bing Zhou, Chenghui Fu, Xuan Xu. Modeling cure fractions in interval-censored competing risks data: An AFT mixture approach[J]. Electronic Research Archive, 2026, 34(9): 6573-6613. doi: 10.3934/era.2026288

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Abstract

This paper proposes a parametric mixture cure model within the accelerated failure time (AFT) framework for interval-censored data with competing risks. The model integrates multinomial logistic regression for the incidence of various event types (including cure) and AFT models for the latency among susceptible individuals. We consider three lifetime distributions (Weibull, lognormal, loglogistic) and develop an expectation-maximization (EM) algorithm for estimation. The large-sample properties of the proposed estimators are established and validated through comprehensive simulations, which show minimal bias, well-aligned standard errors, and coverage probabilities reaching the nominal level. In an empirical application to Lending Club personal loan data, our model, which accounts for default and prepayment as competing risks, reveals distinct covariate mechanisms overlooked by models ignoring competition: Annual income symmetrically "delays default while accelerating prepayment", while loan amount consistently accelerates only prepayment. Model comparison based on Akaike information criterion (AIC) selects the Weibull distribution as optimal.

References

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