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

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.