A Semiparametric Probit Mixture Cure Model for Interval Censored Data with a Cure Fraction

Accurately estimating the incubation period of emerging infectious diseases, defined as the time interval from infection to symptom onset, is essential for informing quarantine strategies and allocating public health resources. To address the challenges of interval-censored data commonly encountered in incubation period studies, as well as the possibility that some infected individuals may never develop symptoms, we propose a semiparametric probit mixture cure model. By introducing two latent variables to simplify the likelihood function, we develop a corresponding EM algorithm for parameter estimation. Under mild regularity conditions, we establish the consistency and asymptotic normality of the proposed estimators. Numerical simulation studies demonstrate that the proposed method performs well even with limited sample sizes. Furthermore, an empirical analysis of real-world COVID-19 data validates the practical applicability of the model. The proposed semiparametric probit mixed cure model offers methodological support for early prevention and control decision-making in response to sudden infectious disease outbreaks.