Copula-based Cox models for dependent current status data with a cure fraction

Traditional survival analysis typically assumes that all subjects will eventually experience the event of interest given a sufficiently long follow-up period. Nevertheless, due to advancements in medical technology, researchers now frequently observe that some subjects never experience the event and are considered cured. Furthermore, traditional survival analysis assumes independence between failure time and censoring time. However, practical applications often reveal dependence between them. Ignoring both the cured subgroup and this dependence structure can introduce bias in model estimates. Among the methods for handling dependent censoring data, the numerical integration process of frailty models is complex and sensitive to the assumptions about the latent variable distribution. In contrast, the copula method, by flexibly modeling the dependence between variables, avoids strong assumptions about the latent variable structure, offering greater robustness and computational feasibility. Therefore, this paper proposes a copula-based method to handle dependent current status data involving a cure fraction. In the modeling process, we establish a logistic model to describe the susceptible rate and a Cox proportional hazards model to describe the failure time and censoring time. In the estimation process, we employ a sieve maximum likelihood estimation method based on Bernstein polynomials for parameter estimation. Extensive simulation experiments show that the proposed method demonstrates consistency and asymptotic efficiency under various settings. Finally, this paper applies the method to lymph follicle cell data, verifying its effectiveness in practical data analysis.