Parametric cure fraction models for interval-censoring with a change-point based on a covariate threshold

Survival models with a cure fraction have received considerable attention in recent years. It becomes a very useful tool for handling situations in which a proportion of subjects under study may never experience the event of interest. Cure fraction models for interval-censored data are less developed compared to the right-censoring case. Moreover, most of the existing cure fraction models share in common the assumption that the effect of a covariate is constant in time and over the range of the covariate. This assumption is not completely valid when a significant change occurs in subjects' failure rate or cure rate. Therefore, this study focuses on developing several classes of parametric survival cure models for interval-censored data incorporating a cure fraction and change-point effect in covariate. The analysis starts with the extension of the existing cure models; mixture cure model (MCM) and Bounded cumulative hazard (BCH) model, with fixed covariates in the presence of interval-censored data. Then, this research introduces a modified cure model as an alternative to the MCM and BCH model. The proposed model has sound motivation in relapse of cancer and can be used in other disease models. The parametric maximum likelihood estimation method is employed to verify the performance of the MCM within the framework of the expectation-maximization (EM) algorithm while the estimation methods for other models are employed in a simpler and straightforward setting. In addition, the models are further developed to accommodate the problem of changepoint effect for the covariate and a smoothed likelihood to obtain relevant estimators is proposed. An estimation method is proposed for right-censored data, and the method is then extended to accommodate interval-censored data. Simulation studies are carried out under various conditions to assess the performances of the models that have been developed. The simulation results indicate that the proposed models and the estimation procedures can produce efficient and reasonable estimators. Application of suggested models to a set of gastric cancer data is demonstrated. The proposed models and approaches can be directly applied to analyze survival data from other relevant fields.

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