Abstract
In competing risks cure models, if there is unobserved heterogeneity among susceptible patients, application of the methods that do not consider this heterogeneity, may lead to invalid results. Therefore, this study aimed to introduce a model to cover the above properties of survival studies. We introduced a unified model by combining a parametric mixture cure gamma frailty model and vertical modeling of competing risks. We obtained estimates of parameters by an iterative method and Laplace transform technique. Then, we calculated the cumulative incidence functions (CIFs) and related confidence bounds by using a bootstrap approach. We conducted an extensive simulation study to evaluate the performance of the proposed model. The results of the simulation study showed the superior performance of our proposed competing risks cure frailty model. Finally, we applied the proposed method to analyze a real dataset of breast cancer patients.
Highlights
Survival modeling is a tool in biostatistics and epidemiology that can help one to predict the risk of disease
No study has combined competing risks models with cure models and univariate frailty models; few articles have been published regarding the combination of competing risks models with cure models (Choi, Huang, and Cormier, 2015; Eloranta et al, 2014; Nicolaie, Taylor, and Legrand, 2018)
Compared to the study of Ghavami et al, 2017, we reported the results of both the competing risks cure model and competing risks cure frailty model to emphasize the importance of examining heterogeneity
Summary
Survival modeling is a tool in biostatistics and epidemiology that can help one to predict the risk of disease. In medical studies, identifying the risk of failure for a given disease is remarkable for patients as well as physicians; this would benefit patients to choose the lifestyle, and it would be guidelines to physicians selecting a specific treatment approach. Competing risks models usually assume that all patients are susceptible; if there is a sufficient follow-up, all patients will experience any of the possible outcomes (Pintilie, 2011). Due to advances in the early detection of diseases and their treatment, some patients may be long-term event-free survivors (cured fraction). When it is confirmed that there is a cured fraction in the study population, typical survival models lead to overestimating the survival of the susceptible subjects, and deployment cure models are recommended (Corbière et al, 2009). In a mixture cure model, the patients consist of two parts, including susceptible patients (uncured patients) and long-term survivor patients (cured patients). The relation between population survival time (S(t)) and the survival time of susceptible (uncured) patients (Su(t)) is defined as follows
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