New estimators for cure rate models

Abstract

If study subjects are tracked long enough, it is a typical assumption in survival analysis that they will eventually experience the event of interest. However, that is not always the case. In reality, it is not uncommon for a portion of the subjects to never witness the event of interest even after a very long followup. In clinical studies, for example, there is a subset of participants who will never relapse. These participants are said to be cured/immune in this scenario because they are not censored in the classic sense. Traditional survival models are inapplicable to modelling such immune individuals. Cure models are survival models that take into consideration subjects that have never been exposed to an event. However, choosing the correct covariates for modelling to better understand an event has been a major problem for researchers. This study is aimed at developing a penalised logistic/Cox proportional hazards mixture cure model that effectively accounts for both the cure status with time-varying covariates and the survival of uncured subjects with time-varying covariates, utilising an elastic net penalty. The penPHcure package is tailored for simulating time-invariant covariates for incidence and time-varying covariates for latency. Developed exclusively in R Studio, it is designed to support LASSO and SCAD penalties. However, our research endeavours to enhance the versatility of the package by incorporating both the elastic net penalty and time-varying covariates for both incidence and latency. To achieve this objective, a meticulous and thorough modification process was undertaken on the penPHcure package, resulting in a locally customised version that has been nicknamed "PenPHcure.AaRN." This modified package does not only provide the capacity to utilise the elastic net penalty, but also to generate time-varying covariates for both incidence and latency, seamlessly integrating these capabilities with its original functionalities. Our proposed model is demonstrated using a genuine dataset examining the duration until death for patients hospitalised with COVID-19 in the Limpopo Province, South Africa. In the concluding remarks, our study also offers possibilities for future work.