# Variable selection in mixture cure models using elastic net penalty: application to COVID-19 data

## TL;DR

This paper introduces a new method for selecting important variables in survival analysis models that account for cured individuals, applied to a study of hospitalized COVID-19 patients.

## Contribution

A penalized logistic/Cox mixture cure model with time-varying covariates and SCAD penalty for variable selection is developed and implemented.

## Key findings

- The modified model effectively handles time-varying covariates in mixture cure analysis.
- The approach was successfully applied to real-world data on hospitalized COVID-19 patients.
- The SCAD penalty improved variable selection and model interpretability.

## Abstract

In survival analysis, it is often assumed that all individuals will eventually experience the event of interest if followed long enough. However, in many real-world scenarios, a subset of individuals remains event-free indefinitely. For instance, in clinical studies, some patients never relapse and are considered cured rather than censored. Traditional survival models are inadequate for capturing this heterogeneity. Mixture cure models address this limitation by distinguishing between cured and susceptible individuals while modeling the survival of the latter. A key challenge in mixture cure modeling is selecting relevant covariates, particularly when dealing with time-varying effects. This study develops a penalized logistic/Cox proportional hazards mixture cure model incorporating time-varying covariates for both the incidence and latency components. The model is implemented using the smoothly clipped absolute deviation (SCAD) penalty to facilitate variable selection and improve model interpretability. To achieve this, we modified the penPHcure package to accommodate SCAD regularization and generate time-varying covariates. The proposed approach is applied to real-world data on the time to death for hospitalized COVID-19 patients in Limpopo Province, South Africa, demonstrating its practical applicability in survival analysis.