  A novel mixture cure frailty model is introduced for handling censored
survival data. Mixture cure models are preferable when the existence of a cured
fraction among patients can be assumed. However, such models are heavily
underexplored: frailty structures within cure models remain largely
undeveloped, and furthermore, most existing methods do not work for
high-dimensional datasets, when the number of predictors is significantly
larger than the number of observations. In this study, we introduce a novel
extension of the Weibull mixture cure model that incorporates a frailty
component, employed to model an underlying latent population heterogeneity with
respect to the outcome risk. Additionally, high-dimensional covariates are
integrated into both the cure rate and survival part of the model, providing a
comprehensive approach to employ the model in the context of high-dimensional
omics data. We also perform variable selection via an adaptive elastic-net
penalization, and propose a novel approach to inference using the
expectation-maximization (EM) algorithm. Extensive simulation studies are
conducted across various scenarios to demonstrate the performance of the model,
and results indicate that our proposed method outperforms competitor models. We
apply the novel approach to analyze RNAseq gene expression data from bulk
breast cancer patients included in The Cancer Genome Atlas (TCGA) database. A
set of prognostic biomarkers is then derived from selected genes, and
subsequently validated via both functional enrichment analysis and comparison
to the existing biological literature. Finally, a prognostic risk score index
based on the identified biomarkers is proposed and validated by exploring the
patients' survival.
