Univariate gradient statistic for a marginal cure rate model with high-dimensional covariates

Abstract

Cure rate models, also known as two-component mixture models, have been well established and widely used in the literature for analyzing the lifetime data of long-term survivors. Owing to the advancement of genomic technology, it is now of interest to identify the significant genes or microarrays that are highly associated with the survival outcome under the cure rate model framework. The identification procedure using these genomic data will involve the technique of variable selection for high-dimensional covariates. However, the cure rate model requires the modeling of the cure fraction and the survival function of the uncured individuals, which inevitably leads to a more complicated variable selection process. In this paper, we propose a gradient-statistic-based variable selection method under a marginal representation of the cure rate model. This marginal model can produce interpretable covariate effects on the overall survival response by relating the marginal mean hazard rate to high-dimensional covariates directly while regarding the cure fraction as a nuisance parameter. A univariate gradient score is then used iteratively to determine significant covariates. Coupled with the use of a False Discovery Rate approach, the top-ranked list of covariates can be easily obtained by controlling the family-wise error rate. The proposed method is evaluated by extensive simulations and illustrated with an application of the TCGA breast cancer dataset which contains more than 400,000 microarrays.