The cure rate models, known as two-component mixture models, have been widely used for the survival data analysis when long-term survivors are observed. In the literature, much of attention has been put on the evaluation of covariate effects on both cure fraction and conditional hazard rate of the model. However, it is tremendously challenging to interpret the covariate effects, especially for high-dimensional covariates, on the overall survival responses from a marginal perspective when the covariates are shared in two components. As motivated by the microarray data of breast cancer from TCGA, it is of interest to identify genes that are highly associated with the survival outcome marginally in the presence of long-term survivors. For this, we propose a marginal mean hazard rate model for high-dimensional covariates. Technically, a novel reparameterization is used to relate the covariates to the marginal mean hazard rate, and the variable selection is implemented based on LASSO-type penalized likelihood function. Intensive simulations are conducted to assess the performance of the proposed model, and the TCGA microarray data of breast cancer are used for illustration.