Quantile forward regression for high-dimensional survival data.

Despite the urgent need for an effective prediction model tailored to individual interests, existing models have mainly been developed for the mean outcome, targeting average people. Additionally, the direction and magnitude of covariates' effects on the mean outcome may not hold across different quantiles of the outcome distribution. To accommodate the heterogeneous characteristics of covariates and provide a flexible risk model, we propose a quantile forward regression model for high-dimensional survival data. Our method selects variables by maximizing the likelihood of the asymmetric Laplace distribution (ALD) and derives the final model based on the extended Bayesian Information Criterion (EBIC). We demonstrate that the proposed method enjoys a sure screening property and selection consistency. We apply it to the national health survey dataset to show the advantages of a quantile-specific prediction model. Finally, we discuss potential extensions of our approach, including the nonlinear model and the globally concerned quantile regression coefficients model.