Robust Model Selection and Estimation for Censored Survival Data with High Dimensional Genomic Covariates

When relating genomic data to survival outcomes, there are three main challenges that are the censored survival outcomes, the high-dimensionality of the genomic data, and the non-normality of data. We propose a method to tackle these challenges simultaneously and obtain a robust estimation of detecting significant genes related to survival outcomes based on Accelerated Failure Time (AFT) model. Specifically, we include a general loss function to the AFT model, adopt model regularization and shrinkage technique, cope with parameters tuning and model selection, and develop an algorithm based on unified Expectation-Maximization approach for easy implementation. Simulation results demonstrate the advantages of the proposed method compared with existing methods when the data has heavy-tailed errors and correlated covariates. Two real case studies on patients are provided to illustrate the application of the proposed method.