Robust regularization for high-dimensional Cox's regression model using weighted likelihood criterion

Variable selection for Cox's proportional hazards regression model has realized extensive use in the analysis of time-to-event data with censoring and predictor variables. These predictors may contain many high leverage points. We study this issue in the context of high-dimensional Cox regression, and propose a novel robust penalized estimator for noisy and non-normal survival data. We make use the appropriate weighting function at each observation in the partial likelihood score equation with the adaptive Lasso penalty on regression coefficients. By using the weighted partial likelihood and l₁-norm, the proposed regularized method is robust to outliers and high leverage points in the predictors. The weight function downweights those observations only if it is necessary, and provide better accuracy and sparsity. The simulation study shows that the proposed regularized method is more robust in estimation and variable selection than the existing penalized methods in the presence of possible high leverage points and heavy-tailed distribution of the response variable. It also yields competitive performance on the two real survival datasets.