LASSO Method for Additive Risk Models with High Dimensional Covariates

1 Summary. The additive risk model is a useful alternative to the proportional hazards model. It postulates that the hazard function is the sum of the baseline hazard function and the regression function of covariates. In this article, we investigate estimation in the additive risk model with right censored survival data and high dimensional covariates. A LASSO (least absolute shrinkage and selection operator) approach is proposed for estimating the regression parameters. We propose using the L 1 boosting algorithm, which is computationally affordable and relatively easy to implement, to compute the LASSO estimates. The V-fold cross validation is applied to select the tuning parameter and the weighted bootstrap is used to estimate the variances of the LASSO estimators. The proposed approach is illustrated with analysis of the PBC clinical data and the DLBCL genomic data. It is shown that this approach can provide interpretable and sparse predictive models with satisfactory predication and classification properties.