Linear and nonlinear variable selection in competing risks data.

Subdistribution hazard model for competing risks data has been applied extensively in clinical researches. Variable selection methods of linear effects for competing risks data have been studied in the past decade. There is no existing work on selection of potential nonlinear effects for subdistribution hazard model. We propose a two-stage procedure to select the linear and nonlinear covariate(s) simultaneously and estimate the selected covariate effect(s). We use spectral decomposition approach to distinguish the linear and nonlinear parts of each covariate and adaptive LASSO to select each of the 2 components. Extensive numerical studies are conducted to demonstrate that the proposed procedure can achieve good selection accuracy in the first stage and small estimation biases in the second stage. The proposed method is applied to analyze a cardiovascular disease data set with competing death causes.