A group bridge approach for component selection in nonparametric accelerated failure time additive regression model. Issue 6 (19th March 2021) - Huang, Longlong
Abstract: We study a nonparametric accelerated failure time (AFT) additive regression model whose covariates have nonparametric effects on the censored survival time. The proposed model is more flexible than the linear AFT model and can be used to perform dimension reduction and model building. Specifically, it can be used to discover the functional forms of all the covariates, whether a function is a zero or nonzero component; if it is a nonzero component, whether it is linear or nonlinear. First, we treat all the components as unknown nonlinear functions. B-splines are used to model these nonparametric components. A group bridge penalized variable selection approach based on the inverse probability-of-censoring weighted least squares is developed to select important nonparametric components and discover their functional forms simultaneously. Meanwhile, we compare the group bridge and group LASSO methods. The simulation results demonstrate that the group bridge method provides more accurate estimation and better selection performance than the group LASSO method, and the proposed method has satisfactory performance even with relatively high censoring rates. Two real data analyses are used to illustrate the application of the proposed method to censored survival data.