Variable selection and prediction for complex survival data analysis

Abstract

Survival analysis methods for time-to-event data are commonly used in biomedical researches. It is essential to select the important variables and identify the correct covariate functional form. After selection of important variables, it is of interest to evaluate the prediction performance of the selected model, typically by receiver oper ating characteristic (ROC) curve. Furthermore, the analysis of time-to-event data is complicated by the presence of interval censoring and dependent competing events, both of which occur frequently in clinical studies. In this dissertation, we set to de velop variable selection and prediction methods for complex survival data. In the first topic, we proposed a two-stage procedure to identify the linear and/or non-linear co variates functional forms simultaneously and estimate the selected covariate effects for competing risks data. Spectral decomposition was used to decompose the nonpara metric covariate function. The adaptive LASSO method was then to select the linear and non-linear components, respectively. We showed that our method achieved good selection accuracy and minimal estimation biases. In the second topic, to evaluate the prediction performance, we extended the ROC function estimation of right-censored competing risks data to interval-censored data. We proved the consistency of the estimator and demonstrated the convergence of estimator in numerical studies. In the third topic, we extended the ROC function for independent survival data to clustered survival data using within-cluster-resampling (WCR) technique. All the three methods had been implemented in real data as illustration.