New Model-based and Deep Learning Methods for Survival Data with or without Competing Risks

Survival data (or time-to-event data) is a special type of data that focus on the time until occurrence of an event of interest. Traditional statistical methods have been based on the survival function or hazard function. This dissertation proposes inference and prediction models for survival data that focus on event time itself and its various quantities. In the first part, a quantile regression model is proposed to associate the inactivity time, a new summary measure for survival data, with covariates under competing risks. Asymptotic properties were derived for the regression coefficient estimators and associated test statistics. Simulation results show that my proposed method works well under the assumed finite sample settings. The proposed method is then illustrated with a real dataset from a breast cancer study. In the second part, a deep learning method for quantile regression, DeepQuantreg, is developed to predict conditional quantile survival time. The Huber check function was adopted in the loss function with inverse probability weights to adjust for censoring. Sim- ulation studies were performed to generate nonlinear censored survival data and compare the deep learning method with the traditional linear quantile regression and nonparametric quantile regression. The proposed method is illustrated with two publicly available breast cancer data sets with gene signatures. In the third part, a deep learning method with an innovative loss function, DeepCENT, is proposed to directly predict survival time. The newly proposed loss function combines the mean square error and the concordance index, which not only consider the prediction accu- racy but also the discriminative performance. Moreover, DeepCENT can handle competing risks. The validity and advantage of DeepCENT were evaluated using simulation studies and illustrated with three publicly available cancer data sets. Public Health Significance: The problem of analyzing survival data arises in many scientific fields, particularly in clinical studies. This dissertation provides several methods for analyzing survival data or competing risks data that not only accommodate heterogeneous covariate effects, but also retain straightforward interpretations. It is more clinically relevant and intuitively appealing than the existing methods, and has the potential to significantly improve the current practice in analyzing time-to-event data