New Model-based and Deep Learning Methods for Survival Data
Yichen Jia, PhD University of Pittsburgh
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. Statistics to summarize time to event have been the popular hazard function. However, the definition of hazard function as the conditional failure rate is not straightforward for patients and clinicians. Therefore, new inference and prediction models for survival data that focus on event time itself and its various quantities with more straightforward interpretation is in need.
In the first part of the talk, a quantile regression model, QRegIT, will be introduced to associate the inactivity time, a new summary measure for survival data, with covariates under competing risks. Asymptotic properties have been derived for the regression coefficient estimators and associated test statistics. Simulation results show that QRegIT works well under the assumed finite sample settings. QRegIT will then be illustrated with a real dataset from a breast cancer study.
In the second part of the talk, a deep learning method for quantile regression, DeepQuantreg, has been developed to predict conditional quantile survival time. The Huber check function has been adopted in the loss function with inverse probability weights to adjust for censoring. Simulation studies have been performed to generate nonlinear censored survival data and compared DeepQuantreg with the traditional linear quantile regression and nonparametric quantile regression. DeepQuantreg will then be illustrated with two publicly available breast cancer data sets with gene signatures.