  The computational prediction algorithm of neural network, or deep learning,
has drawn much attention recently in statistics as well as in image recognition
and natural language processing. Particularly in statistical application for
censored survival data, the loss function used for optimization has been mainly
based on the partial likelihood from Cox's model and its variations to utilize
existing neural network library such as Keras, which was built upon the open
source library of TensorFlow. This paper presents a novel application of the
neural network to the quantile regression for survival data with right
censoring, which is adjusted by the inverse of the estimated censoring
distribution in the check function. The main purpose of this work is to show
that the deep learning method could be flexible enough to predict nonlinear
patterns more accurately compared to existing quantile regression methods such
as traditional linear quantile regression and nonparametric quantile regression
with total variation regularization, emphasizing practicality of the method for
censored survival data. Simulation studies were performed to generate nonlinear
censored survival data and compare the deep learning method with existing
quantile regression methods in terms of prediction accuracy. The proposed
method is illustrated with two publicly available breast cancer data sets with
gene signatures. The method has been built into a package and is freely
available at \url{https://github.com/yicjia/DeepQuantreg}.
