# Deep Learning for Quantile Regression under Right Censoring: DeepQuantreg Source: [Deep Learning for Quantile Regression under Right Censoring: DeepQuantreg]() Collection index: [llms.txt]() Data updated: 2025-10-25T23:07:38.441Z Authors: Yichen Jia, Jong-Hyeon Jeong Published: 2020-07-14T14:31:11.000Z ## Abstract 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}. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Censored Quantile Regression on Weibull (test)](): Censored Quantile Regression; Weibull (test); MSE (Quantile): 1.116. - [Censored Quantile Regression on Norm heavy (test)](): Censored Quantile Regression; Norm heavy (test); MSE: 1.099. - [Censored Quantile Regression on Norm same (test)](): Censored Quantile Regression; Norm same (test); MSE to True Quantile: 0.357. - [Censored Quantile Regression on LogNorm same (test)](): Censored Quantile Regression; LogNorm same (test); MSE to True Quantile: 0.394. - [Censored Quantile Regression on Norm linear (test)](): Censored Quantile Regression; Norm linear (test); MSE (Quantile): 1.172. - [Censored Quantile Regression on LogNorm (test)](): Censored Quantile Regression; LogNorm (test); MSE: 1.279. - [Censored Quantile Regression on Norm uniform (test)](): Censored Quantile Regression; Norm uniform (test); MSE to True Quantile: 2.591. - [Censored Quantile Regression on Norm med. (test)](): Censored Quantile Regression; Norm med. (test); MSE: 0.255. - [Censored Quantile Regression on Norm light (test)](): Censored Quantile Regression; Norm light (test); MSE (Quantile): 0.277. - [Censored Quantile Regression on LogNorm heavy (test)](): Censored Quantile Regression; LogNorm heavy (test); MSE: 2.639. - [Censored Quantile Regression on LogNorm med. (test)](): Censored Quantile Regression; LogNorm med. (test); MSE: 2.087. - [Censored Quantile Regression on LogNorm light (test)](): Censored Quantile Regression; LogNorm light (test); MSE: 0.831. - [Censored Quantile Regression on Norm non-lin (test)](): Censored Quantile Regression; Norm non-lin (test); MSE to True Quantile: 0.818. - [Censored Quantile Regression on Exponential (test)](): Censored Quantile Regression; Exponential (test); MSE to true quantile: 20.046. ## Original sources and implementation [Original paper]() [PDF]()