Censored Quantile Regression Neural Networks for Distribution-Free Survival Analysis
This work provides a distribution-free uncertainty quantification tool for survival analysis, addressing a specific bottleneck in applying neural networks to censored data, though it is incremental in extending linear model techniques to neural networks.
The paper tackles the problem of predicting quantiles for censored survival data using neural networks, introducing a novel algorithm that simultaneously optimizes multiple quantiles with a single network, resulting in better calibration than existing methods on 10 out of 12 real datasets.
This paper considers doing quantile regression on censored data using neural networks (NNs). This adds to the survival analysis toolkit by allowing direct prediction of the target variable, along with a distribution-free characterisation of uncertainty, using a flexible function approximator. We begin by showing how an algorithm popular in linear models can be applied to NNs. However, the resulting procedure is inefficient, requiring sequential optimisation of an individual NN at each desired quantile. Our major contribution is a novel algorithm that simultaneously optimises a grid of quantiles output by a single NN. To offer theoretical insight into our algorithm, we show firstly that it can be interpreted as a form of expectation-maximisation, and secondly that it exhibits a desirable `self-correcting' property. Experimentally, the algorithm produces quantiles that are better calibrated than existing methods on 10 out of 12 real datasets.