Conditional Distribution Function Estimation Using Neural Networks for Censored and Uncensored Data

TL;DR

This paper introduces a neural network-based method for estimating the entire conditional distribution function for censored and uncensored data, avoiding model assumptions and demonstrating superior performance over traditional methods.

Contribution

The paper proposes a novel neural network approach for nonparametric conditional distribution estimation applicable to censored data, extending beyond mean estimation.

Findings

The method performs well in simulations, outperforming partial likelihood and traditional neural networks.

It provides unbiased estimates even when model assumptions are violated.

Real-world data applications confirm its practical utility.

Abstract

Most work in neural networks focuses on estimating the conditional mean of a continuous response variable given a set of covariates.In this article, we consider estimating the conditional distribution function using neural networks for both censored and uncensored data. The algorithm is built upon the data structure particularly constructed for the Cox regression with time-dependent covariates. Without imposing any model assumption, we consider a loss function that is based on the full likelihood where the conditional hazard function is the only unknown nonparametric parameter, for which unconstraint optimization methods can be applied. Through simulation studies, we show the proposed method possesses desirable performance, whereas the partial likelihood method and the traditional neural networks with $L_2$ loss yield biased estimates when model assumptions are violated. We further illustrate the proposed method with several real-world data sets. The implementation of the proposed methods is made available at https://github.com/bingqing0729/NNCDE.