Conditional Distribution Function Estimation Using Neural Networks for Censored and Uncensored Data
Authors: Bingqing Hu, Bin Nan; Volume 24, Issue 223, Pages 1-26, 2023.
Abstract
The majority of research on neural networks focuses on estimating the conditional mean of a continuous response variable based on a given set of covariates. This article, however, explores the estimation of the conditional distribution function using neural networks for both censored and uncensored data. The algorithm is developed based on a specific data structure designed for Cox regression with time-dependent covariates. Without imposing any model assumptions, we propose a loss function that relies on the full likelihood, where the conditional hazard function is the sole unknown nonparametric parameter. Unconstrained optimization methods can be utilized for estimating the conditional hazard function. Through simulation studies, we demonstrate that the proposed method exhibits favorable performance. In contrast, the partial likelihood method and traditional neural networks with $L_2$ loss produce biased estimates when model assumptions are violated. Additionally, we illustrate the effectiveness of the proposed method using several real-world datasets.
[Abstract]