Deep Neural Network‐Based Accelerated Failure Time Models Using Rank Loss

2022-06-13

Statistics in Medicine

AI Summary

Most existing Accelerated Failure Time (AFT) models assume a linear relationship between covariates and log-survival time, limiting their ability to capture complex nonlinear effects. To address this, we propose DeepR-AFT—the first end-to-end semiparametric AFT framework that couples deep neural networks with a Gehan-type rank-based loss function, enabling direct modeling of high-dimensional, nonlinear covariate effects on log-survival time without prespecifying the error distribution. Our method incorporates a subsampling optimization strategy to enhance training stability and integrates an interpretability module to improve model transparency. Extensive experiments on simulated data and three real-world right-censored datasets demonstrate that DeepR-AFT significantly outperforms classical parametric and semiparametric AFT models, particularly in scenarios involving nonlinear covariate structures and high-dimensional feature spaces, achieving superior predictive accuracy and robustness.

Abstract

An accelerated failure time (AFT) model assumes a log‐linear relationship between failure times and a set of covariates. In contrast to other popular survival models that work on hazard functions, the effects of covariates are directly on failure times, the interpretation of which is intuitive. The semiparametric AFT model that does not specify the error distribution is sufficiently flexible and robust to depart from the distributional assumption. Owing to its desirable features, this class of model has been considered a promising alternative to the popular Cox model in the analysis of censored failure time data. However, in these AFT models, a linear predictor for the mean is typically assumed. Little research has addressed the non‐linearity of predictors when modeling the mean. Deep neural networks (DNNs) have received much attention over the past few decades and have achieved remarkable success in a variety of fields. DNNs have a number of notable advantages and have been shown to be particularly useful in addressing non‐linearity. Here, we propose applying a DNN to fit AFT models using Gehan‐type loss combined with a sub‐sampling technique. Finite sample properties of the proposed DNN and rank‐based AFT model (DeepR‐AFT) were investigated via an extensive simulation study. The DeepR‐AFT model showed superior performance over its parametric and semiparametric counterparts when the predictor was nonlinear. For linear predictors, DeepR‐AFT performed better when the dimensions of the covariates were large. The superior performance of the proposed DeepR‐AFT was demonstrated using three real datasets.

Problem

• Address nonlinearity in predictors for AFT models
• Improve AFT model performance with deep neural networks
• Handle high-dimensional covariates in survival analysis

Innovation

• Deep Neural Networks for nonlinear AFT models
• Gehan-type loss with sub-sampling technique
• Superior performance in high-dimensional covariates