Deep Neural Networks for Semiparametric Frailty Models via H-likelihood

TL;DR

This paper introduces a deep neural network-based gamma frailty model for clustered time-to-event data, utilizing a novel h-likelihood approach to improve parameter estimation and prediction accuracy.

Contribution

It develops a new DNN-based gamma frailty model with a profiling-based h-likelihood for joint estimation, enhancing prediction performance over existing methods.

Findings

Improved prediction accuracy demonstrated in experiments.

Inclusion of subject-specific frailties enhances model performance.

Method outperforms existing models in real data analysis.

Abstract

For prediction of clustered time-to-event data, we propose a new deep neural network based gamma frailty model (DNN-FM). An advantage of the proposed model is that the joint maximization of the new h-likelihood provides maximum likelihood estimators for fixed parameters and best unbiased predictors for random frailties. Thus, the proposed DNN-FM is trained by using a negative profiled h-likelihood as a loss function, constructed by profiling out the non-parametric baseline hazard. Experimental studies show that the proposed method enhances the prediction performance of the existing methods. A real data analysis shows that the inclusion of subject-specific frailties helps to improve prediction of the DNN based Cox model (DNN-Cox).