Model Identifiability for Bivariate Failure Time Data with Competing Risk: Non-parametric Cause-specific Hazards and Gamma Frailty

TL;DR

This paper investigates the identifiability of bivariate survival models with competing risks, demonstrating conditions under which models with Gamma frailty are identifiable or not, especially with non-parametric baseline hazards.

Contribution

It provides new theoretical results on the identifiability of models with Gamma frailty and non-parametric hazards in bivariate survival data with competing risks.

Findings

Models with both non-parametric hazards and frailty are not identifiable.

Certain models with parametric frailty are identifiable under general conditions.

Four specific Gamma frailty distributions lead to identifiable models.

Abstract

In survival analysis, frailty variables are often used to model the association in multivariate survival data. Identifiability is an important issue while working with such multivariate survival data with or without competing risks. In this work, we consider bivariate survival data with competing risks and investigate identifiability results with non-parametric baseline cause-specific hazards and different types of Gamma frailty. Prior to that, we prove that, when both baseline cause-specific hazards and frailty distributions are non-parametric, the model is not identifiable. We also construct a non-identifiable model when baseline cause-specific hazards are non-parametric but frailty distribution may be parametric. Thereafter, we consider four different Gamma frailty distributions, and the corresponding models are shown to be identifiable under fairly general assumptions.