Multi-Parameter Regression Survival Modelling with Random Effects

TL;DR

This paper extends multi-parameter regression survival models to clustered data by incorporating random effects in both scale and shape parameters, using h-likelihood estimation, and demonstrates its effectiveness through simulations and real data applications.

Contribution

It introduces a novel extension of MPR models with random effects for multivariate survival data, addressing dependence structures and estimation challenges.

Findings

Effective estimation via h-likelihood demonstrated in simulations

Model flexibility improves fit for clustered survival data

Applications show practical utility in cancer datasets

Abstract

We consider a parametric modelling approach for survival data where covariates are allowed to enter the model through multiple distributional parameters, i.e., scale and shape. This is in contrast with the standard convention of having a single covariate-dependent parameter, typically the scale. Taking what is referred to as a multi-parameter regression (MPR) approach to modelling has been shown to produce flexible and robust models with relatively low model complexity cost. However, it is very common to have clustered data arising from survival analysis studies, and this is something that is under developed in the MPR context. The purpose of this article is to extend MPR models to handle multivariate survival data by introducing random effects in both the scale and the shape regression components. We consider a variety of possible dependence structures for these random effects (independent, shared, and correlated), and estimation proceeds using a h-likelihood approach. The performance of our estimation procedure is investigated by a way of an extensive simulation study, and the merits of our modelling approach are illustrated through applications to two real data examples, a lung cancer dataset and a bladder cancer dataset.