Joint modelling of time-to-event and longitudinal response using robust skew normal-independent distributions

TL;DR

This paper introduces a robust joint modelling approach for longitudinal and time-to-event data using skew normal-independent distributions, addressing non-Gaussian behavior and outliers in biomedical studies.

Contribution

It proposes a novel joint model that incorporates robust skew normal distributions for both longitudinal and event time data, improving estimation under non-Gaussian conditions.

Findings

Enhanced model robustness to skewness and outliers

Improved parameter estimation accuracy

Better handling of non-Gaussian longitudinal data

Abstract

Joint modelling of longitudinal observations and event times continues to remain a topic of considerable interest in biomedical research. For example, in HIV studies, the longitudinal bio-marker such as CD4 cell count in a patient's blood over follow up months is jointly modelled with the time to disease progression, death or dropout via a random intercept term mostly assumed to be Gaussian. However, longitudinal observations in these kinds of studies often exhibit non-Gaussian behavior (due to high degree of skewness), and parameter estimation is often compromised under violations of the Gaussian assumptions. In linear mixed-effects model assumptions, the distributional assumption for the subject-specific random-effects is taken as Gaussian which may not be true in many situations. Further, this assumption makes the model extremely sensitive to outlying observations. We address these issues in this work by devising a joint model which uses a robust distribution in a parametric setup along with a conditional distributional assumption that ensures dependency of two processes in case the subject-specific random effects is given.