Robust joint modelling of longitudinal and survival data with a time-varying degrees-of-freedom parameter

TL;DR

This paper introduces a robust joint modelling approach for longitudinal and survival data that accounts for time-varying outliers and measurement errors, improving accuracy over traditional Gaussian-based models.

Contribution

It proposes a novel model with a time-varying degrees-of-freedom parameter to handle outliers in joint models, supported by simulations and real data analysis.

Findings

Robust models outperform Gaussian models in presence of outliers.

Time-varying robustness captures changing outlier frequencies over time.

Proper estimation of degrees-of-freedom reduces bias and improves efficiency.

Abstract

Repeated measures of biomarkers have the potential of explaining hazards of survival outcomes. In practice, these measurements are intermittently measured and are known to be subject to substantial measurement error. Joint modelling of longitudinal and survival data enables us to associate intermittently measured error-prone biomarkers with risks of survival outcomes. Most of the joint models available in the literature have been built on the Gaussian assumption. This makes them sensitive to outliers. In this work, we study a range of robust models to address this issue. For medical data, it has been observed that outliers might occur with different frequencies over time. To address this, a new model with a time varying robustness is introduced. Through both a simulation study and analysis of two real-life data examples, this research not only stresses the need to account for longitudinal outliers in joint modelling research but also highlights the bias and inefficiency from not properly estimating the degrees-of-freedom parameter. Each technique presented in this work can be fitted using the R package robjm.