ABSTRACT
Monitoring of individual biomarkers has the potential of explaining the hazard of survival outcomes. In practice, these measurements are intermittently observed 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 and thus plays an important role in the analysis of medical data. 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. Of particular interest is the common occurrence in medical data that outliers can occur with different frequencies over time, for example, in the period when patients adjust to treatment changes. Motivated by the analysis of data gathered from patients with primary biliary cirrhosis, a new model with a time-varying robustness is introduced. Through both the motivating example and a simulation study, this research not only stresses the need to account for longitudinal outliers in the analysis of medical data and in joint modelling research but also highlights the bias and inefficiency from not properly estimating the degrees-of-freedom parameter. This work presents a number of methods in addition to the time-varying robustness, and each method can be fitted using the R package robjm.
Subject(s)
Models, Statistical , Research Design , Bias , Computer Simulation , Humans , Longitudinal Studies , Survival AnalysisABSTRACT
The Coxian phase-type distribution is a special type of Markov model which can be utilised both to uncover underlying stages of a survival process and to make inferences regarding the rates of flow of individuals through these latent stages before an event of interest occurs. Such models can be utilised, for example, to identify individuals who are likely to deteriorate faster through a series of disease states and thus require more aggressive medical intervention. Within this paper, a two-stage approach to the analysis of longitudinal and survival data is presented. In Stage 1, a linear mixed effects model is first used to represent how some longitudinal response of interest changes through time. Within this linear mixed effects model, the individuals' random effects can be considered as a proxy measure for the effect of the individuals' genetic profiles on the response of interest. In Stage 2, the Coxian phase-type distribution is employed to represent the survival process. The individuals' random effects, estimated in Stage 1, are incorporated as covariates within the Coxian phase-type distribution so as to evaluate their effect on the individuals' rates of flow through the system represented by the Coxian. The approach is illustrated using data collected on individuals suffering from chronic kidney disease, where focus is given to an emerging longitudinal biomarker of interest - an individual's haemoglobin level.
