Abstract
In many studies, interest lies in determining whether members of the study population will undergo a particular event of interest. Such scenarios are often termed ‘mover–stayer’ scenarios, and interest lies in modelling two sub-populations of ‘movers’ (those who have a propensity to undergo the event of interest) and ‘stayers’ (those who do not). In general, mover–stayer scenarios within data sets are accounted for through the use of mixture distributions, and in this paper, we investigate the use of various random effects distributions for this purpose. Using data from the University of Toronto psoriatic arthritis clinic, we present a multi-state model to describe the progression of clinical damage in hand joints of patients with psoriatic arthritis. We consider the use of mover–stayer gamma, inverse Gaussian and compound Poisson distributions to account for both the correlation amongst joint locations and the possible mover–stayer situation with regard to clinical hand joint damage. We compare the fits obtained from these models and discuss the extent to which a mover–stayer scenario exists in these data. Furthermore, we fit a mover–stayer model that allows a dependence of the probability of a patient being a stayer on a patient-level explanatory variable.
Highlights
Where data are collected on several individuals in a population over time, it is often of interest to fit models that describe the probability of the occurrence of a particular event in time
The negative estimated values of ı1 for both random effects distributions imply that k decreases as the baseline erythrocyte sedimentation rate (ESR) value increases, thereby suggesting that patients with higher baseline ESR values are less likely to have no risk of damage in the hand joints
We considered the mover–stayer inverse Gaussian and compound Poisson power variance function (CP-PVF) random effects, with the patient-specific probability of non-progression modelled as a function of baseline erythrocyte sedimentation rate (ESR)
Summary
Where data are collected on several individuals in a population over time, it is often of interest to fit models that describe the probability of the occurrence of a particular event in time. The idea of mixture probabilities in such models can be used for studies where interest lies in predicting the proportion of patients who recover or are ‘cured’ from a particular disease and will not experience death from the disease in question Such models are often known as ‘long-term survival models’ (where the ‘long-term survivors’ are those who will not experience death from the disease) or ‘cure rate models’ (where a cured fraction of patients will not die owing to the disease). Kuk and Chen [5] developed the cure rate model further, employing a Cox proportional hazards model rather than a fully parametric model In these works, and in many others, a common problem is choosing the most appropriate form of mixture distribution to best describe the disease or failure process under observation. We attempt to consider this problem more closely in this paper
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