Mixture distributions in multi-state modelling: Some considerations in a study of psoriatic arthritis

Aidan O'Keeffe, Brian Tom and Vern Farewell have a new paper in Statistics in Medicine. This considers random effects models for clustered multi-state models, specifically considering the psoriatic arthritis example considered in their previous paper. The particular emphasis in the current paper is comparing models using a continuous gamma frailty term with an extended model that additionally allows a "stayer" component. The latter can be thought of as a joining of the continuous random effects model (e.g. Cook et al 2004) and the "mover-stayer" model (e.g. Cook et al 2002). In a discussion on random effects, particularly where there is a question of finite mass points, it is strange there is no mention of the non-parametric mixing distribution (Laird, JASA 1978). While this hasn't really been considered for continuous time processes (the nearest example is Frydman's model) it wouldn't be particularly hard to implement at least the (not entirely reliable) EM algorithm type approach used in discrete-time by Maruotti and Rocci. The apparent presence or absence of a "stayer" component is likely to be heavily dependent on the parametric assumptions made about the rest of the mixing distribution. A very small random effect is indistinguishable from a zero random effect. The authors do emphasize the need to consider several possible mover-stayer models and consider the biological plausibility of them. It is also worth mentioning that all these issues will also hinge on the appropriateness of other assumes e.g. conditionally time homogeneous Markov processes.