Incorporating frailty in a multi-state model: application to disease natural history modelling of adenoma-carcinoma in the large bowel

Yen, Chen, Duffy and Chen have a new paper in SMMR. This considers methods for incorporating frailty into a progressive multi-state model under interval censoring (the data resemble current status data being a case-cohort design with known sampling probabilities). They note that the accommodation of frailty is made easier by considering a model where only one transition intensity is subject to heterogeneity. The main deficiency of the paper is the lack of reference to the fairly wide existing literature on frailty and random effects models for panel observed multi-state models. In particular, the tracking model of Satten is directly applicable to their data. In the tracking model, a common frailty affects all transition intensities and results in a likelihood that doesn't require numerical integration. Some comment on the extendability of their model to the case of multiple observations per patient would also have been useful.