Multistate event history analysis with frailty

Background: In survival analysis a large literature using frailty models, or models with unobserved heterogeneity, exists. In the growing literature and modelling on multistate models, this issue is only in its infant phase. Ignoring frailty can, however, produce incorrect results. Objective: This paper presents how frailties can be incorporated into multistate models, with an emphasis on semi-Markov multistate models with a mixed proportional hazard structure. Methods: First, the aspects of frailty modeling in univariate (proportional hazard, Cox) and multivariate event history models are addressed. The implications of choosing shared or correlated frailty is highlighted. The relevant differences with recurrent events data are covered next. Multistate models are event history models that can have both multivariate and recurrent events. Incorporating frailty in multistate models, therefore, brings all the previously addressed issues together. Assuming a discrete frailty distribution allows for a very general correlation structure among the transition hazards in a multistate model. Although some estimation procedures are covered the emphasis is on conceptual issues. Results: The importance of multistate frailty modeling is illustrated with data on labour market and migration dynamics of recent immigrants to the Netherlands.