Academic journal article Demographic Research

Multistate Event History Analysis with Frailty

Academic journal article Demographic Research

Multistate Event History Analysis with Frailty

Article excerpt



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.


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.


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.


The importance of multistate frailty modeling is illustrated with data on labour market and migration dynamics of recent immigrants to the Netherlands.

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1. Introduction

Demographers are increasingly interested in understanding life histories or the individual life course, with a focus on events, their sequence, ordering and transitions that people make from one state of life to another. A multistate model describes the transitions people experience as life unfolds. When people may change among a set of multiple states and/or may experience repeated changes through time, a multistate event history model, also known as multistate lifetable and increment-decrement life tables, is a proper choice. Typ- ical examples of such processes in demography include migration, (Rogers 1975; 1995), changes in marital status and other life course processes, (Courgeau and Lelièvre 1992 and Willekens 1999). Many other demographic applications of the multistate models exist. Multistate models are also common in medicine and economics. In medicine, the states can designate conditions such as healthy, diseased and death. For an overview of the use of multistate models in biostatistics, see a.o. Commenges (1999), Hougaard (2000), and Putter, Fiocco, and Geskus (2007). In economics the main application of multistate models has been labour force dynamics; see Flinn and Heckman (1983), Van den Berg (2001) and, Fougère and Kamionka (2008). Poverty dynamics and recidivism are other important applications of multistate models. The methodology of multistate models is dis- cussed in several books; the most important are Andersen et al. (1993), Hougaard (2000), and Aalen, Borgan, and Gjessing (2008).

In our empirical application we focus on the return decision of labour migrants and its relation to labour market dynamics. Many migrants only stay temporarily in the host country. On the one hand, return migration is seen as planned and part of optimal decision making to maximize total utility over the whole life cycle, where return migration is mo- tivated by locational preference for the home country. On the other hand, return migration is seen as unplanned and the result of failure either due to imperfect information about the host country in terms of labor market prospects or the cost of living, or the inability to fulfil the migration plans in terms of target savings. In both cases, return behaviour is intrinsically related to the timing of labour market changes of the individual migrant. Migrants who become unemployed are more prone to leave, but when they find a new job again they are more prone to stay, see Bijwaard, Schluter, and Wahba (2014). Migrants who are employed in high paying jobs have a lower probability of becoming unemployed and can accumulate more savings while working. …

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