Likelihood for Generally Coarsened Observations from Multistate or Counting Process Models

Authors: COMMENGES, DANIEL; GÉGOUT-PETIT, ANNE

Source: Scandinavian Journal of Statistics, Volume 34, Number 2, June 2007 , pp. 432-450(19)

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Abstract:

We consider first the mixed discrete-continuous scheme of observation in multistate models; this is a classical pattern in epidemiology because very often clinical status is assessed at discrete visit times while times of death or other events are observed exactly. A heuristic likelihood can be written for such models, at least for Markov models; however, a formal proof is not easy and has not been given yet. We present a general class of possibly non-Markov multistate models which can be represented naturally as multivariate counting processes. We give a rigorous derivation of the likelihood based on applying Jacod's formula for the full likelihood and taking conditional expectation for the observed likelihood. A local description of the likelihood allows us to extend the result to a more general coarsening observation scheme proposed by Commenges & Gégout-Petit. The approach is illustrated by considering models for dementia, institutionalization and death.

Keywords: coarsening; counting processes; dementia; interval-censoring; likelihood; Markov models; multistate models

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9469.2006.00518.x

Affiliations: 1: INSERM, Université Victor Segalen Bordeaux 2

Publication date: 2007-06-01