Likelihood for generally coarsened observations from multi-state or counting process models.

Daniel Commenges 1, 2 Anne Gégout-Petit 3, 4
4 CQFD - Quality control and dynamic reliability
INRIA Futurs, Université Bordeaux Segalen - Bordeaux 2, Université Sciences et Technologies - Bordeaux 1, CNRS - Centre National de la Recherche Scientifique : UMR5251
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.
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Daniel Commenges, Anne Gégout-Petit. Likelihood for generally coarsened observations from multi-state or counting process models.. Scandinavian Journal of Statistics, Wiley, 2007, 34 (2), pp.432-450. ⟨10.1111/j.1467-9469.2006.00518.x⟩. ⟨hal-00194266⟩



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