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

Daniel Commenges; Anne Gégout-Petit

hal-00194266, version 1

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

Daniel Commenges ^1, 2, Anne Gégout-Petit () ^3, 4

Scandinavian Journal of Statistics 34, 2 (2007) 432-450

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.

1: Biostatistique
INSERM : U875 – Université Victor Segalen - Bordeaux II
2: Institut de Santé Publique, d'Epidémiologie et de Développement (ISPED)
Université Victor Segalen - Bordeaux II
3: Institut de Mathématiques de Bordeaux (IMB)
CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
4: CQFD (INRIA Futurs)
INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR5251

hal-00194266, version 1
http://hal.archives-ouvertes.fr/hal-00194266
oai:hal.archives-ouvertes.fr:hal-00194266
From: Anne Gégout-Petit <>
Submitted on: Friday, 23 May 2008 16:03:50
Updated on: Monday, 20 October 2008 13:32:54

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arXiv: 0805.3658

DOI: 10.1111/j.1467-9469.2006.00518.x

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%% hal-00194266, version 1
%% http://hal.archives-ouvertes.fr/hal-00194266
@article{commenges:hal-00194266,
    hal_id = {hal-00194266},
    url = {http://hal.archives-ouvertes.fr/hal-00194266},
    title = {{Likelihood for generally coarsened observations from multi-state or counting process models.}},
    author = {Commenges, Daniel and G{\'e}gout-Petit, Anne},
    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 \& G{\'e}gout-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},
    language = {English},
    affiliation = {Biostatistique , Institut de Sant{\'e} Publique, d'Epid{\'e}miologie et de D{\'e}veloppement - ISPED , Institut de Math{\'e}matiques de Bordeaux - IMB , CQFD - INRIA Futurs},
    pages = {432-450},
    journal = {Scandinavian Journal of Statistics},
    volume = {34},
    number = {2 },
    audience = {international },
    doi = {10.1111/j.1467-9469.2006.00518.x },
    year = {2007},
    month = Jun,
    pdf = {http://hal.archives-ouvertes.fr/hal-00194266/PDF/CPmodelhome.pdf},
}

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