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Likelihood for Generally Coarsened Observations from Multistate or Counting Process Models

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  • DANIEL COMMENGES
  • ANNE GÉGOUT‐PETIT

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.

Suggested Citation

  • Daniel Commenges & Anne Gégout‐Petit, 2007. "Likelihood for Generally Coarsened Observations from Multistate or Counting Process Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(2), pages 432-450, June.
  • Handle: RePEc:bla:scjsta:v:34:y:2007:i:2:p:432-450
    DOI: 10.1111/j.1467-9469.2006.00518.x
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    Cited by:

    1. Richard J. Cook & Jerald F. Lawless, 2020. "Failure time studies with intermittent observation and losses to follow‐up," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1035-1063, December.
    2. Daniel Commenges & Anne Gégout‐Petit, 2009. "A general dynamical statistical model with causal interpretation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 719-736, June.
    3. Daniel Commenges, 2019. "Dealing with death when studying disease or physiological marker: the stochastic system approach to causality," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 381-405, July.
    4. Boumezoued, Alexandre & Karoui, Nicole El & Loisel, Stéphane, 2017. "Measuring mortality heterogeneity with multi-state models and interval-censored data," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 67-82.

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