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Choice between Semi‐parametric Estimators of Markov and Non‐Markov Multi‐state Models from Coarsened Observations

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  • DANIEL COMMENGES
  • PIERRE JOLY
  • ANNE GÉGOUT‐PETIT
  • BENOIT LIQUET

Abstract

. We consider models based on multivariate counting processes, including multi‐state models. These models are specified semi‐parametrically by a set of functions and real parameters. We consider inference for these models based on coarsened observations, focusing on families of smooth estimators such as produced by penalized likelihood. An important issue is the choice of model structure, for instance, the choice between a Markov and some non‐Markov models. We define in a general context the expected Kullback–Leibler criterion and we show that the likelihood‐based cross‐validation (LCV) is a nearly unbiased estimator of it. We give a general form of an approximate of the leave‐one‐out LCV. The approach is studied by simulations, and it is illustrated by estimating a Markov and two semi‐Markov illness–death models with application on dementia using data of a large cohort study.

Suggested Citation

  • Daniel Commenges & Pierre Joly & Anne Gégout‐Petit & Benoit Liquet, 2007. "Choice between Semi‐parametric Estimators of Markov and Non‐Markov Multi‐state Models from Coarsened Observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(1), pages 33-52, March.
    • Handle: RePEc:bla:scjsta:v:34:y:2007:i:1:p:33-52
    DOI: 10.1111/j.1467-9469.2006.00536.x
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    Cited by:

    1. Li, Jinqing & Ma, Jun, 2019. "Maximum penalized likelihood estimation of additive hazards models with partly interval censoring," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 170-180.
    2. 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.
    3. Daniel Commenges & Benoit Liquet & Cécile Proust-Lima, 2012. "Choice of Prognostic Estimators in Joint Models by Estimating Differences of Expected Conditional Kullback–Leibler Risks," Biometrics, The International Biometric Society, vol. 68(2), pages 380-387, June.
    4. Touraine, Célia & Gerds, Thomas A. & Joly, Pierre, 2017. "SmoothHazard: An R Package for Fitting Regression Models to Interval-Censored Observations of Illness-Death Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i07).
    5. 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.
    6. Pierre Joly & Célia Touraine & Aurore Georget & Jean-François Dartigues & Daniel Commenges & Hélène Jacqmin-Gadda, 2013. "Prevalence Projections of Chronic Diseases and Impact of Public Health Intervention," Biometrics, The International Biometric Society, vol. 69(1), pages 109-117, March.
    7. Li, Chenxi, 2016. "Cause-specific hazard regression for competing risks data under interval censoring and left truncation," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 197-208.
    8. Commenges Daniel & Proust-Lima Cécile & Samieri Cécilia & Liquet Benoit, 2015. "A Universal Approximate Cross-Validation Criterion for Regular Risk Functions," The International Journal of Biostatistics, De Gruyter, vol. 11(1), pages 51-67, May.
    9. Wanneveich, Mathilde & Jacqmin-Gadda, Hélène & Dartigues, Jean-François & Joly, Pierre, 2018. "Projections of health indicators for chronic disease under a semi-Markov assumption," Theoretical Population Biology, Elsevier, vol. 119(C), pages 83-90.

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