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Estimating life expectancy in health and ill health by using a hidden Markov model

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  • Ardo van den Hout
  • Carol Jagger
  • Fiona E. Matthews

Abstract

Population studies with longitudinal follow-up and mortality information can be used to estimate transitions between healthy and unhealthy states before death. When health is defined with respect to cognitive ability during old age, the trajectory of performance is either static or downwards. The paper presents a hidden Markov model to describe the underlying categorized cognitive decline, where observed improvement of cognitive ability is modelled as misclassification. Maximum likelihood is used to estimate the transition intensities between the normal cognitive state, the cognitively impaired state and death. The methodology is extended to estimate total life expectancy and life expectancy with and without cognitive impairment. The paper presents estimates from the Medical Research Council cognitive function and ageing study that began in 1991 and where individuals have had up to eight interviews over the next 10 years. It is shown that the misclassification of the states is mainly caused by not detecting an impaired state. Individuals with more years of education have lower impaired life expectancies. Copyright (c) 2009 Royal Statistical Society.

Suggested Citation

  • Ardo van den Hout & Carol Jagger & Fiona E. Matthews, 2009. "Estimating life expectancy in health and ill health by using a hidden Markov model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 449-465.
  • Handle: RePEc:bla:jorssc:v:58:y:2009:i:4:p:449-465
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9876.2008.00659.x
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    References listed on IDEAS

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    1. Grant Izmirlian & Dwight Brock & Luigi Ferrucci & Caroline Phillips, 2000. "Active Life Expectancy from Annual Follow–Up Data with Missing Responses," Biometrics, The International Biometric Society, vol. 56(1), pages 244-248, March.
    2. Liming Cai & Nathaniel Schenker & James Lubitz, 2006. "Analysis of functional status transitions by using a semi-Markov process model in the presence of left-censored spells," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(4), pages 477-491.
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    Cited by:

    1. Ardo van den Hout & Ekaterina Ogurtsova & Jutta Gampe & Fiona Matthews, 2014. "Investigating healthy life expectancy using a multi-state model in the presence of missing data and misclassification," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(42), pages 1219-1244, April.
    2. Andrew C. Titman, 2011. "Flexible Nonhomogeneous Markov Models for Panel Observed Data," Biometrics, The International Biometric Society, vol. 67(3), pages 780-787, September.
    3. Frans Willekens & Hein Putter, 2014. "Software for multistate analysis," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 31(14), pages 381-420, August.
    4. Jan Beyersmann & Hein Putter, 2014. "A note on computing average state occupation times," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(62), pages 1681-1696, May.

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