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

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.