Semi-Markov modeling of the loss of autonomy among elderly people : application to long-term care insurance.

Summary A major challenge for modern societies, the loss of autonomy in the elderly, also known as dependence, is defined as a state of inability to perform all or part of the Acts of Daily Living (ADL) alone. It appears in the vast majority of cases under the effect of chronic pathologies related to aging. Faced with the significant costs associated with this condition, private insurers have developed a range of products to supplement public assistance. To quantify the risk, a multi-state model is used and the question arises of estimating the transition probabilities between the states (autonomy, death and one or more levels of dependence). Under the Markov hypothesis, these depend only on the current state, an assumption that is too restrictive to account for the complexity of the dependency process. In the more general semi-Markovian framework, these probabilities also depend on the time spent in the current state. In this thesis, we study the need for a semi-Markovian modeling of the process. We highlight the impact of the time spent in dependency on the probabilities of death. We also show that taking into account the diversity induced by the pathologies allows us to improve significantly the adequacy of the proposed model to the studied data. Moreover, we establish that the particular shape of the probability of death as a function of the time spent in dependency can be explained by the mixture of the groups of pathologies that constitute the population of dependent individuals.