Measuring mortality heterogeneity with multi-state models and interval-censored data

In this paper, our aim is to measure mortality rates which are specific to individual observable factors when these can change during life. The study is based on longitudinal data recording marital status and socio-professional features at census times, therefore the observation scheme is interval-censored since individual characteristics are only observed at isolated dates and transition times remain unknown. To this aim, we develop a parametric maximum likelihood estimation procedure for multi-state models that takes into account both interval-censoring and reversible transitions. This method, inspired by recent advances in the statistical literature, allows us to capture characteristic-specific mortality rates, in particular to recover the mortality compensation law at high ages, but also to capture the age pattern of characteristics changes. The dynamics of several population compositions is addressed, and allows us to give explanations on the pattern of aggregate mortality, as well as on the impact on typical life insurance products. Particular attention is devoted to characteristics changes and parameter uncertainty that are both crucial to take into account.