Estimating life expectancy free of dependency : group characterization through the proximity to the deepest dependency path

The aging of population is perhaps the most important problem that developed countries must face in the near future. Dependency can be seen as a consequence of the process of gradual aging. In a health context, this contingency is defined as a lack of autonomy in performing basic activities of daily living that requires the care of another person or significant help. In Europe in general and in Spain in particular this phenomena represents a problem with economic, political, social and demographic implications. The prevalence of dependency in the population, as well as its intensity and its evolution over the course of a person's life are issues of greatest importance that should be addressed. The aim of this work is to estimate life expectancy free of dependency (LEFD) using categorical data and individual dependency trajectories that are obtained using the whole medical history concerning the dependency situation of each individual from birth up to 2008, contained in database EDAD 2008. In particular, we estimate LEFD in several scenarios attending to gender, proximity-group and dependency degree. Proximity-groups are established according to an L2-type distance from the dependency trajectories to a central trend within each age-gender group, using functional data techniques. The main findings are: First, the estimated LEFD curves reach higher values for women than for men; Second, their decreasing rate is higher (and more abrupt) for men than for women; Third, the more the dependency trajectories depart from the central trend, the more the gap between the LEFD for major dependency and the other dependency situations widens; Finally, we show evidence that to estimate LEFD ignoring the partition by proximity-groups may lead to nonrepresentative LEFD estimates.