Modelagem de Mortalidade

Abstract

The constant improvements in nutrition conditions and health systems, with the great advance of medicine in the treatment of diseases, has a strong impact on the quality of human life and also on their life expectancy. This change in human longevity directly a↵ects pension and social security systems, as well as health systems. Hence the need for models capable of capturing and estimating mortality rates at older ages, which has undergone constant changes in recent years. In this sense, this study aimed to study and propose models capable of capturing the dynamics observed in mortality, especially in the elderly. Also seeking to clear up doubts about the inference methods in these models, since there is no agreement in the literature about which inference method should be used for a certain mortality model. Thus, in this work we consider six mortality models, four of which have been extensively studied (Gompertz, Makeham, Gompertz and Makeham models, the method based on the Poisson regression model proved to be much superior to the other three methods, presenting better precision and accuracy. As for the mixture-based models, the method based on the Negative Binomial regression model proved to be better. The application of the models was carried out in two contexts: the first using data with low quality and the second using data with good quality. For the first, we used mortality data in Brazil in 2010, from the DataSus and Census, where the models based on the mixture proved to be superior to the others, presenting an average percentage error of the order 10´1. When we applied the models to the data with good quality, we used the Japanese mortality data in 1993, from the Human Mortality Database, and we obtained good results with models based on mixtures and also on models that consider fragility. Therefore, this work clarifies an important issue regarding the inference methods to be used in mortality models. But one of the main contributions of this work was for the modeling of mortality over 70 years, since the model based on the Gompertz and exponential mixture proved to be very accurate when describing the behavior of mortality over 100 years. Finally, this work also derived the closed form of the residual life function of the -Gompertz and Makeham models. In Missov e Lenart (2013), Missov (2013) there were e↵orts to derive such expressions, however the authors presented wrong expressions that were corrected in this work