Mortality confidence intervals for small areas: a measure of the prediction goodness

Federico López, Universidad de Alcalá de Henares
José Luis Gutierrez de Mesa, Universidad de Alcalá de Henares
Luis Rivera Galicia, Universidad de Alcalá de Henares

With prediction, error measurement is a primary goal of data analysis. There is no exception for mortality projections. In this paper we develop a method to determine the confidence interval for mortality rates in small areas, whose population is much more exposed to random risks than the National population as a whole, much more stable in time for each age. The main result is a predictable confidence interval for the province death risk as a function of the National death risk. We specify a model for the death risk of a province as a sum of the National death risk plus an error term normally distributed whose variance depends on the National value and two predictable parameters. We apply the model to the Spanish particular case and observe an exponential relationship between Spain’s death risk and the estimated variance. The logarithm of the estimated variance is linear in terms of the logarithm of Spain’s death risk.