At a Glance
Estimating Mortality Heterogeneity
Jutta Gampe, Timothy Riffe; in Collaboration with Paul Eilers (Erasmus University Medical Center, Rotterdam, Netherlands), Philippe Lambert (University of Liège, Belgium), Adrien Remund (University of Geneva, Switzerland)
Mortality is not uniform across individuals in a population, and examining mortality differentials is at the core of mortality research. Estimates of the heterogeneity of mortality allow us to assess subgroups particularly amenable to improvements or the identification of best-practice mortality, which can serve as a benchmark in comparisons. A straightforward approach would be to take the empirical raw estimates of death rates and identify the minimal values. But this approach is hampered by the fact that population subgroups usually vary considerably in size. Both the number of people at risk and the number of deaths observed can thus be quite small, which introduces strong variability, as well as zero observed mortality for certain ages.
A sound alternative is a meta-analytic framework that models the observed deaths as outcomes of a latent mortality distribution, which varies over age and time. The observed data are used to estimate this latent distribution. This approach makes it possible to deal with the problems caused by strongly differing subgroup sizes, and to conduct more detailed studies of the mortality distribution. For example, variances and quantiles can be derived as soon as the latent distribution is identified.
Common Empirical Bayes techniques postulate a parametric model for mortality variation (usually Gamma or log-Normal), mostly for mathematical convenience. To estimate this latent distribution of mortality nonparametrically, and thus the shape of the heterogeneity distribution as well, two different approaches can be used: a smooth EM-algorithm and a fully Bayesian P-spline approach. While the EM-algorithm is more closely related to the traditional meta-analytical framework, an optimal smoothing parameter still needs to be found. The fully Bayesian approach automatically determines the optimal amount of smoothing. This project investigates both approaches in several empirical studies.
Ageing, Mortality and Longevity, Statistics and Mathematics