Multiplicative Hazard Models for Studying the Evolution of Mortality

Abstract

Almost all over the world, decreasing mortality rates and increasing life expectancy have led to greater interest in estimating and predicting mortality. Here we describe some of the pitfalls which can result from the use of the standardised mortality ratio (SMR) while evaluating the development of mortality over time, in particular when SMRs are applied to insurance portfolios varying dramatically over time. Although an excellent comparative study of a single-figure index for a number of countries was recently done by Macdonald et al. (1998), we advocate care when attempting to extend this type of method to insurance data. Here we promote the use of genuine multiplicative modelling such as in Felipe et al. (2001), who compared the mortality rates in Denmark and Spain.

A Comparison of Nonparametric Methods in the Graduation of Mortality: Application to Data from the Valencia Region (Spain)

“…A future line of work would be to extend the previous methods to the graduation of mortality data over time with the aim of obtaining dynamic mortality tables. The work by Felipe et al (2001), Guillen et al (2006) and Fledelius et al (2004) go in this direction using kernel bivariante. Twodimensional GAM have been used by Clements et al (2005) to model and predict lung cancer rates.…”

“…The smoothing method is based on a two-dimensional kernel. This methodology has also been applied by Guillen et al (2006) for studying the evolution of mortality rates in different countries and Fledelius et al (2004) in the study of Swedish old-age mortality.…”

Bivariate discrete beta Kernel graduation of mortality data

“…One competitor, denoted as M2, is the local constant estimation method of Felipe et al (2001), which employs a bivariate Epanechnikov kernel with two bandwidths; for further details on this method see Fusaro et al (1993) and Nielsen and Linton (1995) while, for applications, see Guillén et al (2006) and Fledelius et al (2004). The other competitor, denoted as M3, is the P-splines method introduced by Currie et al (2004), which assumes, differently from our approach, a Poisson distributed number of deaths.…”