Smoothing and projecting age-specific probabilities of death by TOPALS

Abstract

BACKGROUNDTOPALS is a new relational model for smoothing and projecting age schedules. The model is operationally simple, flexible, and transparent. OBJECTIVEThis article demonstrates how TOPALS can be used for both smoothing and projecting age-specific mortality for 26 European countries and compares the results of TOPALS with those of other smoothing and projection methods. METHODSTOPALS uses a linear spline to describe the ratios between the age-specific death probabilities of a given country and a standard age schedule. For smoothing purposes I use the average of death probabilities over 15 Western European countries as standard, whereas for projection purposes I use an age schedule of 'best practice' mortality. A partial adjustment model projects how quickly the death probabilities move in the direction of the best-practice level of mortality. RESULTSOn average, TOPALS performs better than the Heligman-Pollard model and the Brass relational method in smoothing mortality age schedules. TOPALS can produce projections that are similar to those of the Lee-Carter method, but can easily be used to produce alternative scenarios as well. This article presents three projections of life expectancy at birth for the year 2060 for 26 European countries. The Baseline scenario assumes a continuation of the past trend in each country, the Convergence scenario assumes that there is a common trend across European countries, and the Acceleration scenario assumes that the future decline of death probabilities will exceed that in the past. The Baseline scenario projects that average European life expectancy at birth will 1 Netherlands Interdisciplinary Demographic Institute. E-mail: beer@nidi.nl.de Beer: Smoothing and projecting age-specific probabilities of death by TOPALS 544http://www.demographic-research.org increase to 80 years for men and 87 years for women in 2060, whereas the Acceleration scenario projects an increase to 90 and 93 years respectively. CONCLUSIONSTOPALS is a useful new tool for demographers for both smoothing age schedules and making scenarios.

A new parametric model to assess delay and compression of mortality

“…One advantage of using death probabilities rather than death rates is that probabilities are easy to interpret and probabilities rather than rates are used for projections and for the calculation of life expectancy using a life table [43, 44]. However, as the age pattern of death probabilities and rates are very similar, our results and conclusions would have been similar if we had modeled rates rather than probabilities.…”

Age Trajectories of Mortality from All Diseases in Five Countries of Central Europe During the Last Decades

“…Year This is the standard Gompertz model used for all-causes mortality, usually over 40 years (e.g., Gompertz 1825;Heligman and Pollard 1980;Makeham 1860;Preston, Heuveline, and Guillot 2001;Vaupel et al 1998;Willemse and Koppelaar 2000;Granados and Ionides 2011;De Beer 2012;Shu and Sherris 2012). Two Gompertz parameters ln[μ 0 ], β, standard deviation of the parameters, coefficient of determination R lin 2 , and the adjusted coefficient of determination R 2 lin 2 (for one predictor x and n points) are calculated in restricted Model 13 using MLS.…”

Estimating age- and sex-specific mortality rates for small areas with TOPALS regression: an application to Brazil in 2010

“…Several statistical models smooth mortality rates or probabilities using spline functions (MACNAB; DEAN, 2001;CURRIE;DURBAN;EILERS, 2004;DE BEER, 2012;CAMARDA, 2012). De Beer (2012)'s TOPALS model uses a linear spline to model the pattern of ratios between age-specific probabilities of death in a population and the corresponding probabilities in a standard schedule.…”

“…Padronização indireta, por exemplo, assume que todas as áreas dentro de uma área maior (microrregiões em uma mesorregião, por exemplo) possuem um padrão de mortalidade idêntico, com diferença constante no nível das taxas logarítmicas por idade. Propomos um método estatístico mais flexível que combina regressão Poisson com um modelo relacional denominado TOPALS (DE BEER, 2012). Usamos o novo método para estimar as taxas específicas de mortalidade em pequenas áreas no Brasil (estados, mesorregiões, microrregiões e municípios) em 2010.…”

“…Such methods assume that all areas within a larger area (for example, microregions within a mesoregion) have identically-shaped log mortality schedules by age. We propose a more flexible statistical estimation method that combines Poisson regression with the TOPALS relational model (DE BEER, 2012). We use the new method to estimate age-specific mortality rates in Brazilian small areas (states, mesoregions, microregions, and municipalities) in 2010.…”