Coherent forecasts of mortality with compositional data analysis

Abstract

BACKGROUNDMortality trends for subpopulations, e.g., countries in a region or provinces in a country, tend to change similarly over time. However, when forecasting subpopulations independently, the forecast mortality trends often diverge. These divergent trends emerge from an inability of different forecast models to offer population-specific forecasts that are consistent with one another. Nondivergent forecasts between similar populations are often referred to as "coherent." METHODSWe propose a new forecasting method that addresses the coherence problem for subpopulations, based on Compositional Data Analysis (CoDa) of the life table distribution of deaths. We adapt existing coherent and noncoherent forecasting models to CoDa and compare their results. RESULTSWe apply our coherent method to the female mortality of 15 Western European countries and show that our proposed strategy would have improved the forecast accuracy for many of the selected countries. The results also show that the CoDa adaptation of commonly used models allows the rates of mortality improvements (RMIs) to change over time. CONTRIBUTIONThis study opens a discussion about the use of age-specific mortality indicators other than death rates to forecast mortality. The results show that the use of life table deaths

Forecasting Causes of Death by Using Compositional Data Analysis: The Case of Cancer Deaths

“…This section briefly describes CODA that is essential to the models suggested and further details can be found in Aitchison (), Pawlowsky‐Glahn and Buccianti () and Bergeron‐Boucher et al . (). As life table deaths are constructed by multiplying age‐specific probabilities of dying into an arbitrary initial birth cohort which is also known as the radix, they contain only relative information and sum to the initial cohort in each year (Bergeron‐Boucher et al ., ).…”

“…(). As life table deaths are constructed by multiplying age‐specific probabilities of dying into an arbitrary initial birth cohort which is also known as the radix, they contain only relative information and sum to the initial cohort in each year (Bergeron‐Boucher et al ., ). Changes in the number of life table deaths for a specific age group must therefore be offset by changes in the other age groups, which is the fundamental feature in compositional data.…”

“…In contrast Bergeron‐Boucher et al . () considered a single‐decrement life table but several populations. Further analysis can be found in the on‐line supplementary material, which examines the influence of the number of causes of deaths included on the accuracy of the cancer forecasts.…”

“…CODA was also used by Bergeron‐Boucher et al . () for coherent forecasts of all‐cause mortality in different countries. One important difference between modelling cause‐specific deaths rates and deaths distributions is that deaths are directly dependent on each other on an aggregated level, as avoided deaths from one cause will result in an increase of deaths from some other cause.…”

“…VECM‐CoDA and 2S‐CoDA make use of compositional data analysis similarly to the model that was presented in Bergeron‐Boucher et al . () but differ fundamentally in the way that mortality is modelled. VECM‐CoDA and 2S‐CoDA model several causes of death from a multiple‐decrement life table in a single population.…”