Abstract
This study analyzed whether there are different patterns of mortality decline among low-mortality countries by identifying the role played by all the mortality components. We implemented a cluster analysis using a functional data analysis (FDA) approach, which allowed us to consider age-specific mortality rather than summary measures, as it analyses curves rather than scalar data. Combined with a functional principal component analysis, it can identify what part of the curves is responsible for assigning one country to a specific cluster. FDA clustering was applied to the data from 32 countries in the Human Mortality Database from 1960 to 2018 to provide a comprehensive understanding of their patterns of mortality. The results show that the evolution of developed countries followed the same pattern of stages (with different timings): (1) a reduction of infant mortality, (2) an increase of premature mortality and (3) a shift and compression of deaths. Some countries were following this scheme and recovering the gap with precursors; others did not show signs of recovery. Eastern European countries were still at Stage (2), and it was not clear if and when they will enter Stage 3. All the country differences related to the different timings with which countries underwent the stages, as identified by the clusters.
Highlights
In recent decades, best-practice life expectancy has increased with unexpected rapidity and exceeded the highs previously held by several countries; laggards have been catching up, and former leaders have been falling behind (Oeppen & Vaupel, 2002)
We employed the same set of knots for every curve so that the estimation of the splines coefficients was performed on the same age intervals. This is more appropriate for the functional cluster analysis and Functional principal component analysis (FPCA) that will be applied in the following on the basis coefficients
We inspected the evolution of mortality schedules in Human Mortality Database (HMD) countries by means of a functional clustering method, which allowed us to consider mortality patterns as functions and avoid analysing only a component of mortality or a summary measure like life expectancy, which is a mixture of all mortality components but without a clear distinction of their contribution to longevity progresses
Summary
Best-practice life expectancy has increased with unexpected rapidity and exceeded the highs previously held by several countries; laggards have been catching up, and former leaders have been falling behind (Oeppen & Vaupel, 2002). The shifting and compression dynamics of mortality at older ages have been extensively investigated (Kannisto, 2001; Canudas-Romo, 2008; Thatcher et al, 2010; Ebeling et al, 2018) As another example, Zanotto et al (2020) focused their analysis on premature mortality. Debón et al (2017) grouped EU countries through fuzzy c-means cluster analysis of mortality surfaces and found similar results They raised the issue of the selection of mortality indicators to characterize the clusters and proposed the use of non-parametric techniques (e.g., classification and regression trees, or CART, and random forests) to rank indicators, based on their capacity to discriminate between-group inequalities
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