Multivariate Control Chart and Lee–Carter Models to Study Mortality Changes

Abstract

The mortality structure of a population usually reflects the economic and social development of the country. The purpose of this study was to identify moments in time and age intervals at which the observed probability of death is substantially different from the pattern of mortality for a studied period. Therefore, a mortality model was fitted to decompose the historical pattern of mortality. The model residuals were monitored by the T2 multivariate control chart to detect substantial changes in mortality that were not identified by the model. The abridged life tables for Colombia in the period 1973–2005 were used as a case study. The Lee–Carter model collects information regarding violence in Colombia. Therefore, the years identified as out-of-control in the charts are associated with very early or quite advanced ages of death and are inversely related to the violence that did not claim as many victims at those ages. The mortality changes identified in the control charts pertain to changes in the population’s health conditions or new causes of death such as COVID-19 in the coming years. The proposed methodology is generalizable to other countries, especially developing countries.

Implications of the SARS-Cov-2 Pandemic for Mortality Forecasting: Case Study for the Czech Republic and Spain

“…Lee and Carter [14] proposed a "method for modeling and forecasting mortality: A model of age-specific death rates with a time component and a fixed relative age component, and a time series model (an autoregressive integrated moving average-ARIMA) of the time component." (Booth,Maindonald,and Smith [15]) (Diaz-Rojo, Debon, and Mosquera [9]). They defined their model to fit the matrix of mortality rates as (3):…”

“…"The mortality changes identified in the control charts pertain to changes in the population's health conditions or new causes of death such as COVID-19 in the coming years." (Diaz-Rojo, Debon, and Mosquera [9]).…”

“…A similar method-the Lee-Carter model-for mortality forecasting was also used by Diaz-Rojo, Debon, and Mosquera [9]. They found out that changes in mortality patterns might be due to COVID-19.…”

Hybrid of the Lee-Carter Model with Maximum Overlap Discrete Wavelet Transform Filters in Forecasting Mortality Rates

“…Mortality studies are essential in understanding the demographic structure and indicating the health status of a population. The analysis of mortality and its historical trends enables a country to comprehend its population dynamics and serves as a foundation for formulating economic and social policies [1]. Actuaries used mortality forecasts to project cash flows and evaluate premiums as well as reserves in life insurance and pension plans.…”

A recursive model of residual life prediction for human beings with health information from activities of daily living and memory

“…Currently, live expectancy surpasses the age of 60 (de Cabo & Mattason, 2019;DESA, 2007;Fitzmaurice et al, 2019;Rudd et al, 2020;Word Health Organization, 2015). This demographic brings unprecedented opportunities and challenges.…”