Severine Arnold (-Gaille)

Causes-of-Death Mortality: What Do We Know on Their Dependence?

Over the last century, the assumption usually made was that causes of death are independent, although it is well-known that dependancies exist. Recent developments in econometrics allow, through Vector Error Correction Models (VECMs), to model multivariate dynamic systems including time dependency between economic variables. Common trends that exist between the variables may then be highlighted, the relation between these variables being represented by a long-run equilibrium relationship. In this work, VECMs are developed for causes-of-death mortality. We analyze the five main causes of death across 10 major countries representing a diversity of developed economies. The World Health Organization website provides cause-of-death information for about the last 60 years. Our analysis reveals that long-run equilibrium relationships exist between the five main causes of death, improving our understanding of the nature of dependence between these competing risks over recent years. It also highlights that countries usually had different past experience in regard to cause-of-death mortality trends, and, thus, applying results from one country to another may be misleading.

Forecasting Mortality Trends Allowing for Cause-of-Death Mortality Dependence

Longevity risk is among the most important factors to consider for pricing and risk management of longevity products. Past improvements in mortality over many years, and the uncertainty of these improvements, have attracted the attention of experts, both practitioners and academics. Since aggregate mortality rates reflect underlying trends in causes of death, insurers and demographers are increasingly considering cause-of-death data to better understand risks in their mortality assumptions. The relative importance of causes of death has changed over many years. As one cause reduces, others increase or decrease. The dependence between mortality for different causes of death is important when projecting future mortality. However, for scenario analysis based on causes of death, the assumption usually made is that causes of death are independent. Recent models, in the form of Vector Error Correction Models (VECMs), have been developed for multivariate dynamic systems and capture time dependency with common st...

Modelling Cause-of-Death Mortality and the Impact of Cause-Elimination

Abstract The analysis of causal mortality provides rich insight into changes in mortality trends that are hidden in population-level data. Therefore, we develop and apply a multinomial logistic framework to model causal mortality. We use internationally classified cause-of-death categories and data obtained from the World Health Organization. Inherent dependence amongst the competing causes is accounted for in the framework, which also allows us to investigate the effects of improvements in, or the elimination of, cause-specific mortality. This has applications to scenario-based forecasting often used to assess the impact of changes in mortality. The multinomial model is shown to be more conservative than commonly used approaches based on the force of mortality. We use the model to demonstrate the impact of cause-elimination on aggregate mortality using residual life expectancy and apply the model to a French case study.

Time-Evolution of Age-Dependent Mortality Patterns in Mathematical Model of Heterogeneous Human Population

The widely-known Gompertz law of mortality states the exponential increase of mortality with age in human populations. Such an exponential increase is observed at the adulthood span, roughly after the reproductive period, while mortality data at young and extremely old ages deviate from it. The heterogeneity of human populations, i.e. the existence of subpopulations with different mortality dynamics, is a useful consideration that can explain age-dependent mortality patterns across the whole life-course. A simple mathematical model combining the heterogeneity of populations with an assumption that the mortality in each subpopulation grows exponentially with age has been proven to be capable of reproducing the entire mortality pattern in a human population including the observed peculiarities at early- and late-life intervals. In this work we fit this model to actual (Swedish) mortality data for consecutive periods and consequently describe the evolution of mortality dynamics in terms of the evolution of the model parameters over time. We have found that the evolution of the model parameters validates the applicability of the compensation law of mortality to each subpopulation separately. Furthermore, our study has indicated that the population structure changes so that the population tends to become more homogeneous over time. Finally, our analysis of the decrease of the overall mortality in a population over time has shown that this decrease is mainly due to a change in the population structure and to a lesser extent to a reduction of mortality in each of the subpopulations, the latter being represented by an alteration of the parameters that outline the exponential dynamics.

Improving Longevity and Mortality Risk Models with Common Stochastic Long-Run Trends

Modeling mortality and longevity risk presents challenges because of the impact of improvements at different ages and the existence of common trends. Modeling cause of death mortality rates is even more challenging since trends and age effects are more diverse. Despite this, successfully modeling these mortality rates is critical to assessing risk for insurers issuing longevity risk products including life annuities. Longevity trends are often forecasted using a Lee-Carter model. A common stochastic trend determines age-based improvements. Other approaches fit an age-based parametric model with a time series or vector autoregression for the parameters. Vector Error Correction Models (VECM), developed recently in econometrics, include common stochastic long-run trends. This paper uses a stochastic parameter VECM form of the Heligman-Pollard model for mortality rates, estimated using data for circulatory disease deaths in the United States over a period of 50 years. The model is then compared with a version of the Lee-Carter model and a stochastic parameter ARIMA Heligman-Pollard model. The VECM approach proves to be an improvement over the Lee-Carter and ARIMA models as it includes common stochastic long-run trends.

On the heterogeneity of human populations as reflected by mortality dynamics

The heterogeneity of populations is used to explain the variability of mortality rates across the lifespan and their deviations from an exponential growth at young and very old ages. A mathematical model that combines the heterogeneity with the assumption that the mortality of each constituent subpopulation increases exponentially with age, has been shown to successfully reproduce the entire mortality pattern across the lifespan and its evolution over time. In this work we aim to show that the heterogeneity is not only a convenient consideration for fitting mortality data but is indeed the actual structure of the population as reflected by the mortality dynamics over age and time. In particular, we show that the model of heterogeneous population fits mortality data better than other commonly used mortality models. This was demonstrated using cohort data taken for the entire lifespan as well as for only old ages. Also, we show that the model can reproduce seemingly contradicting observations in late-life mortality dynamics. Finally, we show that the homogenisation of a population, observed by fitting the model to actual data of consecutive periods, can be associated with the evolution of allele frequencies if the heterogeneity is assumed to reflect the genetic variations within the population.

Age Patterns and Trends in Mortality by Cause of Death and Implications for Modeling Longevity Risk

Mortality rates have shown significant improvements in countries around the world over a lengthy period. Trends have varied by country and by age, despite common improvements. An analysis of changes in causes of death provides a better understanding of the underlying changes in mortality rates and provides information about potential future improvements. This paper provides an analysis of mortality rate age patterns and trends for the main causes of death (circulatory system, cancer, respiratory system, accidents, infectious diseases) for nine major countries (USA, Australia, Switzerland, Japan, Singapore, Italy, Norway, Sweden, United Kingdom) over approximately the last 50 years. The pattern by age and the trends in mortality rates differ significantly by cause. Mortality rates from diseases of the circulatory system have decreased over the last 50 years, while mortality rates due to cancer have shown some decreases for younger ages although they have increased at the older ages. Death rates from external causes have generally decreased especially at the young ages although not for all countries. It is unlikely that the trends in circulatory death rates will continue and the importance and uncertainty of future changes in cancer death rates are critical to any longevity risk model.

Cause-of-Death Mortality: What Can Be Learned from Population Dynamics?

This paper analyses cause-of-deathmortality changes and its impacts on the whole population evolution. The study combines cause-of-death analysis and population dynamics techniques. Our aim is to measure the impact of cause-of-death reduction on the whole population age structure, and more specifically on the dependency ratio which is a crucial quantity for pay-as-you-go pension systems. Although previous studies on causes of death focused on mortality indicators such as survival curves or life expectancy, our approach provides additional information by including birth patterns. As an important conclusion, our numerical results based on French data show that populationswith identical life expectancies can present important differences in their age pyramid resulting from different cause-specific mortality reductions. Sensitivities to fertility level and population flows are also given.

Mind the Gap: A Study of Cause-Specific Mortality by Socioeconomic Circumstances

Socioeconomic groups may be exposed to varying levels of mortality; this is certainly the case in the United Kingdom, where the gaps in life expectancy, differentiated by socioeconomic circumstances, are widening. The reasons for such diverging trends are yet unclear, but a study of cause-specific mortality may provide rich insight into this phenomenon. Therefore, we investigate the relationship between socioeconomic circumstances and cause-specific mortality using a unique dataset obtained from the U.K. Office for National Statistics. We apply a multinomial logistic framework; the reason is twofold. First, covariates such as socioeconomic circumstances are readily incorporated, and, second, the framework is able to handle the intrinsic dependence amongst the competing causes. As a consequence of the dataset and modeling framework, we are able to investigate the impact of improvements in cause-specific mortality by socioeconomic circumstances. We assess the impact using (residual) life expectancy, a measure of aggregate mortality. Of main interest are the gaps in life expectancy among socioeconomic groups, the trends in these gaps over time, and the ability to identify the causes most influential in reducing these gaps. This analysis is performed through the investigation of different scenarios: first, by eliminating one cause of death at a time; second, by meeting a target set by the World Health Organization (WHO), called WHO 25 × 25; and third, by developing an optimal strategy to increase life expectancy and reduce inequalities.

Periodic or Generational Actuarial Tables: Which One to Choose?

The increase in life expectancy over the past several decades has been impressive and represents a key challenge for institutions that provide life insurance products. Indeed, when a new actuarial table is released with updated survival and death rates, such institutions need to update the amount of mathematical reserve that they need to set aside to guarantee the future payments of their annuities. As mortality forecasting techniques are currently well developed, it is relatively easy to forecast mortality over several decades and to directly use these forecast rates in the determination of the mathematical reserve needed to guarantee annuity payments. Future mortality evolution is then directly incorporated into the liabilities valuation of an institution, and it is thus commonly believed that such liabilities should not require much updating when a new actuarial table is released. In this paper, we demonstrate that contrary to this common belief, institutions that use generational tables (namely, tables including future mortality evolution) will most likely need to make more important adjustments (positive or negative) to their liabilities than will institutions using periodic (static) tables whenever a new table is released. By using three very different models to project mortality, we demonstrate that our findings are inherent in the required long horizons of the forecasts needed in the generational approach, with the uncertainty surrounding the forecast values increasing with the horizon. Therefore, generational tables may introduce more instability in a pension institution’s accounts than periodic tables.