Mortality Forecasts Research Articles

Where people die (1974—2030): past trends, future projections and implications for care

Background: Ageing nations have growing needs for end of life care, but these have never been projected in detail. We analysed past trends in place of death (1974—2003) and projected likely trends to 2030 in England and Wales and from these need for care. Methods: Mortality trends and forecasts were obtained from official statistics. Future scenarios were modelled using recent five-year trends in age and gender specific home death proportions to estimate numbers of deaths by place to 2030, accounting for future changes in the age and gender distribution of deaths. Results: Annual numbers of deaths fell by 8% from 1974 to 2003, but are expected to rise by 17% from 2012 to 2030. People will die increasingly at older ages, with the percentage of deaths among those aged 85 and expected to rise from 32% in 2003 to 44% in 2030. Home death proportions fell from 31% to 18% overall, and at an even higher rate for people aged 65 and over, women and noncancer deaths. If recent trends continue, numbers of home deaths could reduce by 42% and fewer than 1 in 10 will die at home in 2030. Annual numbers of institutional deaths (currently 440936) will be 530409 by 2030 (20% increase). Conclusions: In England and Wales home deaths have been decreasing. The projections underline the urgent need for planning care to accommodate a large increase of ageing and deaths. Either inpatient facilities must increase substantially, or many more people will need community end of life care from 2012 onwards. Palliative Medicine 2008; 22 : 33—41

Norway's Prime Minister Jens Stoltenberg: leader on MDG4

Norway's Prime Minister Jens Stoltenberg: leader on MDG4

Can we achieve Millennium Development Goal 4? New analysis of country trends and forecasts of under-5 mortality to 2015

Global efforts have increased the accuracy and timeliness of estimates of under-5 mortality; however, these estimates fail to use all data available, do not use transparent and reproducible methods, do not distinguish predictions from measurements, and provide no indication of uncertainty around point estimates. We aimed to develop new reproducible methods and reanalyse existing data to elucidate detailed time trends. We merged available databases, added to them when possible, and then applied Loess regression to estimate past trends and forecast to 2015 for 172 countries. We developed uncertainty estimates based on different model specifications and estimated levels and trends in neonatal, post-neonatal, and childhood mortality. Global under-5 mortality has fallen from 110 (109-110) per 1000 in 1980 to 72 (70-74) per 1000 in 2005. Child deaths worldwide have decreased from 13.5 (13.4-13.6) million in 1980 to an estimated 9.7 (9.5-10.0) million in 2005. Global under-5 mortality is expected to decline by 27% from 1990 to 2015, substantially less than the target of Millennium Development Goal 4 (MDG4) of a 67% decrease. Several regions in Latin America, north Africa, the Middle East, Europe, and southeast Asia have had consistent annual rates of decline in excess of 4% over 35 years. Global progress on MDG4 is dominated by slow reductions in sub-Saharan Africa, which also has the slowest rates of decline in fertility. Globally, we are not doing a better job of reducing child mortality now than we were three decades ago. Further improvements in the quality and timeliness of child-mortality measurements should be possible by more fully using existing datasets and applying standard analytical strategies.

Negative binomial version of the LeeCarter model for mortality forecasting

Mortality improvements pose a challenge for the planning of public retirement systems as well as for the private life annuities business. For public policy, as well as for the management of financi...

Negative binomial version of the Lee–Carter model for mortality forecasting

AbstractMortality improvements pose a challenge for the planning of public retirement systems as well as for the private life annuities business. For public policy, as well as for the management of financial institutions, it is important to forecast future mortality rates. Standard models for mortality forecasting assume that the force of mortality at age x in calendar year t is of the form exp(αx + βxκt). The log of the time series of age‐specific death rates is thus expressed as the sum of an age‐specific component αx that is independent of time and another component that is the product of a time‐varying parameter κt reflecting the general level of mortality, and an age‐specific component βx that represents how rapidly or slowly mortality at each age varies when the general level of mortality changes. The parameters are usually estimated via singular value decomposition or via maximum likelihood in a binomial or Poisson regression model. This paper demonstrates that it is possible to take into account the overdispersion present in the mortality data by estimating the parameter in a negative binomial regression model. Copyright © 2007 John Wiley & Sons, Ltd.

Smoothing the Lee–Carter and Poisson log-bilinear models for mortality forecasting

Mortality improvements pose a challenge for the planning of public retirement systems as well as for the private life annuities business. For public policy, as well as for the management of financial institutions, it is important to forecast future mortality rates. Standard models for mortality forecasting assume that the force of mortality at age x in calendar year t is of the form exp(αx + βxκt ). The log of the time series of age-specific death rates is thus expressed as the sum of an age-specific component αx that is independent of time and another component that is the product of time-varying parameter κt reflecting the general level of mortality, and an age-specific component βx that represents how rapidly or slowly mortality at each age varies when the general level of mortality changes. This model is fitted to historical data. The resulting estimated κt 's are then modeled and projected as stochastic time series using standard Box–Jenkins methods. However, the estimated βx's exhibit an irregular pattern in most cases, and this produces irregular projected life tables. This article demonstrates that it is possible to smooth the estimated βx's in the Lee–Carter and Poisson log-bilinear models for mortality projection. To this end, penalized least-squares/maximum likelihood analysis is performed. The optimal value of the smoothing parameter is selected with the help of cross validation.

Forecasting Hungarian mortality rates using the Lee-Carter method

A modified version of the popular Lee-Carter method (Lee-Carter 1992) is applied to forecast mortality rates in Hungary for the period 2004–2040 on the basis of mortality data between 1949 and 2003 both for men and women. Another case is also considered based on a restricted data set corresponding to the period 1989–2003. The model fitted to the data of the period 1949–2003 forecasts increasing mortality rates for men between ages 45 and 55, pointing out that the Lee-Carter method is hardly applicable for countries where mortality rates exhibit trends as peculiar as in Hungary. However, models fitted to the data for the last 15 years both for men and women forecast decreasing trends similarly to the case of countries where the method was successfully applied. Hence one gets a better fit in this way, however, further concerns suggest that the Lee-Carter model, which is celebrated and widely used in actuarial practice, does not necessarily give sufficiently good prediction.

Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee‐Carter Framework

AbstractLongevity risk is a major issue for insurers and pension funds, especially in the selling of annuity products. In that respect, securitization of this risk could offer great opportunities for hedging. This article proposes to design survivor bonds which could be issued directly by insurers. In order to guaranty some transparency in the product, the survivor bond is based on a public mortality index. The classical Lee‐Carter model for mortality forecasting is used to price a risky coupon survivor bond based on this index.

Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions

We compare the short- to medium-term accuracy of five variants or extensions of the Lee-Carter method for mortality forecasting. These include the original Lee-Carter, the Lee-Miller and Booth-Maindonald-Smith variants, and the more flexible Hyndman-Ul

Robust forecasting of mortality and fertility rates: A functional data approach

A new method is proposed for forecasting age-specific mortality and fertility rates observed over time. This approach allows for smooth functions of age, is robust for outlying years due to wars and epidemics, and provides a modelling framework that is easily adapted to allow for constraints and other information. Ideas from functional data analysis, nonparametric smoothing and robust statistics are combined to form a methodology that is widely applicable to any functional time series data observed discretely and possibly with error. The model is a generalization of the Lee–Carter (LC) model commonly used in mortality and fertility forecasting. The methodology is applied to French mortality data and Australian fertility data, and the forecasts obtained are shown to be superior to those from the LC method and several of its variants.

Longevity and adjustment in pension annuities, with application to Finland

The aim of this paper is twofold. First, the improvement in adult mortality in Finland is studied. Lee-Carter (LC) Poisson log-bilinear model is used for mortality forecasting. Secondly, the paper studies how the pension annuities are adjusted to unexpected mortality pattern. A formula for funded plan is proposed. Application is made with Finnish mortality rates predicted using the LC model.

Forecasting Cause-Age Specific Mortality Using Two Random Processes

Mortality forecasts are critical information for assessing the health of a population and are necessary for making informed decisions about how best to direct health-related resources and activities. Timeliness in making health statistics available is crucial to identify and address current health problems. Being motivated to meet these needs, we propose a method to forecast the number of cause-age specific deaths through a two random processes model. Unlike the previous methods, the new method incorporates both cross-sectional and longitudinal correlations into our model without a high-dimensional problem. A bootstrap confidence interval is presented to measure the validity of our model and to detect an unusual occurrence of deaths. Our data analysis demonstrates that our method gives promising results compared with the true final counts.

Fuzzy formulation of the Lee–Carter model for mortality forecasting

In this paper, a fuzzy formulation of the Lee–Carter [Lee, R.D., Carter, L.R., 1992. Modeling and forecasting U.S. mortality. J. Amer. Statist. Assoc. 419 (87), 659–675] model is proposed. The standard Lee–Carter (LC) model, which uses singular value decomposition, assumes that the errors have a constant variance over all ages. This statement, however, does not often hold. The advantage of such a fuzzy approach is that the errors are viewed as fuzziness of the model structure; hence the homoscedasticity is not an issue.

A Bayesian forecasting model: predicting U.S. male mortality

This article presents a Bayesian approach to forecast mortality rates. This approach formalizes the Lee-Carter method as a statistical model accounting for all sources of variability. Markov chain Monte Carlo methods are used to fit the model and to sample from the posterior predictive distribution. This paper also shows how multiple imputations can be readily incorporated into the model to handle missing data and presents some possible extensions to the model. The methodology is applied to U.S. male mortality data. Mortality rate forecasts are formed for the period 1990-1999 based on data from 1959-1989. These forecasts are compared to the actual observed values. Results from the forecasts show the Bayesian prediction intervals to be appropriately wider than those obtained from the Lee-Carter method, correctly incorporating all known sources of variability. An extension to the model is also presented and the resulting forecast variability appears better suited to the observed data.

Extending Lee–Carter Mortality Forecasting

ABSTRACT The Lee–Carter method for mortality forecasting is outlined, discussed and improved utilizing standard time series approaches. The new framework, which integrates estimation and forecasting, delivers more robust results and permits more detailed insight into underlying mortality dynamics. An application to women's mortality data illustrates the methods.

Evaluating and extending the Lee–Carter model for mortality forecasting: Bootstrap confidence interval

This paper first studies the performance of the Lee–Carter [J. Am. Stat. Assoc. 419 (87) (1992) 659–675] model for mortality forecasting on the Nordic countries. Three approaches for computing the model parameters are compared: Singular Value Decomposition, Weighted Least Square and Maximum Likelihood Estimation. Hypothetical projections are also made, based on variable period intervals. Secondly, the paper addresses an extension to the Lee–Carter method: a residual bootstrapped technique is used to construct confidence intervals for forecasted life expectancies. Uncertainties produced with this method incorporate the variability from all parameters in the model, while the original Lee–Carter method focuses on the variability in the time-varying parameter.

Coherent mortality forecasts for a group of populations: An extension of the lee-carter method

Mortality patterns and trajectories in closely related populations are likely to be similar in some respects, and differences are unlikely to increase in the long run. It should therefore be possible to improve the mortality forecasts for individual countries by taking into account the patterns in a larger group. Using the Human Mortality Database, we apply the Lee-Carter model to a group of populations, allowing each its own age pattern and level of mortality but imposing shared rates of, change by age. Our forecasts also allow divergent patterns to continue for a while before tapering off. We forecast greater longevity gains for the United States and lesser ones for Japan relative to separate forecasts.

Time series analysis and stochastic forecasting: An econometric study of mortality and life expectancy

Methods for time series modeling of mortality and stochastic forecasting of life expectancies are explored, using Canadian data. Consideration is given first to alternative indexes of aggregate mortality. Age-sex group system models are then estimated. Issues in the forecasting of life expectancies are discussed and their quantitative implications investigated. Experimental stochastic forecasts are presented and discussed, based on nonparametric, partially parametric, and fully parametric methods, representing alternatives to the well known Lee-Carter method. Some thoughts are offered on the interpretation of historical data in generating future probability distributions, and on the treatment of demographic uncertainty in long-run policy planning.

Outlier analysis and mortality forecasting: The United Kingdom and Scandinavian countries

The Lee-Carter model and its variants have been extensively employed by actuaries, demographers, and many others to forecast age-specific mortality. In this study, we use mortality data from England and Wales, and four Scandinavian countries to perform time-series outlier analysis of the key component of the Lee-Carter model – the mortality index. We begin by employing a systematic outlier detection process to ascertain the timing, magnitude, and persistence of any outliers present in historical mortality trends. We then try to match the identified outliers with imperative events that could possibly justify the vacillations in human mortality levels. At the same time, we adjust the effect of the outliers for model re-estimation. A new iterative model re-estimation method is proposed to reduce the chance of erroneous model specification. The empirical results indicate that the outlier-adjusted model could achieve more efficient forecasts of variables such as death rates and life expectancies. Finally, we point out that the Lee-Carter forecasts are especially vulnerable to outliers near the forecast origin, and discuss the potential limitations of the application of the Lee-Carter model to mortality forecasting.

Forecasting Morality in Developed Countries: Insights from a Statistical, Demographic and Epidemiological Perspective

Foreword. Preface. List of Authors. List of Figures. List of Tables. Part 1: Introduction. 1. A Review of Demographic Forecasting Models for Mortality. 2. A Review of Epidemiological Approaches to Forecasting Mortality and Morbidity. Part 2: Theoretical Perspectives on Forecasting Mortality. 3. A Regression Model of Mortality, with Application to the Netherlands. 4. Forecasting Mortality from Regression Models: the Case of the Netherlands. 5. Gompertz in Context: the Gompertz and Related Distributions. 6. Comparing Theoretical Age Patterns of Mortality Beyond the Age of 80. Part 3: From Theory to Practice. 7. Predicting Mortality from Period, Cohort or Cause-Specific Trends: a Study of Four European Countries. 8. Incorporating Risk Factor Epidemiology in Mortality Projections. 9. Projecting Mortality in Population Forecasts in the Netherlands. 10. The Latest Mortality Forecasts in the European Union. Part 4: Issues for the Future: More Consistency and Transparency. 11. Mortality Models Incorporating Theoretical Concepts of Ageing. 12. Towards an Integration of the Statistical, Demographic and Epidemiological Perspectives in Forecasting Mortality.