Long-range trends in adult mortality: Models and projection methods

In the study reported here, I had two objectives: (1) to test a new version of the logistic model for the pattern of change over time in age-specific adult mortality rates and (2) to develop a new method for projecting future trends in adult mortality. A test of the goodness of fit of the logistic model for the force of mortality indicated that its slope parameter is nearly constant over time. This finding suggests a variant of the model that is called the shifting logistic model. A new projection method, based on the shifting mortality model, is proposed and compared with the widely used Lee-Carter procedure.     

Applying Lee-Carter under conditions of variable mortality decline

The Lee-Carter method of mortality forecasting assumes an invariant age component and most applications have adopted a linear time component. The use of the method with Australian data is compromised by significant departures from linearity in the time component and changes over time in the age component. We modify the method to adjust the time component to reproduce the age distribution of deaths, rather than total deaths, and to determine the optimal fitting period in order to address non-linearity in the time component. In the Australian case the modification has the added advantage that the assumption of invariance is better met. For Australian data, the modifications result in higher forecast life expectancy than the original Lee-Carter method and official projections, and a 50 per cent reduction in forecast error. The model is also expanded to take account of age-time interactions by incorporating additional terms, but these are not readily incorporated into forecasts.     

Applying Lee-Carter under conditions of variable mortality decline

The Lee-Carter method of mortality forecasting assumes an invariant age component and most applications have adopted a linear time component. The use of the method with Australian data is compromised by significant departures from linearity in the time component and changes over time in the age component. We modify the method to adjust the time component to reproduce the age distribution of deaths, rather than total deaths, and to determine the optimal fitting period in order to address non-linearity in the time component. In the Australian case the modification has the added advantage that the assumption of invariance is better met. For Australian data, the modifications result in higher forecast life expectancy than the original Lee-Carter method and official projections, and a 50 per cent reduction in forecast error. The model is also expanded to take account of age-time interactions by incorporating additional terms, but these are not readily incorporated into forecasts.     

香港人口死亡率演变及其未来发展

与其它发展地区类似 ,二战以后香港人口死亡率已经经历了显著的下降 ,达到了一个非常低的水平。在这种极低水平的现状下 ,香港人口死亡率进一步下降的空间还有多大呢 ?本文基于香港人口死亡率历史数据 ,探讨了其演变趋势 ,同时利用Lee -Carter模型对香港未来 5 0年分性别的人口死亡率进行了预测。如果我们将预测结果与最近的官方预测数据进行比较 ,可以发现 ,本文Lee -Carter模型预测的未来香港人口死亡率下降趋势比官方预测结果要乐观     

两人群引力模型框架下的中国死亡率预测①--结合美国相应数据

Lee－Carter系列模型是对一个人群的死亡率动态建模和预测的模型。由于中国死亡率抽样数据的质量问题导致模型预测的效果不如国外文献所反映的那么精确。本文在两人群引力模型框架下结合中国和美国同期死亡率数据建模，并将结果与相应的单人群模型比较。研究表明，引力模型与APC模型相结合取得了最好的效果，在此基础上本文预测2025年老年抚养比会急剧上升到23．32％，2030年的婚配男性人口超出女性约2079万，婴幼青少年20年间累计死亡人数约293万。     

Including the Smoking Epidemic in Internationally Coherent Mortality Projections

We present a new mortality projection methodology that distinguishes smoking- and non-smoking-related mortality and takes into account mortality trends of the opposite sex and in other countries. We evaluate to what extent future projections of life expectancy at birth (e ₀) for the Netherlands up to 2040 are affected by the application of these components. All-cause mortality and non-smoking-related mortality for the years 1970–2006 are projected by the Lee-Carter and Li-Lee methodologies. Smoking-related mortality is projected according to assumptions on future smoking-attributable mortality. Projecting all-cause mortality in the Netherlands, using the Lee-Carter model, leads to high gains in e ₀ (4.1 for males; 4.4 for females) and divergence between the sexes. Coherent projections, which include the mortality experience of the other 21 sex- and country-specific populations, result in much higher gains for males (6.4) and females (5.7), and convergence. The separate projection of smoking and non-smoking-related mortality produces a steady increase in e ₀ for males (4.8) and a nonlinear trend for females, with lower gains in e ₀ in the short run, resulting in temporary sex convergence. The latter effect is also found in coherent projections. Our methodology provides more robust projections, especially thanks to the distinction between smoking- and non-smoking-related mortality.     

Lee-Carter估计模式推算中国农村老年人口死亡率的研究

死亡率的估算与人口老龄化密切相关,中国60岁及以上老年人口主要集中在农村地区,本文运用Lee-Carter模型对农村分性别单岁组的死亡率数据进行建模,预测出农村人口死亡率与期望寿命的发展趋势。     

Extending the Lee-Carter Method to Model the Rotation of Age Patterns of Mortality Decline for Long-Term Projections

In developed countries, mortality decline is decelerating at younger ages and accelerating at old ages, a phenomenon we call “rotation.” We expect that this rotation will also occur in developing countries as they attain high life expectancies. But the rotation is subtle and has proved difficult to handle in mortality models that include all age groups. Without taking it into account, however, long-term mortality projections will produce questionable results. We simplify the problem by focusing on the relative magnitude of death rates at two ages (0 and 15–19) while making assumptions about changes in rates of decline at other ages. We extend the Lee-Carter method to incorporate this subtle rotation in projection. We suggest that the extended Lee-Carter method could provide plausible projections of the age pattern of mortality for populations, including those that currently have very high life expectancies. Detailed examples are given using data from Japan and the United States.     

Optimizing the Lee-Carter Approach in the Presence of Structural Changes in Time and Age Patterns of Mortality Improvements

Researchers using the Lee-Carter approach have often assumed that the time-varying index evolves linearly and that the parameters describing the age pattern of mortality decline are time-invariant. However, as several empirical studies suggest, the two assumptions do not seem to hold when the calibration window begins too early. This problem gives rise to the question of identifying the longest calibration window for which the two assumptions hold true. To address this question, we contribute a likelihood ratio–based sequential test to jointly test whether the two assumptions are satisfied. Consistent with the mortality structural changes observed in previous studies, our testing procedure indicates that the starting points of the optimal calibration windows for most populations fall between 1960 and 1990. Using an out-of-sample analysis, we demonstrate that in most cases, models that are estimated to the optimized calibration windows result in more accurate forecasts than models that are fitted to all available data or data beyond 1950. We further apply the proposed testing procedure to data over different age ranges. We find that the optimal calibration windows for age group 0–49 are generally shorter than those for age group 50–89, indicating that mortality at younger ages might have undergone (another) structural change in recent years.     

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.     

Modeling and Forecasting Health Expectancy: Theoretical Framework and Application

Life expectancy continues to grow in most Western countries; however, a major remaining question is whether longer life expectancy will be associated with more or fewer life years spent with poor health. Therefore, complementing forecasts of life expectancy with forecasts of health expectancies is useful. To forecast health expectancy, an extension of the stochastic extrapolative models developed for forecasting total life expectancy could be applied, but instead of projecting total mortality and using regular life tables, one could project transition probabilities between health states simultaneously and use multistate life table methods. In this article, we present a theoretical framework for a multistate life table model in which the transition probabilities depend on age and calendar time. The goal of our study is to describe a model that projects transition probabilities by the Lee-Carter method, and to illustrate how it can be used to forecast future health expectancy with prediction intervals around the estimates. We applied the method to data on the Dutch population aged 55 and older, and projected transition probabilities until 2030 to obtain forecasts of life expectancy, disability-free life expectancy, and probability of compression of disability.     

Trends in Mortality Decrease and Economic Growth

The vast literature on extrapolative stochastic mortality models focuses mainly on the extrapolation of past mortality trends and summarizes the trends by one or more latent factors. However, the interpretation of these trends is typically not very clear. On the other hand, explanation methods are trying to link mortality dynamics with observable factors. This serves as an intermediate step between the two methods. We perform a comprehensive analysis on the relationship between the latent trend in mortality dynamics and the trend in economic growth represented by gross domestic product (GDP). Subsequently, the Lee-Carter framework is extended through the introduction of GDP as an additional factor next to the latent factor, which provides a better fit and better interpretable forecasts.     

Steep increase in best-practice cohort life expectancy

We analyze trends in best-practice life expectancy among female cohorts born from 1870 to 1950. Cohorts experience declining rather than constant death rates, and cohort life expectancy usually exceeds period life expectancy. Unobserved mortality rates in non-extinct cohorts are estimated using the Lee-Carter model for mortality in 1960–2008. Best-practice cohort and period life expectancies increased nearly linearly. Across cohorts born from 1870 to 1920 the annual increase in cohort length of life was 0.43 years. Across calendar years from 1870 to 2008, the annual increase was 0.28 years. Cohort life expectancy increased from 53.7 years in the 1870 cohort to 83.8 years in the 1950 cohort. The corresponding cohort/period longevity gap increased from 1.2 to 10.3 years. Among younger cohorts, survival to advanced ages is substantially higher than could have been anticipated by period mortality regimes when these cohorts were young or middle-aged. A large proportion of the additional expected years of life are being lived at ages 65 and older. This substantially changes the balance between the stages of the life cycle.     

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. All correspondence to Frank T. Denton. This paper is a revised version of one presented at the Annual Congress of the European Society for Population Economics, Athens, Greece, June 2001. The underlying work was carried out as part of the SEDAP (Social and Economic Dimensions of an Aging Population) Research Program supported by the Social Sciences and Humanities Research Council of Canada, Statistics Canada and the Canadian Institute for Health Information. Ronald Lee provided comments that were very helpful in revising an earlier version of the paper. We thank him and participants at the ESPE session at which that version was presented. We thank also the Journal's anonymous referees. Responsible editor: Junsen Zhang.     

A flexible two-dimensional mortality model for use in indirect estimation

Mortality estimates for many populations are derived using model life tables, which describe typical age patterns of human mortality. We propose a new system of model life tables as a means of improving the quality and transparency of such estimates. A flexible two-dimensional model was fitted to a collection of life tables from the Human Mortality Database. The model can be used to estimate full life tables given one or two pieces of information: child mortality only, or child and adult mortality. Using life tables from a variety of sources, we have compared the performance of new and old methods. The new model outperforms the Coale-Demeny and UN model life tables. Estimation errors are similar to those produced by the modified Brass logit procedure. The proposed model is better suited to the practical needs of mortality estimation, since both input parameters are continuous yet the second one is optional.     

Reconsidering mortality compression and deceleration: an alternative model of mortality rates

In this research we develop a model of mortality rates that parameterizes mortality deceleration and compression, permits hypothesis tests for change in these parameters over time, and allows for formal gender comparisons. Our model fits mortality data well across all adult ages 20-105 for 1968-1992 U.S. white data, and the results offer some confirmation of findings of mortality research using conventional methods. We find that the age at which mortality deceleration begins is increasing over time, that decompression of mortality is occurring, and that these trends vary substantially across genders, although male and female mortality patterns appear to be converging to some extent.     

A Flexible Bayesian Model for Estimating Subnational Mortality

Reliable subnational mortality estimates are essential in the study of health inequalities within a country. One of the difficulties in producing such estimates is the presence of small populations among which the stochastic variation in death counts is relatively high, and thus the underlying mortality levels are unclear. We present a Bayesian hierarchical model to estimate mortality at the subnational level. The model builds on characteristic age patterns in mortality curves, which are constructed using principal components from a set of reference mortality curves. Information on mortality rates are pooled across geographic space and are smoothed over time. Testing of the model shows reasonable estimates and uncertainty levels when it is applied both to simulated data that mimic U.S. counties and to real data for French départements. The model estimates have direct applications to the study of subregional health patterns and disparities.     

The use of model life tables to estimate mortality for the United States in the late nineteenth century

This paper seeks to extend our knowledge about mortality in the late nineteenth century United States by using census mortality data for older children and teenagers to fit model tables. The same method can also be used with partially underregistered death data. The most commonly used model tables, the Coale and Demeny West Model, apparently do not adequately depict the changing shape of mortality over the period 1850--1910. An alternative model life table system is presented, based on the Brass two parameter logit system and available reliable life tables from the period 1850--1910. The two parameter system must be reduced to a one parameter system by means of estimated relationships between the parameters so that the fitting procedure can be used. The resulting model system is, however, heavily dependent on the experience of northern, industrial states, especially Massachusetts.     

Sex mortality differences in The United States: The role of cohort smoking patterns

This article demonstrates that over the period 1948-2003, sex differences in mortality in the age range 50-84 widened and then narrowed on a cohort basis rather than on a period basis. The cohort with the maximum excess of male mortality was born shortly after the turn of the century. Three separate data sources suggest that the turnaround in sex mortality differences is consistent with sex differences in cigarette smoking by cohort. An age-period-cohort model reveals a highly significant effect of smoking histories on men's and women's mortality. Combined with recent changes in smoking patterns, the model suggests that sex differences in mortality will narrow dramatically in coming decades.     

Sex differences in mortality as a social indicator

Using a macro-sociological model, this paper argues that the status of women is an important determinant of sex mortality differences. This is done first by examining data from India which is known to have an excessively high level of female mortality. The examination is further extended by a pooled cross-section and time series analysis of the excess of female life expectancy over male life expectancy for 83 countries.