The analysis of seasonality in births and deaths

"Monthly data on live births and stillbirths and quarterly data on mortality and infant mortality in Poland are analyzed for the period 1983-1985. The aim is to evaluate and compare seasonal fluctuations in these variables in Katowice voivodship and in Poland as a whole. Effects of seasonal factors are estimated separately for males and females and urban-rural areas via a regression model. For births, effects of seasonality are similar in Katowice and Poland, while for deaths significant differences are observed.     

中国人口死亡率改善水平比较分析

 中国第六次人口普查数据如期公布,本文利用1981-2010年人口普查和人口抽样调查提供的死亡率数据,对四次人口普查期间中国人口死亡率改善水平进行深层次分析,分别按年龄、性别、城乡、是否投保等进行对比,并与其他国家的数据对比,旨在探讨中国人口死亡率变化趋势和不同分类人群死亡率改善的差异、成因及变动趋势,最终为长寿风险管理提供依据。主要结论是：建国以来,中国人口死亡率持续改善,死亡率改善程度随年龄的增长呈下降趋势,近十年来死亡率改善程度最高,特别是婴儿和55岁以上人口尤为明显。在大部分年龄组上,女性死亡率改善水平高于男性,市人口死亡率改善水平明显高于镇和乡,投保商业保险人口的死亡率改善水平高于全国人口,我国人口的死亡率改善水平高于对比国家,这反映了我国人民生活和医疗水平的实质提高,也表明未来死亡率还有较大的下降空间。     

中国高龄人口死亡率随机波动趋势分析

本文采用1996-2010年国家统计局公布的死亡率数据,以70岁男性人口作为高龄人口的代表,基于中国人口死亡率数据较少的特点,突破了传统Lee-Carter模型的框架,直接从死亡率改善产生的原因入手,采取Monte Carlo方法建立中国高龄人口死亡率随机波动趋势模型。通过对不同死亡率改善原因进行组合,从中选取最优模型来探究死亡率的随机趋势性与波动性的关系,更好的克服了死亡率普遍被低估的事实,使得对未来死亡率的预测更加准确与稳妥。     

Error models for official mortality forecasts

"The Office of the Actuary, U.S. Social Security Administration, produces alternative forecasts of mortality to reflect uncertainty about the future.... In this article we identify the components and assumptions of the official forecasts and approximate them by stochastic parametric models. We estimate parameters of the models from past data, derive statistical intervals for the forecasts, and compare them with the official high-low intervals. We use the models to evaluate the forecasts rather than to develop different predictions of the future. Analysis of data from 1972 to 1985 shows that the official intervals for mortality forecasts for males or females aged 45-70 have approximately a 95% chance of including the true mortality rate in any year. For other ages the chances are much less than 95%."     

我国男女两性老龄人口死亡率联合建模与预测

老龄人口死亡率建模和预测是长寿风险度量和养老金风险管理的基础。在我国,退休年龄及以上老龄人口死亡数据稀少,随机波动大,构建能够捕捉老龄人口死亡率随性别、年龄和时间变动的动态预测模型成为难题。本文采用Logistic两人口死亡率模型研究我国老龄人口死亡率的建模与预测。首先,运用死亡率数据质量较好的我国台湾地区数据,对模型结构进行选择,并检验模型的稳健性和预测性能。其次,基于我国大陆地区死亡率数据对模型结构进行二次验证和选择,应用所选模型对大 陆地区老龄死亡率进行建模和预测。结果显示,对于我国男女老龄死亡率的拟合和预测,Logistic 两人口模型均优于单人口CBD模型。最后,运用Logistic两人口死亡率模型对死亡率在年龄和时间两个维度上外推和预测,计算出时期和队列老龄人口分年龄的预期余寿,为养老金精算评估和长寿风险分析提供更准确的数据支持。     

Empirical Bayes procedures for stabilizing maps of U.S. cancer mortality rates

"The geographic mapping of age-standardized, cause-specific death rates is a powerful tool for identifying possible etiologic factors, because the spatial distribution of mortality risks can be examined for correlations with the spatial distribution of disease-specific risk factors. This article presents a two-stage empirical Bayes procedure for calculating age-standardized cancer death rates, for use in mapping, which are adjusted for the stochasticity of rates in small area populations. Using the adjusted rates helps isolate and identify spatial patterns in the rates. The model is applied to sex-specific data on U.S. county cancer mortality in the white population for 15 cancer sites for three decades: 1950-1959, 1960-1969, and 1970-1979. Selected results are presented as maps of county death rates for white males."     

Pricing longevity-linked derivatives using a stochastic mortality model

Abstract

We propose a 2-factor MBMM model with exponential Lévy process to develop a stochastic mortality process. The two components are fitted by two independent NIG distributions. Compared to Lee–Carter model or 1-factor MBMM model, our mortality model explains more variation and improves the goodness of fit by including the second time component. Based on the improved model, we price three longevity-linked financial instruments, namely the longevity bond, q-forward and s-forward. The pricing is demonstrated on English and Welsh males aged 65 in 2013. Results indicate that the 2-factor MBMM model gives the highest price for mortality-related type of contract.     

A progressive rise in stomach cancer-related mortality rate during 1970–1995 in Japanese individuals over 85 years of age

A large number of studies have shown a gradual fall in stomach cancer-related mortality rate during the last decade. Here we analyzed the pattern of stomach cancer-related mortality rates in Japanese aged>85 years from 1970 to 1995. We used data for the entire population of Japan. The magnitude of change was measured by relative risk and cause-elimination life tables to distinguish time trends in mortality rates of stomach cancer for individuals over 85 years of age compared with other age groups (55–84 years). In the over-85 age group, stomach cancer mortality increased from 374 in 1970 to 662 in 1995 per 100,000 (77%) for males and from 232 to 296 per 100,000 (27%) for females. Using the 55–59 years group as the reference category, the relative risk increased from 2.3 to 9.9 and from 2.8 to 11.1 in men and women, respectively. The effects of mortality on life expectancy also increased 1.5 times and 1.1 times, respectively. Our results showed a rise of stomach cancer mortality in Japanese aged over 85 years, which paralleled the increase in relative risk and negative contribution to life expectancy. While the mortality of younger age groups is decreasing, the change over from increase to decrease in the over-85 age group is only just beginning.     

Empirical bayesInterval estimates: An application to geographical epidemiology

Summary Empirical Bayes estimates have been advocated as an improvement for mapping rare diseases or health events aggregated in small areas. In particular different parametric approaches have been proposed for dealing with non-normal data, assuming that disease occurrencies follow non-homogeneous Poisson law, whose parameters are treated as random variables. This paper shows how to conduct a complete Empirical Bayes analysis under an exchangeable model in the context of Geographical Epidemiology. Three different approaches for defining confidence limits obtained using a parametric bootstrap are compared: method 1 relies only on the first and second moment of the bootstrapped posterior distributions; method 2 computes the centiles of the bootstrapped posteriors; method 3 equates to α the average of the probabilities derived from the estimated bootstrapped cumulative posterior distributions. The simple Poisson-Gamma formulation was used to model mortality data on Larynx Cancer in the Local Health Units of Tuscany (1980–82 males). Two areas of significant elevated risk are identified.     

The Effects of Variations in the Components of Change on the Size and Structure of The Australian Population: 1911-66

The main aim of the study was to estimate separately the effects of the variations in the components of population change and the effects of their mutual interactions on the size and age structure and other characteristics of the Australian population during 1911-66. The method proposed, called here the factorial projection method, is to project the population over the period under consideration, under different assumptions according to a 2×2×2 factorial design, utilizing the observed variations in fertility, mortality and migration. It was found that, apart from the effects of variations in the components occurring individually, the two factor interaction effects– the interaction effects of the changes occurring simultaneously in two of the components (viz. fertility and mortality or mortality and migration or fertility and migration)–on the population size, were considerable. The contribution of migration to the working age group was greater than its effect on the total size, and mortality improvement played a more prominent role in increasing the size of the old age population, while the reduction in fertility caused a higher proportion in the old age group and thus increased the mean age of the population both in the case of males and females. The two factor interaction effects were not negligible in changing the size of the school age population, population in the working age group and also in the old age group. But the interaction of migration and the decline in fertility was the only interaction effect which was important in changing the percentage age distribution and the mean age of the male and female population.     

Theory and techniques of demographic forecasting

This paper focuses on theories and techniques for forecasting fertility and mortality. Period and cohort analyses of fertility and mortality in Germany over the past century are first discussed. Alternative techniques for forecasting future trends in these variables in the Federal Republic of Germany are then outlined. The economic and social policy consequences of different mortality and fertility assumptions are also briefly noted.     

Assessing Differential Area Mortality Trends via Bayesian Random Effects

Changes in area mortality are important for assessing spatial health inequality. They are likely to be differentiated by age as well as spatially and may vary by demographic strata (e.g., gender, ethnic group). A simple approach assumes linear improvement in log mortality risks, with noninteracting area and age coefficients. By contrast, this article considers parsimonious models for mortality change allowing nonlinear trends and interactions between ages and areas in mortality levels and trends. A case study considers trends in mortality in 32 London boroughs over the 8-year period 1999–2006 for deaths data disaggregated by age, sex, and area.     

Alternative models for the heterogeneity of mortality risks among the aged

The authors examine how sensitive the estimates of heterogeneity in the mortality risks in a population are to the choices of two types of function, "one describing the age-specific rate of increase of mortality risks for individuals and the other describing the distribution of mortality risks across individuals." U.S. data from published Medicare mortality rates for the period 1968-1978 are used to analyze total mortality among the aged. "In addition, national vital statistics data for the period 1950-1977 were used to analyze adult lung cancer mortality. For these data, the estimates of structural parameters were less sensitive to reasonable choices of the heterogeneity distribution (gamma vs. inverse Gaussian) than to reasonable choices of the hazard rate function (Gompertz vs. Weibull)."     

Bootstrap方法在死亡模型中的应用

 由于不同国家死亡率改善现象不同,世界各国所使用的死亡率模型皆不尽相同,而且不同年龄段的死亡率模型也不同。实际中,我们常常采用Gompertz模型、Makeham模型、Weibull模型等拟合高年龄段人口的死亡率,但是因高年龄段人口的死亡数据资料不够充分,较少有人以统计的观点给出模型适合性的检验过程。因此本研究提出利用Bootstrap方法检验死亡模型假设的方法,包括模型适合性的检验、参数估计、参数假设检验等。最后,本文应用中国1997－2007年65－89岁人口的粗死亡率数据,提出适合的死亡模型,然后给出利用Bootstrap方法进行死亡模型检验的全过程。     

A longitudinal analysis of infant and senescent mortality using mixture models

We construct a mixture distribution including infant, exogenous and Gompertzian/non-Gompertzian senescent mortality. Using mortality data from Swedish females 1751–, we show that this outperforms models without these features, and compare its trends in cohort and period mortality over time. We find an almost complete disappearance of exogenous mortality within the last century of period mortality, with cohort mortality approaching the same limits. Both Gompertzian and non-Gompertzian senescent mortality are consistently present, with the estimated balance between them oscillating constantly. While the parameters of the latter appear to be trending over time, the parameters of the former do not.     

Higher female than male mortality in some countries of South Asia: a digest

A statistical study was made of sex ratios and mortality in Ceylon, Pakistan, and India. Contrary to general expectations, female mortality was higher than male mortality. A greater divergence in the sex ratio was found with increased age. Female emigration and abnormal sex ratios at birth are discounted as explanations of the phenomenon. It is considered that underenumeration of females in the census and higher female mortality rates, especially during the reproductive years and childhood, are responsible for the inverted sex ratio. The projected sex ratios for these countries are not reflected in the model life tables derived from international experience.     

The Risk of a Mortality Catastrophe

We develop a continuous-time model for analyzing and valuing catastrophe mortality contingent claims based on stochastic modeling of the force of mortality. We derive parameter estimates from a 105-year time series of U.S. population mortality data using a simulated maximum likelihood approach based on a particle filter. Relying on the resulting parameters, we calculate loss profiles for a representative catastrophe mortality transaction and compare them to the “official” loss profiles that are provided by the issuers to investors and rating agencies. We find that although the loss profiles are subject to great uncertainties, the official figures fall significantly below the corresponding risk statistics based on our model. In particular, we find that the annualized incidence probability of a mortality catastrophe, defined as a 15% increase in aggregated mortality probabilities, is about 1.4%—compared to about 0.1% according to the official loss profiles.     

有限数据下Lee-Carter模型在人口死亡率预测中的应用

Lee-Carter模型是当今世界上最流行的死亡率建模与预测模型,传统的Lee-Carter模型在样本量很大时才能得到较好的效果,而中国的死亡率数据量较少,且部分年限的数据缺失,从而难以达到较好的预测效果。本文基于Li等(2004)提出的有限数据死亡率建模方法,同时考虑样本量不足的影响,采用韩猛等(2010)提出的“双随机过程”建模,构建了有限数据下中国人口死亡率的预测模型,并用于对未来死亡率变动趋势和人口寿命的预测,最后将预测结果与保险公司采用的死亡率改善因子以及社会养老保险个人账户中采用的计发月数进行对比分析,给出了若干相关结论和有关死亡率风险管理的建议。     

Mortality and life expectancy of the population in the active ages

The author analyzes recent mortality trends in the USSR. Differences according to sex, Union republic, and urban or rural area are examined. Reasons for increased mortality rates are considered, and primary causes of death are described.     

Tracing studies and analysis of the effect of loss to follow-up on mortality estimation from patient registry data

Summary. Before patient registries are used for studies of the long-term mortality that is associated with chronic medical conditions, the potential bias resulting from patients who become lost to follow-up must be investigated. A study design, used for a systemic lupus erythematosus patient registry, is described. The design involves tracing patients who are defined as 'lost to follow-up' according to specific criteria. This provides supplementary information on the mortality experience of patients who are lost to (regular) follow-up. Some methods of analysis are described, based on comparing the mortality experience of patients when under regular follow-up with the experience of patients after they are deemed to be lost to follow-up. The effect of loss to follow-up, death reporting and visits to the clinic on estimation procedures is illustrated and recommendations are made for patient registries which are to be used in mortality studies.