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)."     

基于均衡关系的中国人口死亡率预测模型

人口死亡率反映了人口的死亡程度,准确预测死亡率是人口科学及人口经济学研究的重点之一,同时也是长寿风险测量的重要数据基础。基于Lee-Carter模型,探索中国大陆与台湾地区死亡率的相关性,通过协整分析考虑两地死亡率的长期均衡关系,创新性地建立基于相关性的向量误差修正模型(VECM),克服传统自回归移动平均模型(ARIMA)使用有限数据进行预测的局限性;均方预测误差作为检验标准,结果表明:基于VECM模型的预测效果比传统的预测效果更佳;基于中国大陆地区和台湾地区的死亡率长期均衡关系,可以为两地联合长寿债券的定价提供重要参考。     

Coherent mortality forecasting by the weighted multilevel functional principal component approach

In human mortality modelling, if a population consists of several subpopulations it can be desirable to model their mortality rates simultaneously while taking into account the heterogeneity among them. The mortality forecasting methods tend to result in divergent forecasts for subpopulations when independence is assumed. However, under closely related social, economic and biological backgrounds, mortality patterns of these subpopulations are expected to be non-divergent in the future. In this article, we propose a new method for coherent modelling and forecasting of mortality rates for multiple subpopulations, in the sense of nondivergent life expectancy among subpopulations. The mortality rates of subpopulations are treated as multilevel functional data and a weighted multilevel functional principal component (wMFPCA) approach is proposed to model and forecast them. The proposed model is applied to sex-specific data for nine developed countries, and the results show that, in terms of overall forecasting accuracy, the model outperforms the independent model and the Product-Ratio model as well as the unweighted multilevel functional principal component approach.     

On the use of surrogate end points in randomized trials

In a recent paper Day and Duffy proposed a strategy for designing a randomized trial of different breast cancer screening schedules. Their strategy was based on the use of predictors of mortality determined by patients' factors at diagnosis as surrogates for true mortality. On the basis of the Prentice criterion for validity of a surrogate end point, and data from earlier studies of breast cancer case survival, they showed that, not only would the trial require a much shorter follow-up, but also that the information (i.e. inverse variance) for evaluating a treatment effect on mortality would be greater by a factor of nearly 3 if the predictors of mortality were used, compared with a trial in which mortality was actually observed. Although these results are technically correct, we believe that the conceptual strategy on which they are based is flawed, and that the fundamental problem is the Prentice criterion itself. In this paper the technical issues are discussed in detail, and an alternative structure for evaluating the validity of surrogate end points is proposed.     

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。     

Measures of mortality in the study of individuals infected with the human immunodeficiency virus in the UK haemophilia population

Two statistical issues that have arisen in the course of a study of mortality and disease related to the human immunodeficiency virus (HIV) in the haemophilia population of the UK are discussed. The first of these concerns methods of standardization for age and it is shown that, when the mortality of HIV-infected individuals with different severities of haemophilia are compared, an analysis based on the ratio of observed to national expected deaths suggests that mortality in HIV-infected individuals depends on the severity of their haemophilia. This conclusion is inappropriate and mortality in HIV-infected individuals is, in fact, similar regardless of severity of haemophilia. The second part of the paper discusses the effect of using various end points for studies of survival and progression of HIV-related disease. In the present example it was possible to calculate relative survival in HIV-infected individuals, i.e. survival after correcting for mortality expected in the absence of HIV infection. An analysis based on absolute survival gave a very similar picture of the effect of age at infection to an analysis based on relative survival, whereas an analysis based on the time to diagnosis of acquired immune deficiency syndrome (AIDS) underestimated the effect substantially and the possible alternative end point of time to AIDS or HIV-related death was shown to be subject to considerable misclassification error.     

An uncertainty principle in demography and the unisex issue

"The purpose of this article is to show that if many characteristics affect the mortality of individuals, there are intrinsic limits to the ability of demographers to answer two elementary questions:" whether the force of mortality in the last year was more or less severe in one country relative to that in a second, and whether an individual's chance of survival would have been greater in one or the other of the two countries. The author notes that the conclusions are applicable to all demographic crude rates. "The possibility of encountering Simpson's paradox suggests that since sex is only one of many possible stratifying variables that appear to affect mortality, the use of mortality tables distinguished by sex and by no other variables is, in the absence of information about the importance of other variables, demographically arbitrary."     

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.     

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。     

Presentation of methods applied in the projection of infant mortality

The author describes a variety of analytical equations which attempt to determine the major factors influencing infant mortality in Poland during the period 1960-1980. The models' values for forecasting future trends in infant mortality are then discussed.     

The population of the USSR

Official population data for the USSR for 1986 and 1987 are presented. Tables are included on age and sex distribution; rural and urban population; birth, death, and natural increase rates, 1970-1986; fertility and mortality by sex, 1970-1986; birth order; age-specific birth rates by rural and urban area and Union republic; age-specific death rates, 1970-1986; infant mortality, 1970-1986; life expectancy, 1926-1986; life tables; marriage and age at marriage; and divorce.     

A comparison of models for dynamic life tables. Application to mortality data from the Valencia Region (Spain)

The graduation of mortality data aims to estimate the probabilities of death at age x, q ( x ), by means of an age-dependent function, whose parameters are adjusted from the crude probabilities that are directly obtainable from the data. However, current life tables have a problem, the need for periodic updates due to changes in mortality over short periods of time. The table containing mortality rates for different ages in different years, q ( xt ), is called a dynamic life table, which captures mortality variation over time. This paper proposes a review of the most commonly used dynamic models and compares the results obtained by each of them when applied to mortality data from the Valencia Region (Spain). The result of the comparison leads us to the conclusion that the Lee-Carter method offers the best results for both sexes, while that based on Heligman and Pollard functions provides the best fit for men alone. Our working method is of additional interest as it may be applied to mortality data for a wide range of ages in any geographical location, allowing the most appropriate dynamic life table to be selected for the case at hand.     

The impact of deviations from the definition of live births on the rate of infant mortality

It is first noted that the definition of a live birth in Poland includes both weight at birth and signs of life. The author contends that the weight measure is often inaccurate, especially near the 1,000 gram limit. The result is that the infant mortality rate is underestimated. Calculations of the upper and lower limits of infant mortality for various years are presented.     

Main changes and differentiations in the health status of Poland's population with allowances for international mortality comparisons

The health status of the population of Poland is analyzed for the postwar period, with emphasis on the 1980s. Trends in mortality, and particularly in excess male mortality, are described and compared with other European countries.     

Trends in inequality in infant mortality in the north of England, 1921–1973, and their association with urban and social structure

Summary.  The paper analyses a time series of infant mortality rates in the north of England from 1921 to the early 1970s at a spatial scale that is more disaggregated than in previous studies of infant mortality trends in this period. The paper describes regression methods to obtain mortality gradients over socioeconomic indicators from the censuses of 1931, 1951, 1961 and 1971 and to assess whether there is any evidence for widening spatial inequalities in infant mortality outcomes against a background of an overall reduction in the infant mortality rate. Changes in the degree of inequality are also formally assessed by inequality measures such as the Gini and Theil indices, for which sampling densities are obtained and significant changes assessed. The analysis concerns a relatively infrequent outcome (especially towards the end of the period that is considered) and a high proportion of districts with small populations, so necessitating the use of appropriate methods for deriving indices of inequality and for regression modelling.     

Establishing the nadir of the body mass index-mortality relationship: a case study

The relationship between body weight and mortality is examined using U.S. data from the National Health and Nutrition Examination Survey I (NHANES I) Epidemiologic Follow-up Study concerning 13,242 individuals, the emphasis being on identifying the body mass index associated with the lowest levels of mortality. Factors such as smoking status, sex, race, and age are taken into consideration. The results suggest that only the interaction between race and body mass index is significant.     

A tilting algorithm for the estimation of fractional age survival probabilities

Life tables used in life insurance determine the age of death distribution only at integer ages. Therefore, actuaries make fractional age assumptions to interpolate between integer age values when they have to value payments that are not restricted to integer ages. Traditional fractional age assumptions as well as the fractional independence assumption are easy to apply but result in a non-intuitive overall shape of the force of mortality. Other approaches proposed either require expensive optimization procedures or produce many discontinuities. We suggest a new, computationally inexpensive algorithm to select the parameters within the LFM-family introduced by Jones and Mereu (Insur Math Econ 27:261–276, 2000). In contrast to previously suggested methods, our algorithm enforces a monotone force of mortality between integer ages if the mortality rates are monotone and keeps the number of discontinuities small.     

Distributional results for special cases of the jolly-seber model

The multinomial-binomial approach to the Jolly-Seber capture- recapture model is used as a basis to derive explicit probability distributions for special cases of the Jolly-Seber model:no recruitment, or no mortality. Also given are the residual distributions that allow tests of these restricted models compared to the general Jolly-Seber model. Losses on capture are allowed. The special case distribution is also derived for no recruitment and no mortality, but allowing losses on capture; this is a generalized version of Darroch's closed capture-recapture model. Here, however, it was not possible to obtain a closed form residual distribution.     

Population growth among different nationalities in the USSR

The authors examine ethnic differences in population trends in the USSR using data from official sources, including the censuses from 1959 to 1989. They look at differentials in fertility, general mortality, and infant mortality and their causes. They also note that, out of the 18 major nationalities, 5 have reproduction rates below replacement level: Russians, Ukrainians, Georgians, Lithuanians, and Jews. Data are included on population size, growth rates, and fertility rates by ethnic group.