ESTIMATING PROCESSES OF COUNTS FROM CROSS-SECTIONAL AGGREGATE DATA, WITH AN APPLICATION TO MULTISTATE LIFE TABLES AND HEALTH EXPECTANCIES

This paper discusses the estimation of time‐dependent probabilities of a finite state‐space discrete‐time process using aggregate cross‐sectional data. A large‐sample version of multistate logistic regression is described and shown to be useful for analysing multistate life tables. The technique is applied to the estimation of disability‐free, severely disabled and other disabled survival curves and health expectancies in Australia, based on data from national health surveys in 1988, 1993 and 1998. A conclusion is that there has been a general upward trend in the future time expected to be spent in a state of disability, the picture being more pessimistic for males than females. For example, during 1988‐1998 the estimated increase in male life expectancy at birth of 2.7 years is decomposed as a decrease of 1.2 years in disability‐free health (life) expectancy and increases of 1.3 and 2.6 years, respectively, in states of severe disability and other disability.     

Incidence-based estimates of life expectancy of the healthy for the UK: coherence between transition probabilities and aggregate life-tables

Summary.  Will the UK's aging population be fit and independent, or suffer from greater chronic ill health? Life expectancy of healthy people represents the expected number of years of healthy well-being that a life-table cohort would experience if age-specific rates of mortality and disability prevailed throughout the cohort's lifetime. Robust estimation of this life expectancy is thus essential for examining whether additional years of life are spent in good health and whether life expectancy is increasing faster than the decline of rates of disability. The paper examines a means of generating estimates of life expectancy for people who are healthy and unhealthy for the UK that are consistent with exogenous population mortality data. The method takes population transition matrices and adjusts these in a statistically coherent way so as to render them consistent with aggregate life-tables.     

Women in the nation

A selection of statistical data on women in the former Soviet Union is presented for the years 1979, 1989, 1990, and 1991. The data concern number of women by republic and by age group; marriage, divorce, and birth rates; number of household members and singles; infant mortality; abortion and natality; life expectancy; single mothers; education; and employment.     

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.     

Analysis of functional status transitions by using a semi-Markov process model in the presence of left-censored spells

Summary.  To analyse functional status transitions in the older population better, we fit a semi-Markov process model to data from the 1992–2002 Medicare Current Beneficiary Survey. We used an analogue of the stochastic EM algorithm to address the problem of left censoring of spells in longitudinal data. The iterative algorithm converged robustly under various initial values for the unobserved elapsed durations of spells in progress at base-line. Results on life expectancy and recovery from functional limitations based on the semi-Markov process model differ from those based on the traditional multistate life-table method. The proposed treatment of left-censored spells has the potential to expand the modelling capability that is available to researchers in fields where left censoring is a concern.     

Estimation of long-term trends and variation in avian survival probabilities using random effects models

We obtained banding and recovery data from the Bird Banding Laboratory (operated by the Biological Resources Division of the US Geological Survey) for adults from 129 avian species that had been continuously banded for > 24 years. Data were partitioned by gender, banding period (winter versus summer), and by states/provinces. Data sets were initially screened for adequacy based on specific criteria (e.g. minimum sample sizes). Fifty-nine data sets (11 waterfowl species, the Mourning Dove and Common Grackle) met our criteria of adequacy for further analysis. We estimated annual survival probabilities using the Brownie et al. recovery model {St, ft} in program MARK. Trends in annual survival and temporal process variation were estimated using random effects models based on shrinkage estimators. Waterfowl species had relatively little variation in annual survival probabilities (mean CV = 8.7% and 10% for males and females, respectively). The limited data for other species suggested similar low temporal variation for males, but higher temporal variation for females (CV = 40%). Evidence for long-term trends varied by species, banding period and sex, with no obvious spatial patterns for either positive or negative trends in survival probabilities. An exception was Mourning Doves banded in Illinois/Missouri and Arizona/New Mexico where both males (slope = -0.0122, se = 0.0019 and females (slope = -0.0109 to -0.0128, se = 0.0018 -0.0032) exhibited declining trends in survival probabilities. We believe our approach has application for large-scale monitoring. However, meaningful banding and recovery data for species other than waterfowl is very limited in North America.     

ASSOCIATIONS BETWEEN AIR POLLUTION AND HOSPITAL VISITS FOR CARDIOVASCULAR DISEASES IN THE ELDERLY IN SYDNEY USING BAYESIAN STATISTICAL METHODS

Using generalized linear models (GLMs), Jalaludin  et al. (2006;  J. Exposure Analysis and Epidemiology   16 , 225–237) studied the association between the daily number of visits to emergency departments for cardiovascular disease by the elderly (65+) and five measures of ambient air pollution. Bayesian methods provide an alternative approach to classical time series modelling and are starting to be more widely used. This paper considers Bayesian methods using the dataset used by Jalaludin  et al.  (2006) , and compares the results from Bayesian methods with those obtained by Jalaludin  et al.  (2006) using GLM methods.     

Factors influencing Soay sheep survival

We present a survival analysis of Soay sheep mark recapture and recovery data. Unlike previous conditional analyses, it is not necessary to assume equality of recovery and recapture probabilities; instead these are estimated by maximum likelihood. Male and female sheep are treated separately, with the higher numbers and survival probabilities of the females resulting in a more complex model than that used for the males. In both cases, however, age and time aspects need to be included and there is a strong indication of a reduction in survival for sheep aged 7 years or more. Time variation in survival is related to the size of the population and selected weather variables, by using logistic regression. The size of the population significantly affects the survival probabilities of male and female lambs, and of female sheep aged 7 or more years. March rainfall and a measure of the North Atlantic oscillation are found to influence survival significantly for all age groups considered, for both males and females. Either of these weather variables can be used in a model. Several phenotypic and genotypic individual covariates are also fitted. The only covariate which is found to influence survival significantly is the type of horn of first-year female sheep. There is a substantial variation in the recovery probabilities over time, reflecting in part the increased effort when a population crash was expected. The goodness of fit of the model is checked by using graphical procedures.     

Objective Testing Procedures in Linear Models: Calibration of the p-values

Abstract.  An optimal Bayesian decision procedure for testing hypothesis in normal linear models based on intrinsic model posterior probabilities is considered. It is proven that these posterior probabilities are simple functions of the classical F -statistic, thus the evaluation of the procedure can be carried out analytically through the frequentist analysis of the posterior probability of the null. An asymptotic analysis proves that, under mild conditions on the design matrix, the procedure is consistent. For any testing hypothesis it is also seen that there is a one-to-one mapping – which we call calibration curve – between the posterior probability of the null hypothesis and the classical bi p -value. This curve adds substantial knowledge about the possible discrepancies between the Bayesian and the p -value measures of evidence for testing hypothesis. It permits a better understanding of the serious difficulties that are encountered in linear models for interpreting the p -values. A specific illustration of the variable selection problem is given.     

Women in the USSR

This is a selection of statistical data on women in the USSR; it covers the period 1970-1989. Tabular data are provided on the number of women by Union republic; the number of women and men by age group and rural or urban area; women's educational levels, sources of income, and occupations; family size for the whole country and for rural and urban areas; women's marital status by age; marriages and divorces; divorce by women's education, age, and number of children; birth rate by Union republic and by nationality; abortion and childbirth for selected years and by Union republic; maternal deaths by Union republic; infant deaths; and female life expectancy.     

A panel data analysis of the effects of wages, standard hours and unionization on paid overtime work in Britain

Summary.  This study examines the effects of the basic wage rate, standard working hours and unionization on paid overtime work in Britain by using individual level data from the New Earnings Survey over the period 1975–2001. For this purpose we estimate a panel data model. We show that to obtain consistent estimates it is important to allow for both the censoring of paid overtime hours at 0 and for correlations between the explanatory variables and unobserved individual-specific effects. The main empirical results are that a reduction in standard hours increases both the incidence of overtime and overtime hours, whereas an increase in the wage rate decreases the incidence of overtime but brings a small increase in overtime hours for those working overtime. For men the effects are stronger than for women. Union coverage is of minor empirical importance. The occupation and industry structure of employment has shifted from high to lower overtime jobs. Taken together, these economic variables can explain almost half of the changing incidence of overtime for men, and most of the change in overtime hours worked by women, but are less successful in explaining the changes in overtime hours worked by men or the incidence of overtime for women.     

Regional differences in life expectancy

An analysis of life tables constructed for the 49 voivodships of Poland for the years 1973-1975 and 1976-1980 is presented. The life tables have been prepared for periods of several years to avoid distortions due to data inadequacies for the smaller voivodships. The paper is in two parts: Part 2 is concerned with the major causes of death and the effect of their elimination on life expectancy.     

Clustering work and family trajectories by using a divisive algorithm

Summary.  We present an approach to the construction of clusters of life course trajectories and use it to obtain ideal types of trajectories that can be interpreted and analysed meaningfully. We represent life courses as sequences on a monthly timescale and apply optimal matching analysis to compute dissimilarities between individuals. We introduce a new divisive clustering algorithm which has features that are in common with both Ward's agglomerative algorithm and classification and regression trees. We analyse British Household Panel Survey data on the employment and family trajectories of women. Our method produces clusters of sequences for which it is straightforward to determine who belongs to each cluster, making it easier to interpret the relative importance of life course factors in distinguishing subgroups of the population. Moreover our method gives guidance on selecting the number of clusters.     

Unemployed and their caseworkers: should they be friends or foes?

Summary.  In many countries, caseworkers in public employment offices have dual roles of counselling and monitoring unemployed people. These roles often conflict, which results in important caseworker heterogeneity: some consider providing services to their clients and satisfying their demands as their primary task. However, others may pursue their own strategies, even against the will of the unemployed person. They may assign jobs and labour market programmes without the consent of the unemployed person. On the basis of a very detailed linked jobseeker–caseworker data set for Switzerland, we investigate the effects of caseworkers' co-operativeness on the probabilities of employment of their clients. Modified statistical matching methods reveal that caseworkers who place less emphasis on a co-operative and harmonic relationship with their clients increase their chances of employment in the short and medium term.     

Still-births among the offspring of male radiation workers at the Sellafield nuclear reprocessing plant: detailed results and statistical aspects

Summary. This study investigates whether there was evidence of increasing risk of still-birth with increasing paternal exposure to ionizing radiation received during employment at the Sellafield nuclear installation before the child was conceived. A significant positive association is found between the total paternal preconceptional exposure to external ionizing radiation and the risk of still-birth (after adjustment for year of birth, social class, birth order and paternal age, odds ratio at 100 mSv 1.24 (95% confidence interval 1.04–1.45)). A summary of the principal scientific findings of this study has been published in the Lancet . This paper describes in detail the statistical methods that were used in the investigation and presents the results in full.     

Does social mobility affect the size of the socioeconomic mortality differential?: evidence from the Office for National Statistics Longitudinal Study

The effect of social mobility on the socioeconomic differential in mortality is examined with data from the Office for National Statistics Longitudinal Study. The analyses involve 46 980 men aged 45–64 years in 1981. The mortality risk of the socially mobile is compared with the mortality risk of the socially stable after adjustment for their class of origin (their social class in 1971) and class of destination (their social class in 1981) separately. Among those in employment there is some evidence that movement out of their class of origin is in the direction predicted by the idea of health-related social mobility. This evidence, however, seems strongest for causes of death which are least likely to have been preceded by prolonged incapacity. Movement into the class of destination, however, shows the opposite relationship with mortality. Compared with the socially stable members of their class of destination, the upwardly mobile tend to have higher mortality and the downwardly mobile tend to have lower mortality. This relationship with the class of destination, it is suggested, may explain why socioeconomic mortality differentials do not widen with increasing age.     

Estimation of life expectancy in the Middle Ages

Summary. In the Middle Ages data on landholders were recorded. We use a selection of these data for estimating the life expectancy of adult males from the higher ranks of English society. The data consist of the age at which the landholder inherited land, a sequence of ages at which he was known to be alive and possibly the age at death. We explain that the date of death is left truncated and right censored at an unknown censoring time. We propose a model to fit (a selection of) the data, we give estimators of the unknown parameters in the model and we present estimates of adult life expectancy.     

基于VaR方法的长寿风险自然对冲模型

随着死亡率的下降与预期寿命的提高,保险公司面对着不容忽视的长寿风险。基于VaR方法探讨了长寿风险管理中的自然对冲策略,然后在对中国男性人口死亡率预测的基础上,给出了保险公司自然对冲长寿风险所需的最优产品结构,并进一步考查了利率、签单年龄、缴费方式等因素对最优产品结构的影响。     

Women in the USSR

This is a selection of statistical data on women from the 1989 Soviet census. The data include total female population by republic; rural and urban female population; women's age distribution, income, labor force participation, educational status, and life expectancy; marriage and divorce; birth weight of children born to unmarried women; induced abortion; maternal mortality; and infant mortality.     

Monitoring contemporary student flows and characteristics: secondary analyses using the Labour Force Survey and the General Household Survey

This paper examines trends in the participation in higher education by disadvantaged social groups over the recent period of higher education expansion and reform. It has been suggested that disadvantaged groups can recoup by participation at mature ages and this question is examined. The data sources used are the Labour Force Survey (1986–1995), which yielded 13384 students (6747 men and 6637 women) and the General Household Survey (1984–1992) which yielded 1936 students (982 men and 954 women). From a perspective of equal opportunities, the relative participation of young people from manual and non-manual origins does not appear to have changed over the period considered, but there is some evidence of increased relative participation by people from manual class origins as mature students. Mature students from such origins were older than those from non-manual class origins, as were mature women than mature men, with consequences for employability. From a perspective of lifelong learning, the recent expansion has been successful, with more entrants from the unemployed. Considerable percentages of women also enter from full-time housework, and increasing percentages from manual work. However, as in the past, many entrants had been successful in becoming employed before entry, some being seconded by employers. Despite these changes, the greatest absolute take-up has been from middle class youth. Early employment outcomes were examined and suggest some discrimination against mature students. It is possible that the increased cost of higher education, in the context of an expanded labour market of graduates, may deter some mature students.