The compression of deaths above the mode

Kannisto (2001) has shown that as the frequency distribution of ages at death has shifted to the right, the age distribution of deaths above the modal age has become more compressed. In order to further investigate this old-age mortality compression, we adopt the simple logistic model with two parameters, which is known to fit data on old-age mortality well (Thatcher 1999). Based on the model, we show that three key measures of old-age mortality (the modal age of adult deaths, the life expectancy at the modal age, and the standard deviation of ages at death above the mode) can be estimated fairly accurately from death rates at only two suitably chosen high ages (70 and 90 in this study). The distribution of deaths above the modal age becomes compressed when the logits of death rates fall more at the lower age than at the higher age. Our analysis of mortality time series in six countries, using the logistic model, endorsed Kannisto’s conclusion. Some possible reasons for the compression are discussed.compression of mortality, lexis model, logistic model, modal age of death, oldest old mortality decline, standard deviation

ICC-dementia (International Centenarian Consortium - dementia): an international consortium to determine the prevalence and incidence of dementia in centenarians across diverse ethnoracial and sociocultural groups.

BACKGROUND: Considerable variability exists in international prevalence and incidence estimates of dementia. The accuracy of estimates of dementia in the oldest-old and the controversial question of whether dementia incidence and prevalence decline at very old age will be crucial for better understanding the dynamics between survival to extreme old age and the occurrence and risk for various types of dementia and comorbidities. International Centenarian Consortium - Dementia (ICC-Dementia) seeks to harmonise centenarian and near-centenarian studies internationally to describe the cognitive and functional profiles of exceptionally old individuals, and ascertain the trajectories of decline and thereby the age-standardised prevalence and incidence of dementia in this population. The primary goal of the ICC-Dementia is to establish a large and thorough heterogeneous sample that has the power to answer epidemiological questions that small, separate studies cannot. A secondary aim is to examine cohort-specific effects and differential survivorship into very old age. We hope to lay the foundation for further investigation into risk and protective factors for dementia and healthy exceptional brain ageing in centenarians across diverse ethnoracial and sociocultural groups. METHODS: Studies focusing on individuals aged ≥95 years (approximately the oldest 1 percentile for men, oldest 5th percentile for women), with a minimum sample of 80 individuals, including assessment of cognition and functional status, are invited to participate. There are currently seventeen member or potential member studies from Asia, Europe, the Americas, and Oceania. Initial attempts at harmonising key variables are in progress. DISCUSSION: General challenges facing large, international consortia like ICC-Dementia include timely and effective communication among member studies, ethical and practical issues relating to human subject studies and data sharing, and the challenges related to data harmonisation. A specific challenge for ICC-Dementia relates to the concept and definition of'abnormal' in this exceptional group of individuals who are rarely free of physical, sensory and/or cognitive impairments

Trends in healthy life expectancy in Hong Kong SAR 1996–2008

Although Hong Kong has one of the best life expectancy (LE) records in the world, second only to Japan for women, we know very little about the changes in the health status of the older adult population. Our article aims to provide a better understanding of trends in both chronic morbidity and disability for older men and women. The authors compute chronic morbidity-free and disability-free life expectancy and the proportion of both in relation to total LE using the Sullivan method to examine whether Hong Kong older adults are experiencing a compression of morbidity and disability and whether there is any gender difference in relation to mortality and morbidity. The results of this study show that Hong Kong women tend to outlive Hong Kong men but are also more likely to suffer from a ‘double disadvantage’, namely more years of life with more chronic morbidity and disability. There has also been a significant expansion of chronic morbidity, as chronic morbidity-free life expectancy (CMFLE) decreased substantially for both genders from 1996 to 2008. Although disability-free life expectancy (DFLE) increased during this period, it increased at a slower pace compared to LE. The proportion of life without chronic morbidity also declined remarkably during these 12 years. Among the advanced ages, the proportion of remaining life in good health without disability has decreased since 1996, indicating a relative expansion of disability

Scalar expansion and normal longevity in Hong Kong

This thesis first establishes a theoretical platform by reviewing and synthesizing the debates over the rectangularization of the survival curve and its links to the limits to life expectancy. An improved approach to normal life durations has been conceptually developed and empirically tested in relation to the limits to human longevity. Three dimensions have been proposed to disentangle the complexity of the transformations of the survival curve (1) horizontalization (2) verticalization and (3) longevity extension. The second purpose is to provide an analytical assessment of different indicators for measuring the transformations of the survival curve and the compression of mortality. The most relevant indicators, proposed and selected, are the horizontal “N” index, C50, the prolate index K and the prolate “N” index, four standard deviations above the mode for measuring the maximum life span within normal life durations and the mode. Building on the work of Comfort (1964) “scalar expansion of the survival curve” and the last work of Kannisto (2001) “invisible wall”, testable hypotheses are formulated and tested for examining the limits to normal longevity. A complete set of “Normal” indicators (i.e., late mode (M), standard deviation above the late mode (SD(M+)), four standard deviations from the late mode (4SD(M+)) indicating minimum life span and maximum life span in the normal distribution) has been proposed. Based on the normal approach, I also introduce the impact of the elimination of cancer and heart diseases on normal life durations rather than just examining its impact on the mean longevity. More importantly, this approach provides an alternative to estimate the lower bound of deaths related to the ageing process. Using newly constructed life tables for Hong Kong 1976-2001, the empirical results reveal that the survival curve is more horizontal than vertical and the increase in the maximum normal longevity becomes stagnate, particularly for females in the period of 1996-2001 remaining at age 117.7. The findings are in favour of hypothesis 2 - a distant invisible wall in which M has been increasing monotonically, whereas SD(M+) and 4SD(M+) decrease at a steady pace over time, denoting that more Hong Kong people die at similar advanced ages under normal life durations unaffected by premature deaths. The combination of the increase in M in synergy with the decrease in SD(M+) accentuates the increase in the age corresponding to the minimum life span, a sign of postponed ageing process. Symmetrically, the fall in SD(M+) exactly compensates the rise in M resulting in a constant or slowly mounting maximum life span, disclosing an invisible wall. Following this pattern, the survival curve will be completely rectangular when a convergence takes place in which the maximum normal longevity reaches 121 years, M and the minimum life span converge to the maximum normal longevity and SD(M+) becomes zero for both sexes in Hong Kong by the year of 2126. Key words: Rectangularization, Survival curve, Indicators, Limits, Human longevity, Normal life durations, Hong Kon

Arthur Roger Thatcher's contributions to longevity research: A Reflexion

Arthur Roger Thatcher, CB, died in London on February 13, 2010, at 83 years of age. He was actively engaged in demographic research until his death. One of his last papers, The Compression of Deaths above the Mode, is published in this volume of Demographic Research (Thatcher et al., 2010). Roger signed the copyright agreement for the paper on January 24, just a few weeks before his death. Another contribution will appear in a forthcoming monograph entitled Supercentenarians (Maier et al., 2010). In this note, we, the co-authors of his Demographic Research paper, will briefly review his remarkable research accomplishments. Roger Thatcher was born in Birmingham in 1926. He worked for 26 years as a statistician in several national government offices. Later, he served as Registrar General for England and Wales, and was Director of the Office of Population Censuses and Survey (OPCS) from 1978 to 1986. A short description of his professional career up to his retirement can be found in Population Trends (1986). He had a long-standing affinity for the history of actuarial sciences and statistics in England, taking particular interest in the early years of the Statistical Society of London, and helping to compile extracts from its 1830s Proceedings (see Boreham et al., 1988 and Rosenbaum, 2001). He published a historical abstract (1970) of British labour-force statistics back to 1886. Thatcher was also a scientist with broad interests, publishing papers in a wide range of fields, such as archaeology, mathematics (number theory), and cosmology (1972, 1973 and 1982)

Modal age at death: lifespan indicator in the era of longevity extension. Vienna Yearbook of Population Research|Vienna Yearbook of Population Research 2013 11|

This paper examines and demonstrates the importance of the adult modal age at death (M) in longevity research. Unlike life expectancy at birth (e0) and median age at death, M is determined solely by old-age mortality as far as mortality follows a bathtub curve. It represents the location of old-age death heap in the age distribution of deaths, and captures mortality shifts more accurately than conditional life expectancies such as e65. Although M may not be directly determined from erratic mortality data, a recently developed method for deriving M from the P-spline-smoothed mortality curve based on penalised Poisson likelihood is highly effective in estimating M. Patterns of trends and differentials in M can be noticeably different from those in other lifespan measures, as indicated in some examples. In addition, major mathematical models of adult mortality such as the Gompertz, logistic and Weibull models can be reformulated using M, which plays a critical role as the mortality level parameter in those models

Exemplary Care among Chinese Dementia Familial Caregivers

Objective: This study investigates the feasibility of using the Exemplary Care Scale (ECS) among Chinese dementia familial caregivers, and reports its psychometric properties. Method: Back translation was used to develop the Chinese version of ECS (C-ECS). Three hundred and ninety-seven dyads of caregivers and their relatives with dementia responded to an assessment battery which included questions on care recipients’ cognition, behavioral and psychological symptoms, daily activities assistance, social support, and caregiver well-being. Results: Results of an exploratory principal component analysis revealed two subscales in the 11-item C-ECS: considerate caregiving and preserving esteem. C-ECS and its subscales demonstrated sufficient reliability, as well as criteria-related validity through its association with care recipient’s cognition and health, and caregivers’ well-being and social support. Discussion: Our findings provide preliminary support to C-ECS as a reliable and valid measure of exemplary caregiving among Hong Kong Chinese familial dementia caregivers. In the light of the increasing importance of familial care in dementia care planning, we recommend the use of this brief scale in regular caregiver assessment in research and service delivery