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What Difference Would It Make if Cancer Were Eradicated? An Examination of the Taeuber Paradox

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Abstract

The immediate effect of discovering a way to cure cancer would be a reduction in the number of deaths in the United States by the number of people now dying from that cause. Within a short time, however, deaths from other causes would increase, and the net long-term effect would be relatively small. A parameter is derived that measures how much the expectation of life is increased by a marginal reduction in any cause of death. That parameter is additive in the several causes and has other advantages, though it does not avoid the assumption of independence.

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... In this paper we take a closer look at the life table entropy and provide additional insights for understanding how it relates to changes in mortality and survival. Unlike previous work that relied on univariate calculus (e.g., Demetrius, 1974Demetrius, , 1975Demetrius, , 1976Demetrius, , 1978Demetrius, , 1979Goldman and Lord, 1986;Keyfitz, 1977), we provide a more rigorous development and a further description of the life table entropy using the calculus of variations. This approach has previously been used in demographic research (Arthur, 1984;Beltrán-Sánchez and Soneji, 2011;Preston, 1982), and as we show, it * Corresponding author. ...
... The life table entropy is commonly used throughout demography to study the relative changes in life expectancy associated with changes in age-specific mortality rates. In this section we review the construction of the entropy due to Keyfitz (1977) (see Appendix A.1 for a brief history), and then present our main analytical results. ...
... Consider now a relative increase ϵ > 0 in µ -that is, a proportional increase in µ at all ages -similar to that proposed by Keyfitz (1977). Then the new mortality function is (1 + ϵ)µ(s) (note that ∆µ = ϵµ, so that ∆µ/µ = ϵ), the new probability of surviving from birth to age x is Without loss of generality, let us specialize to the most studied case of life expectancy-life expectancy at birth: ...
Article
The life table entropy provides useful information for understanding improvements in mortality and survival in a population. In this paper we take a closer look at the life table entropy and use advanced mathematical methods to provide additional insights for understanding how it relates to changes in mortality and survival. By studying the entropy (H) as a functional, we show that changes in the entropy depend on both the relative change in life expectancy lost due to death (e(†)) and in life expectancy at birth (e0). We also show that changes in the entropy can be further linked to improvements in premature and older deaths. We illustrate our methods with empirical data from Latin American countries, which suggests that at high mortality levels declines in H (which are associated with survival increases) linked with larger improvements in e0, whereas at low mortality levels e(†) made larger contributions to H. We additionally show that among countries with low mortality level, contributions of e(†) to changes in the life table entropy resulted from averting early deaths. These findings indicate that future increases in overall survival in low mortality countries will likely result from improvements in e(†). Copyright © 2015. Published by Elsevier Inc.
... In other words, immediate effect of discovering a way to cure a disease would be a reduction in the number of deaths by the number of people now dying from that cause. Within a short time, however, deaths from other causes would increase because of universal law of "destruction of any thing created" and the net long-term effect would be relatively small (Keyfitz 1977). ...
... The most likely reason may be in the conceptual and computational simplicity attached to PYLL. The common applications have been in assessing gain in life expectancy after assumed elimination of a disease (Keyfitz, 1977;Tsai et al, 1978;Lai and Hardy, 1999), comparing the relative importance of different causes of death and ranking the different causes of death in terms of their effect on the society (Ramakrishna and Raman, 1972;Gupta and Rao, 1973;Mackenbach et al, 1999). ...
... That is why elimination of a particular cause raises the probability of death from other causes. Keyfitz (1977) rightly stated, the immediate effect of discovering a way to cure a disease would be a reduction in the number of deaths by the number of people now dying from that cause. Within a short time, however, deaths from other causes would increase, and the net long-term effect would be relatively small. ...
Thesis
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Knowledge of survival is essential in the community level management of a disease. Broadly, there are two approaches of population-based study of survival from a disease, the direct (i.e., classical) approach and the indirect approach. With classical approaches, survival studies deal with evaluating overall performance of a group of patients in terms of quality and quantity of life after diagnosis/treatment. There are numerous difficulties in the conduct of a population-based survival study in the context of developing countries, including India. While planning a population based survival study, one has to consider the possibility of a substantial amount of financial and other resources including the time required. Subsequently, loss to follow-up is a typical problem encountered in survival studies, causing biased estimates. In view of these difficulties with the classical approach, the overall aim of the present study was to propose an indirect methodology for the study of survival. Specific objectives were to a) suggest an indirect methodology for the study of survival, b) demonstrate empirical application of the methodology and c) validate the proposed methodology. Proposed methodology is based on life table techniques and uses current data on incidence and mortality from the disease. It involves the estimation of expected years free of disease (EYFD), expected years with disease (EYWD), expected years of life lost (EYLL) and average duration of disease (ADD) and their comparison over a time period. Empirical application was carried out for mouth and lung cancers in males and cancers of breast and cervix in females as well as for all sites combined together in each sex. Cancer incidence and mortality data by age and sex for the years 1989, 1993, 1997 and 2001 were obtained from published reports of Mumbai Cancer Registry, India. All causes of deaths for these years were obtained from Mumbai Municipal Corporation. Three life tables were constructed by applying various attrition factors: (a) risk of death from all causes; (b) risk of incidence and that of death from other causes; and (c) risk of death from other causes only. The expectation of life from the second life table gave EYFD. EYWD and EYLL were calculated by suitable subtractions among three expectations of life. ADD was calculated by dividing person years lived with disease by number developing the disease. In order to arrive at total number developing the disease, a break-up of those arriving to the last open-end age interval in second life table was required. The break-up was required into those developing and those not developing the disease before dying. This was obtained by employing an iteration procedure. It was noted that during 1993-2001, EYFD for all sites increased from 59.4 to 62.1 and from 63.8 to 66 years in males and females respectively. EYLL was about 0.8 year in males and 1 year in females. Similarly, EYWD was 0.6 and 1 year in males and females respectively. ADD for all sites varied from 4 to 4.7 years in both sexes. It was about 6 years for mouth cancers and 2 years for lung cancers in males and 4-5 years for breast and cervical cancers in females. An indication of improvement in survival indices was observed in females. Given the difficulties in conduct of classical survival studies, the proposed method may provide a useful tool for the study of survival, especially for ’all sites’ and major sites of cancer, viable for the developing countries. Proposed method may also be useful in having a regular audit of the prognostic factors prevailing in a population. Further, it also has potentials to be utilized for the estimation of various indices of burden of disease, like, PYLL, DALY, etc.
... Keyfitz' entropy is a dimensionless indicator of the relative variation in the length of life compared to life expectancy (Keyfitz 1977;Demetrius 1978). It is usually defined as ...
... In this paper, we bring both perspectives together and shed light on the dynamics behind changes in Keyfitz' entropy. Keyfitz (1977) first proposedH as a life table function that measures the change in life expectancy at birth consequent on a proportional change in age-specific rates. Since then, several authors have been interested in this measure and its use (Demetrius 1978(Demetrius , 1979Mitra 1978;Goldman and Lord 1986;Vaupel 1986;Hakkert 1987;Hill 1993;Fernández and Beltrán-Sánchez 2015). ...
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BACKGROUND Indicators of relative inequality of lifespans are important because they capture the dimensionless shape of aging. They are markers of inequality at the population level and express the uncertainty at the time of death at the individual level. In particular, Keyfitz' entropy $\bar{H}$ represents the elasticity of life expectancy to a change in mortality and it has been used as an indicator of lifespan variation. However, it is unknown how this measure changes over time and whether a threshold age exists, as it does for other lifespan variation indicators. RESULTS The time derivative of $\bar{H}$ can be decomposed into changes in life disparity $e^\dagger$ and life expectancy at birth $e_o$. Likewise, changes over time in $\bar{H}$ are a weighted average of age-specific rates of mortality improvements. These weights reflect the sensitivity of $\bar{H}$ and show how mortality improvements can increase (or decrease) the relative inequality of lifespans. Further, we prove that $\bar{H}$, as well as $e^\dagger$, in the case that mortality is reduced in every age, has a threshold age below which saving lives reduces entropy, whereas improvements above that age increase entropy. CONTRIBUTION We give a formal expression for changes over time of $\bar{H}$ and provide a formal proof of the threshold age that separates reductions and increases in lifespan inequality from age-specific mortality improvements.
... The lifetable entropy is a dimensionless indicator of the relative variation in the length of life compared to life expectancy at birth (Leser 1955;Keyfitz 1968Keyfitz , 1977Demetrius 1974Demetrius , 1978. It is usually defined as ...
... Leser (1955) first derived the lifetable entropy as the elasticity of life expectancy. Keyfitz (1977) proposed H as a lifetable function "that measures the change in life expectancy at birth consequent on a proportional change in age-specific rates" (Keyfitz 1977: 413). Since then, several authors have been interested in this measure and its use (Demetrius 1978(Demetrius , 1979Mitra 1978;Goldman and Lord 1986;Vaupel 1986;Hakkert 1987;Hill 1993;Fernández and Beltrán-Sánchez 2015). ...
... The lifetable entropy is a dimensionless indicator of the relative variation in the length of life compared to life expectancy at birth (Leser 1955;Keyfitz 1968Keyfitz , 1977Demetrius 1974Demetrius , 1978. It is usually defined as ...
... Leser (1955) first derived the lifetable entropy as the elasticity of life expectancy. Keyfitz (1977) proposed H as a lifetable function "that measures the change in life expectancy at birth consequent on a proportional change in age-specific rates" (Keyfitz 1977: 413). Since then, several authors have been interested in this measure and its use (Demetrius 1978(Demetrius , 1979Mitra 1978;Goldman and Lord 1986;Vaupel 1986;Hakkert 1987;Hill 1993;Fernández and Beltrán-Sánchez 2015). ...
Article
Full-text available
Background: Indicators of relative variation of lifespans are markers of inequality at the population level and of uncertainty at the time of death at the individual level. In particular, the lifetable entropy H represents the elasticity of life expectancy to a change in mortality. However, it is unknown how this measure changes over time and whether a threshold age exists, as it does for other lifespan variation indicators. Results: The time derivative of H can be decomposed into changes in life disparity e† and life expectancy at birth eo. Likewise, changes over time in H are a weighted average of age-specific rates of mortality improvements. These weights reflect the sensitivity of H and show how mortality improvements can increase (or decrease) the relative inequality of lifespans. Further, we prove that in the assumption that mortality is reduced at all ages, H, as well as e†, has a threshold age below which saving lives reduces entropy, whereas improvements above that age increase entropy. Contribution: We give a formal expression for changes of H over time and provide a formal proof of the existence of a unique threshold age that separates reductions and increases in lifespan variation as a result age-specific mortality improvements.
... The conventional view is that, in a case of such dependence, the effect of cancer eradication on life expectancy would be even smaller. As Keyfitz (1977) wrote: "since the most common kind of dependence must be a positive one, people saved from cancer would be more susceptible to heart and other diseases". The directions (positive or negative) of correlations among diseases can be empirically estimated using data on multiple causes of death. ...
... Additional analyses show that mortality from cancer may have a positive correlation with some diseases as Keyfitz (1977) expected. The presence of such a correlation may mask the effects of reducing mortality from cancer on total mortality and life expectancy for certain treatment strategies. ...
Article
Demographic calculations evaluating the role of chronic diseases in life expectancy use the assumption that diseases are independent. Disease independence was a plausible hypothesis in the era of infectious diseases. However, the health problems of modern populations are closely connected with diseases of the elderly i.e., with chronic non-communicable diseases that often have common risk factors. The existence of such common genetic and non-genetic risk factors makes chronic diseases mutually dependent. In this chapter, we provide evidence of trade-offs between cancer and other diseases as well as between cancer and aging changes. The Multiple Cause of Death data are used to evaluate correlations among mortality rules from cancer and other major health disorders, including heart disease, stroke, diabetes, Alzheimer’s and Parkinson’s diseases, and asthma. Significant negative correlations between cancer and some of the selected diseases are detected. These correlations show regular patterns of change over time. The chapter describes possible mechanisms of disease dependence including pleiotropic effects of genetic factors and discusses appropriate methods of statistical analysis of disease dependence.
... More than 250 years ago, Bernoulli and d'Alembert investigated the impact on survivorship and life expectancy by eliminating a cause of death (Karn 1931). More recently, changes in life expectancy due to small proportional changes in the total or cause-specific mortality have been described by Keyfitz (1977Keyfitz ( , 1985, Vaupel (1986), and Vaupel and Canudas Romo (2003). These and other results have been summarized by Wrycza and Baudisch (2012), who also present results on changes in life expectancy that are introduced by other types of perturbations in age-specific mortality. ...
Article
BACKGROUND Demographers and epidemiologists have investigated the dependence of life expectancy on proportional changes in the age-specific mortality. OBJECTIVE To develop an approach that allows estimation of change in life expectancy from proportional changes in age-specific mortality and to identify aspects of the death rate that influence the accuracy of the estimation. RESULTS We obtain an exact expression for the first derivative of the life expectancy with respect to the proportional change in age-specific mortality when the age-specific death rate is log-linear in age. We use the result to establish bounds for the change in life expectancy following a proportional change of the mortality. The result shows that the change in life expectancy is approximately linear in the logarithm of the proportional change of the mortality. In populations with low infant mortality, the slope of this linear relationship is essentially equal to minus the inverse of the slope of the log-linear age dependence of the death rate. CONTRIBUTION In a wide range of mortality scenarios, the relationship between change in life expectancy and the logarithm of the proportional change of the mortality allows accurate approximation of a difference in life expectancy from a ratio of death rates.
... In order to explain the dynamics behind changes in mortality, demographers have developed several techniques to decompose changes in life expectancy by different components of mortality, such as ages and causes of death. Some methods focus on discrete differences between two life expectancies (Pollard 1982; Arriaga 1984; Pressat 1985; Andreev, Shkolnikov, and Begun 2002; Firebaugh et al. 2014) while others consider continuous changes (Vaupel 1986; Keyfitz 1977; Vaupel and Canudas-Romo 2003; Beltrán-Sánchez, Preston, and Canudas-Romo 2008; Horiuchi, Wilmoth, and Pletcher 2008). We follow the latter approach of a continuous decomposition of changes in life expectancy by variability and shifting effects using a recent expression of the Gompertz mortality model. ...
Article
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Background In most developed countries, mortality reductions in the first half of the 20th century were highly associated with changes in lifespan disparities. In the second half of the 20th century, changes in mortality are best described by a shift in the mortality schedule, with lifespan variability remaining nearly constant. These successive mortality dynamics are known as compression and shifting mortality, respectively. Objective To understand the effect of compression and shifting dynamics on mortality changes, we quantify the gains in life expectancy due to changes in lifespan variability and changes in the mortality schedule, respectively. Methods We introduce a decomposition method using newly developed parametric expressions of the force of mortality that include the modal age at death as one of their parameters. Our approach allows us to differentiate between the two underlying processes in mortality and their dynamics. Results An application of our methodology to the mortality of Swedish females shows that, since the mid-1960s, shifts in the mortality schedule were responsible for more than 70% of the increase in life expectancy. Conclusions The decomposition method allows differentiation between both underlying mortality processes and their respective impact on life expectancy, and also determines when and how one process has replaced the other.
... For example, this approach has been widely used in past cause-elimination and cause-delay models; see e.g. Keyfitz (1977), Tsai et al. (1978), Manton et al. (1980b), Olshansky (1987Olshansky ( , 1988, and Manton (1991), amongst others. Since 1968, the United States decennial life tables have been published with a special report that focuses on the impact of eliminating causes using Chiang's approach (which will also be referred to as the force of mortality approach or the instantaneous approach); see Bayo (1968), Greville et al. (1975), Curtin and Armstrong (1988), Anderson (1999). ...
Article
The analysis of causal mortality provides rich insight into changes in mortality trends that are hidden in population level data. Therefore, we develop and apply a multinomial logistic framework to model causal mortality. We use internationally classified cause-of-death categories and data obtained from the World Health Organization. Inherent dependence amongst the competing causes is accounted for in the framework, which also allows us to investigate the effects of improvements in, or the elimination of, cause-specific mortality. This has applications to scenario-based forecasting often used to assess the impact of changes in mortality. The multinomial model is shown to be more conservative than commonly used approaches based on the force of mortality. We use the model to demonstrate the impact of cause-elimination on aggregate mortality using residual life expectancy and apply the model to a French case study.
... Life table entropyH is the elasticity of life expectancy with respect to a proportional change in mortality. This was first derived by Leser (1955), and was restated by Keyfitz (1977aKeyfitz ( , 1977b in continuous formulation. Demetrius (1974Demetrius ( , 1975Demetrius ( , 1976Demetrius ( , 1979 applied information theory in both biology and demography, andH was one of the quantities he used. ...
Article
Background: Life table entropy is a quantity frequently used in demography; e.g., as a measure of heterogeneity in age at death, or as the elasticity of life expectancy with regards to proportional changes in age-specific mortality. It is therefore instructive to calculate its value for the widely used Gompertz-Makeham mortality model. Objective: I present and prove a simple expression of life table entropy for the Gompertz-Makeham model, which ties together the parameters of the model with demographically relevant quantities. Comments: The relationship shows that entropy is easily calculated from the parameters of the given model, life expectancy e0 and the average age in the stationary population χ. The latter enters the equation only if the Makeham term c is different from zero.
... Consequently, human life expectancy has extended to reach its current levels. Nevertheless, referring to the measure of mortality entropy developed by Keyfitz (1977), Olshansky, Rudberg, Carnes, Cassel and Brody (1991) and Olshansky, Carnes and Désesquelles (2001) argued that further declines in mortality would produce a diminishing effect on human longevity for populations with life expectancies at birth reaching or surpassing 80 years. The aging of organism can be related to a finite number of cell divisions (Hayflick 1965). ...
Article
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The mortality declines since 1750 have transformed the nations to a state far apart from what they were previously. With the long-term trends in life expectancy at birth in the developed world consistently increasing, a "new converging world" is likely emerging. However, the possibility of trading-off health for longevity looms ahead. Based on previous findings of a possible expansion of morbidity in Taiwan over the past decade, this paper focuses on cancer prevalence in order to examine the substitution of morbidity for fatality. Given a definition of the cancer prevalence growth rate, we explain that cancer fatality is inversely related to the prevalence growth. Using data on the number of cancer patients being actively treated from National Health Insurance (NHI) claim records, of people who have died of cancer and other causes from the national death registry, and newly diagnosed cases from the national cancer registry, we determined that, while the contribution of new cases is decreasing, the prevalence of cancer has increased over the past decade. We further determined that the increase in the prevalence of cancer is primarily the result of decreasing fatality with the cure of cancer playing a minor role in the process. The substitution of cancer prevalence for fatality is established.
... Methods to calculate such contributions have been developed by a United Nations (1982) report, Pollard (1982Pollard ( , 1988, Arriaga (1984), Pressat (1985) and Andreev (1982), see also Andreev et al. (2002), who focused on the difference in life expectancy between two periods of time. Keyfitz (1977Keyfitz ( , 1985 considered continuous change and derived a formula that relates the time-derivative of life expectancy to the entropy of life table survivorship, although not as a general method of decomposition. More recently, efforts have also been taken to calculate cause-decomposition considering continuous change (Vaupel andCanudas-Romo 2003, Beltran-Sanchez et al. 2008). ...
Article
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BACKGROUND A new measure of the number of life years lost due to specific causes of death is introduced. METHODS This measure is based on the cumulative incidence of death, it does not require "independence" of causes, and it satisfies simple balance equations: "total number of life years lost = sum of cause-specific life years lost", and "total number of life years lost before age x + temporary life expectancy between birth and age x = x". RESULTS The measure is contrasted to alternatives suggested in the demographic literature and all methods are illustrated using Danish and Russian multiple decrement life-tables.
... is the elasticity of life expectancy with respect to a proportional change in mortality. This was first derived by Leser (1955), and was restated by Keyfitz (1977aKeyfitz ( ,1977b in a continuous formulation. Mitra (1978), Goldman and Lord (1986) and Vaupel (1986) independently derived the mathematical expression for life disparity e † , and showed that H = e † /e 0 . ...
Article
Background: Variance in life span σ2 and life expectancy lost due to death e† are important demographic indicators of life disparity. Objective: I show that the variance in age at death equals the average squared remaining life expectancy at death. Based on this finding, I also show that the average squared difference in remaining life expectancy at death equals the difference between σ2 and e†2. Comments: Calculations of some of the quantities involved for the Gompertz-Makeham mortality model with varying parameters produce complex patterns.
... Várias são as críticas que se fazem a este modelo, entre as quais podemos destacar aquelas que consideram que a hipótese de atribuir a morte a uma única causa seria insatisfatória, pois a morte de um indivíduo pode ser devida à interação de vários riscos de morte (Guralnick, 1965); e de eliminar totalmente uma determinada causa de morte (Wong, 1977;Keyfitz, 1977;Tsai, Lee, 1975;. É possível que seja mais prático em termos de políticas e/ou atitudes de saúde pública a serem tomadas o conhecer os efeitos da redução parcial de uma causa de morte, em vez de sua total eliminação. ...
Article
A mortalidade infantil, calculada a partir da relação entre o número de óbitos de menores de um ano e o de nascidos vivos, além de ser um dos indicadores clássicos da saúde, também é muito utilizada como indicador das condições sócio-econômicas de um país ou região. Geralmente seus níveis são associados com o grau de desenvolvimento das áreas pesquisadas e com as condições de vida das diferentes camadas sociais, culturais e econômicas da população (Laurenti, 1975; Taucher, 1979). Embora não exista uma teoria geral sobre os condicionan-tes que determinam a mortalidade e os mecanismos pelas quais elas atuam, diversos modelos tem sido elaborados na tentativa de explicar o processo saúde-doença-morte dos menores de um ano. Meegama, no modelo analítico proposto para estudar a mortalidade neonatal, (Meegama, 1980), considera quatro tipos de fatores: • fatores que podem ser eliminados através de medidas preventivas; • fatores relacionados com medidas curativas; • variáveis demográficas: idade da mãe, por exemplo; • causas de morte congênitas. XI Encontro Nacional de Estudos Populacionais da ABEP 1783 1 Chefe da Divisão de Produção de Indicadores Demográficos da Fundação SEADE. No modelo de Mosley e Chen, considera-se que a redução da mortalidade infantil estaria influenciada por determinantes próxi-mos, ou variáveis intermediárias, e por fatores sociais e econômicos. Os determinantes próximos têm um papel intermediário entre o nível da mortalidade infantil, que a influenciam diretamente, e os fatores sócio-econômicos, culturais, políticos e outros. Por sua vez, o impacto dos fatores sócio-econômicos sobre a saúde somente é processado através de seus efeitos sobre os determinantes próximos (Mosley, Chen, 1984). Por sua vez, Palloni identifica dois tipos de intervenções: as verticais, que têm por finalidade atingir um número limitado de doenças, proporcionando as bases para sua erradicação mediante procedimentos preventivos ou curativos e; as horizontais, que têm por finalidade atingir um maior número de doenças, na medida que estão direcionados a melhorar e/ou ampliar o saneamento básico, a um maior acesso aos serviços médicos, a proporcionar subsídios à dieta alimentar etc. Os resultados destas ações estão relacionados, no pri-meiro caso, à sua manutenção, sendo possível ocorrer retrocessos se estas deixarem de operar e, ao nível econômico e social, no caso das intervenções horizontais (Palloni, 1985).
... It is much easier to reduce infectious diseases than such complex chronic and degenerative diseases as heart disease, cancer, Alzheimer's disease, and AIDS (Tuljapurkar et al. 2000). The Taeuber Paradox (Keyfitz 1977) reveals that especially at older ages diseases are interrelated, so that the elimination of one disease may not substantially reduce overall mortality (Tuljapurkar and Boe 1998). Although cancer contributes to about one-quarter of all deaths in the U.S., the large majority of these deaths occur at older ages, so its elimination might add just a little over three years to life expectancy at birth (Anderson 1999). ...
Article
Objective This article provides a timely assessment of U.S. life expectancy given recent stalls in the growth of length of life, the continuing drop in international rankings of life expectancy for the United States, and a period of growing social and economic insecurity. Methods Time-series analysis is used on over 70 years of data from the Human Mortality Database to forecast future life expectancy to the year 2055. ResultsThe results show limited improvements in U.S. life expectancy at birth, less than three years on average, for both men and women. Conclusions Even in uncertain times, it is important to look forward in preparing for the needs of future populations. The results presented here underscore the relevance of policy and health initiatives aimed at improving the nation's health and reveal important insight into possible limits to mortality improvement over the next five decades.
... Yet, in addition, the pursuit of longevity would necessarily involve the performance or at least a discussion of an extensive program of fundamental and applied biomedical studies, dedicated to the maximal possible control over the deteriorative aging process from the "inside". Granted that the deteriorative aging process lies at the root of chronic agerelated diseases, the pursuit of longevity via maximal feasible amelioration of this process would also mean the pursuit of health and quality of life [32,33]. ...
Article
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Despite the common apprehensions regarding the aging population, this work aims to argue, on both deontological and utilitarian moral grounds, that any increase in general life-expectancy will be beneficial for the Middle East, countering the common fears associated with this increase. A set of ethical arguments concerning increasing longevity is presented, from both the deontological and utilitarian perspective. A wide selection of economic, psychological, demographic and epidemiological literature and databases is analyzed to determine common correlates of extended longevity. On the deontological grounds, the value of extended longevity is derived from the value of life preservation, regardless of its term. On the utilitarian grounds, the value of extended longevity is demonstrated by its correlation with further human values, such as education level and intellectual activity, economic prosperity, equality, solidarity and peacefulness. With the common apprehensions of stagnation and scarcity due to life extension found wanting, the pursuit of longevity by the population can be seen as a cross-cultural and cross-generational good. Though the current study mainly refers to sources and data relevant to the Middle East, a similar pro-longevity argument can be also made for other cultural contexts. In view of its numerous benefits, normatively, the goal of longevity should be set clearly and openly by the society, and actively pursued, or at least discussed, in academia, the political system and broader public.
... g . Keyfitz ( 1977 ) , Tsai et al . ( 1978 ) , Manton et al . ...
Article
Changes in underlying mortality rates significantly impact insurance business as well as private and public pension systems. Individual mortality studies have data limitations; aggregate mortality studies omit many relevant details. The study of causal mortality represents the middle ground, where population data is used while cause-of-death information is retained. We use internationally classified cause-of-death categories and data obtained from the World Health Organization. We model causal mortality simultaneously in a multinomial logistic framework. Consequently, inherent dependence amongst the competing causes is accounted for. This framework allows us to investigate the effects of improvements in, or the elimination of, cause-specific mortality in a sound probabilistic way. This is of particular interest for scenario-based forecasting purposes. We show the multinomial model is more conservative than a force-of-mortality approach. Finally, we quantify the impact of cause-elimination on aggregate mortality using residual life expectancy and apply our model to a French case study.
... Even though a particular disease may represent a large portion of all deaths, its elimination may not assure huge gains in life expectancy. On the contrary, it may result in relatively modest life expectancy increases, a phenomenon called "The Taeuber Paradox" (Keyfitz 1977). For example, even though cancer currently accounts for nearly one-quarter of all U.S. deaths, its elimination might add just 3.4 years to life expectancy at birth (Anderson 1999). ...
... (The elimination of cancer has received considerable attention, for example.) Without attempting to be exhaustive, we note the following: an early contribution is Keyfitz (1977); a selection of more recent ones includes Nusselder et al. (1996), Mackenbach et al. (1999), Manuel et al. (2003), Kintner (2004; see " Cause‐Elimination Life Tables " ), Somerville and Francombe (2005), and Beltrán‐Sánchez et al. (2008). This literature makes use of cause‐ of‐death data originating with registered death certificates. ...
Article
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RÉSUMÉ Les sondages sur les conditions de santé chroniques fournissent des informations sur la prédominance mais pas l'incidence et le processus de changement au sein de la population. Notre étude a révelé comment "les dynamiques d'âge" des conditions chroniques—les probabilités de contracter des conditions aux âges divers, de passer d'un état d'une maladie chronique à l'autre, et de mourir—peuvent être déduites des données sur la prédominance de ces conditions, qui peuvent être considerées comme irreversibles. Les matrices de transition de probabilité ont été construites pour les groupes d'âge successifs, la séquence représentant la dynamique d'âge des conditions de santé pour une population sédentaire. Nous avons simulé la trajectoire de vie d'une cohorte sous les probabilités initiales, et encore sous les probabilités altérées, afin d'explorer les effets de la réduction du taux d'incidence ou de la mortalité associée à une condition particulière. Nous avons démontré que ces enquêtes sur les conditions chroniques peuvent être rendues encore plus valables en permettant le calcul des probabilités de transition qui définissent le processus de vieillissement pour des conditions chroniques.
... A cure for cancer would only have the effect of giving people the opportunity to die of heart disease'. 9 Fortunately, medical research is progressing globally without leaving behind other pathologies of high mortality. ...
Article
Radiological Oncology, like the rest of medical specialties, is beginning to provide can personalized therapies. The ongoing scientific advances enable a great degree of precision in diagnoses and therapies. To fight cancer, from a radiotherapy unit, requires up-to-date equipment, professionals with different specialties working in synchrony (doctors, physicists, biologists, etc.) and a lot of research. Some of the new therapeutic tendencies are immunotherapy, nanoparticles, gene therapy, biomarkers, artificial intelligence, etc. A new clinical paradigm in which new professional networks are inevitable is arising. The mission of translational research is to become a scientific engine in the clinical space.
... Lifespan variability measures include the interquartile range, Gini coefficient, coefficient of variation, and standard deviation. In demography, metrics such as the life table entropy (H ) and life disparity (e †) have been introduced due to their useful interpretations (Leser 1955;Keyfitz 1977;Goldman and Lord 1986;Vaupel 1986;Vaupel and Canudas-Romo 2003). ...
Article
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The study of the mortality differences between groups has traditionally focused on metrics that describe average levels of mortality, for example life expectancy and standardized mortality rates. Additional insights can be gained by using statistical distance metrics to examine differences in lifespan distributions between groups. Here, we use a distance metric, the non-overlap index, to capture the sociological concept of stratification, which emphasizes the emergence of unique, hierarchically layered social strata. We show an application using Finnish registration data that cover the entire population over the period from 1996 to 2017. The results indicate that lifespan stratification and life-expectancy differences between income groups both increased substantially from 1996 to 2008; subsequently, life-expectancy differences declined, whereas stratification stagnated for men and increased for women. We conclude that the non-overlap index uncovers a unique domain of inequalities in mortality and helps to capture important between-group differences that conventional approaches miss.
... Though these theories did not appear to refer to any specific goals of life extension, they were designed for a thorough quantitative elucidation of the aging process, deemed a necessary precondition for any actual intervention. Indeed, despite positing a formal theory of lifespan limitation, Strehler was among the most active seekers of life-prolonging means, mainly focusing on enzymatic mechanisms of DNA repair, as he believed that an improved DNA repair system can protect the stability of the human genes against mutations and thus radically increase the human lifespan (Strehler 1960b;Kahn 1985). ...
Chapter
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Is maintaining good health potentially compatible with a significant or radical life extension? Historically, these phenomena have often been seen as conflicting. Their potential principal incompatibility has often been derived from either health (functional capacity) or lifespan being understood as finite or limited values. The various concepts of limitations to the lifespan or health quantity are surveyed in this work in their historical development, with reference to several dominant theories of aging and mortality. The incompleteness and ambiguities of the limitation theories are demonstrated. Thus, even when proposing limits to the lifespan or healthspan, these limits have often been seen, even by the same authors, as flexible and modifiable. The exact conditions under which lifespan and healthspan “limitations” end and the “possibilities” of their enhancement begin have remained uncertain in the absence of a reliable quantitative formal theory of aging and mortality. An alternative “life-extensionist” view assumes the potential replenishment of any vital resources expended, and thus presumes no inherent natural limitations to either the lifespan or health quantity (functional capacity). The validity of either of those views may be tested in the future with the development of new medical technologies and a better theoretical understanding of health, aging and mortality.
... Turnover Generation time T Number of years required for an average individual in the population to replace itself This approach avoids uncertainties associated with the longevity of spores and seeds (Burns et al., 2010;Caswell, 2001;Salguero-Gómez, Jones, Jongejans, et al., 2016;Silvertown & Franco, 1993) and assures the comparability with species without such life cycle stages. To calculate S and H (Demetrius, 1974;Keyfitz, 1977), we first obtained the age-specific survivorship curve (l x ) and the agespecific fertility trajectory (m x ) following Caswell (2001, pp. 118-121), and implemented the formulae described in Table 1. ...
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Aquatic and terrestrial environments display stark differences in key environmental factors and phylogenetic composition but their consequences for the evolution of species’ life history strategies remain poorly understood. Here, we examine whether and how life history strategies vary between terrestrial and aquatic species. We use demographic information for 685 terrestrial and 122 aquatic animal and plant species to estimate key life history traits. We then use phylogenetically corrected least squares regression to explore potential differences in trade‐offs between life history traits between both environments. We contrast life history strategies of aquatic vs. terrestrial species in a principal component analysis while accounting for body dimensions and phylogenetic relationships. Our results show that the same trade‐offs structure terrestrial and aquatic life histories, resulting in two dominant axes of variation that describe species’ pace‐of‐life and reproductive strategies. Terrestrial plants display a large diversity of strategies, including the longest‐lived species in this study. Aquatic animals exhibit higher reproductive frequency than terrestrial animals. When correcting for body size, mobile and sessile terrestrial organisms show slower paces of life than aquatic ones. Aquatic and terrestrial species are ruled by the same life history trade‐offs, but have evolved different strategies, likely due to distinct environmental selective pressures. Such contrasting life history strategies have important consequences for the conservation and management of aquatic and terrestrial species. A free plain language summary can be found within the Supporting Information of this article
... However, they are not interchangeable as they differ in their formal properties and in the underlying concept they measure (van Raalte and Caswell 2013). For this reason, we use six measures of lifespan variation: the standard deviation at birth 0 and the coefficient of variation CV; lifespan disparity † (Vaupel and Canudas-Romo 2003) and lifetable entropy (Keyfitz 1977;Leser 1955); the relative and absolute Gini coefficients, 0 and 0 respectively (Hanada 1983;Shkolnikov, Andreev, and Begun 2003). Each pair comprises an absolute measure and its relative counterpart. ...
... To fill these research gaps, the present study provides a comprehensive examination of the loss of LE due to RID in 195 countries/territories over a period of almost three decades. Loss of LE due to RID is an important indicator measuring the health impacts of RID and an easy and powerful way to quantify the life-shortening effect of RID at a population level (Chiang, 1979;Keyfitz, 1977;Tsai et al., 1978). The study provides the first examination of the loss of LE due to RID at both the global and country/territory levels, providing a timely and more nuanced understanding of the changing disease burden of RID and the consequences of RID on population and public health. ...
Article
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Understanding of the patterns of and changes in mortality from respiratory infectious diseases (RID) and its contribution to loss of life expectancy (LE) is inadequate in the existing literature. With rapid sociodemographic changes globally, and the current COVID-19 pandemic, it is timely to revisit the disease burden of RID. Using the approaches of life table and cause-eliminated life table based on data from the Global Burden of Disease Study (GBD), the study analyses loss of LE due to RID in 195 countries/territories and its changes during the period 1990–2017. Results indicate that loss of LE due to RID stood at 1.29 years globally in 2017 globally and varied widely by age, gender, and geographic location, with men, elderly people, and populations in middle/low income countries/territories suffering a disproportionately high loss of LE due to RID. Additionally, loss of LE due to RID decreased remarkably by 0.97 years globally during the period 1990–2017 but increased slightly among populations older than 70 years and in many high income countries/territories. Results suggest that RID still pose a severe threat for population and public health, and that amid dramatic sociodemographic changes globally, the disease burden of RID may resurge. The study presents the first examination of the life-shortening effect of RID at the global and country/territory levels, providing new understanding of the changing disease burden of RID and shedding light on the potential consequences of the current COVID-19 pandemic.
... Similarly, Mehta et al. (2020) bring evidence of stagnation in cardiovascular disease mortality, holding back the increase of US life expectancy. Therefore, it has become crucial to delve into the study of cause-specific mortality, underlining longevity patterns that should be exploited to achieve more accurate demographic forecasting (Manton et al. 1976;Keyfitz 1977;Manton et al. 1986;Caselli et al. 2006;Dimitrova et al. 2013). The cause-specific mortality rates include more peculiar information with respect to the aggregate mortality, which can shed light on the mortality evolution. ...
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Life expectancy at birth has attracted interest in various fields, as a health indicator that measures the quality of life. Its appeal relies on the ability to enclose and summarize all the factors affecting longevity. However, more granular information, provided by social indicators such as cause-of-death mortality rates, plays a crucial role in defining appropriate policies for governments to achieve well-being and sustainability goals. Unfortunately, their availability is not always guaranteed. Exploiting the relationship between life expectancy at birth and cause-of-death mortality rates, in this paper we propose an indirect model to produce estimates of death rates due to specific causes using the summary indicator of life expectancy at birth, thus the general levels of the observed mortality. By leveraging on a constrained optimization procedure, we ensure a robust framework where the cause-specific mortality rates are coherent to the aggregate mortality. The main advantage is that indirect estimations allow us to overcome the data availability problem: very often the cause-specific mortality data are incomplete, whereas data on the aggregate mortality are not. Using data from the Human Cause-of-Death Database, we show a numerical application of our model to two different countries, Russia and Spain, which have experienced a different evolution of life expectancy and different leading causes of death. In Spain, we detected the impact of several public health policies on the lowered levels of cancer deaths and related life expectancy increases. As regards the Russia, our results catch the effects of the anti-alcohol campaign of 1985–1988 on longevity changes.
... Lifespan variation reveals the uncertainty about the eventual age at death at the individual level, and measures how evenly mortality conditions are shared at the population level. There exist several indicators to measure lifespan variation (for an overview, see Shkolnikov et al. 2003;van Raalte and Caswell 2013), such as the entropy of the life table (Leser, 1955;Keyfitz, 1977;Demetrius, 1978), the standard deviation or variance of the age-at-death distribution (as applied in Tuljapurkar and Edwards 2011), the coefficient of variation (as applied in Aburto, Wensink et al. 2018), years of life lost (e † ) (Goldman and Lord, 1986;Vaupel, 1986;Hakkert, 1987;Vaupel and Canudas Romo, 2003), or the Gini coefficient (Hanada, 1983). ...
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The Gini coefficient of the life table is a concentration index that provides information on lifespan variation. Originally proposed by economists to measure income and wealth inequalities, it has been widely used in population studies to investigate variation in ages at death. We focus on a complementary indicator, Drewnowski's index, which is as a measure of equality. We study its mathematical properties and analyze how changes over time relate to changes in life expectancy. Further, we identify the threshold age below which mortality improvements are translated into decreasing lifespan variation and above which these improvements translate into increasing lifespan inequality. We illustrate our theoretical findings simulating scenarios of mortality improvement in the Gompertz model. Our experiments demonstrate how Drewnowski's index can serve as an indicator of the shape of mortality patterns. These properties, along with our analytical findings, support studying lifespan variation alongside life expectancy trends in multiple species.
... To measure the effects of excess mortality on life expectancy, we used a simple methodological approach that differs from Aburto et al. (2021a) and Castro et al. (2021b). The basic idea is to use life table entropy H (Demetrius, 1974;Fernandez & Beltrán-Sánchez, 2015;Keyfitz, 1977) and the proportion of excess mortality in 2020 in each country and see how these two measures affect current life expectancy. The entropy of the life table describes the association between the relative changes in life expectancy with changes in age-specific mortality rates (Demetrius, 1974), and the P-scores measure the proportion that mortality in time t and region y exceeds its usual level in comparison with the mortality in y in time t-1 (Giattino et al., 2021). ...
Article
In this paper, we measure the effect of the 2020 COVID-19 pandemic wave at the national and subnational levels in selected Latin American countries that were most affected: Brazil, Chile, Ecuador, Guatemala, Mexico, and Peru. We used publicly available monthly mortality data to measure the impacts of the pandemic using excess mortality for each country and its regions. We compare the mortality, at national and regional levels, in 2020 to the mortality levels of recent trends and provide estimates of the impact of mortality on life expectancy at birth. Our findings indicate that from April 2020 on, mortality exceeded its usual monthly levels in multiple areas of each country. In Mexico and Peru, excess mortality was spreading through many areas by the end of the second half of 2020. To a lesser extent, we observed a similar pattern in Brazil, Chile, and Ecuador. We also found that as the pandemic progressed, excess mortality became more visible in areas with poorer socioeconomic and sanitary conditions. This excess mortality has reduced life expectancy across these countries by 2-10 years. Despite the lack of reliable information on COVID-19 mortality, excess mortality is a useful indicator for measuring the effects of the coronavirus pandemic, especially in the context of Latin American countries, where there is still a lack of good information on causes of death in their vital registration systems. Supplementary information: The online version contains supplementary material available at 10.1186/s41118-021-00139-1.
... The entropy concept, which was first introduced by Keyfitz (1977aKeyfitz ( , 1977b, ...
... Many steps are involved in this assessment, but as Nathan Keyfitz pointed out when considering the effect of eliminating a cause of death, the difference "depends on the average time that elapses before the persons rescued will die of some other cause." 15 In the case at hands, the effect of a new cause of death on longevity depends on the average time that would have elapsed before the persons who died from that cause would have died from other causes. In life table notations, that average is: This difference relates to the concept of "potential years of life lost," 16 which has been popularized by burden of disease assessments as Years of Life Lost (YLL): . ...
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The impact of COVID-19 on the individual lifespan can be measured by the difference in period life expectancy at birth (PLEB), an intuitive indicator of mortality conditions during a reference period. When mortality conditions are changing rapidly, however, that intuitive interpretation of the PLEB for short reference periods and of its change conflict with the assumptions under which the PLEB is derived. To avoid assumptions about future mortality, I propose measuring instead the Mean Unfulfilled Lifespan (MUL), defined as the average difference between the actual and otherwise expected ages at death in a recent death cohort. For fine-grained tracking of the pandemic, I also provide an empirical shortcut to MUL estimation for small areas or short periods. I estimate quarterly MUL values for the first half of 2020 in 142 national populations and 91 sub-national populations in Italy, Spain and the US. Across countries, the highest quarterly values were reached in the second quarter in Peru (3.90 years) and in Ecuador (4.59 years). Higher quarterly values still were found in New York and New Jersey, where individuals died respectively 5.41 and 5.56 years younger on average than their expected age at death. Using a seven-day rolling window, I estimate the MUL peaked at 7.32 years in Lombardy, 8.96 years in Madrid, and 8.93 years in New York, but reached 12.86 years for the entire month of April in Guayas (Ecuador). These results illustrate how the MUL provides an intuitive metric to track the pandemic without requiring assumptions about future mortality.
... The assessment involves a relatively copious amount of life table manipulations, but decades ago Nathan Keyfitz provided most useful insights as to what these manipulations boil down to. Considering the related issue of estimating the increase in PLEB brought by the permanent elimination of a cause of death, he summarized that the increase "depends on the average time that elapses before the persons rescued will die of some other cause" [10]. Conversely, the decrease induced by a new cause of death depends on the average time that would have elapsed before the persons who died from the new cause would have died from other causes. ...
Article
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Declines in period life expectancy at birth (PLEB) provide seemingly intuitive indicators of the impact of a cause of death on the individual lifespan. Derived under the assumption that future mortality conditions will remain indefinitely those observed during a reference period, however, their intuitive interpretation becomes problematic when period conditions reflect a temporary mortality “shock”, resulting from a natural disaster or the diffusion of a new epidemic in the population for instance. Rather than to make assumptions about future mortality, I propose measuring the difference between a period average age at death and the average expected age at death of the same individuals (death cohort): the Mean Unfulfilled Lifespan (MUL). For fine-grained tracking of the mortality impact of an epidemic, I also provide an empirical shortcut to MUL estimation for small areas or short periods. For illustration, quarterly MUL values in 2020 are derived from estimates of COVID-19 deaths that might substantially underestimate overall mortality change in affected populations. These results nonetheless illustrate how MUL tracks the mortality impact of the pandemic in several national and sub-national populations. Using a seven-day rolling window, the empirical shortcut suggests MUL peaked at 6.43 years in Lombardy, 8.91 years in New Jersey, and 6.24 years in Mexico City for instance. Sensitivity analyses are presented, but in the case of COVID-19, the main uncertainty remains the potential gap between reported COVID-19 deaths and actual increases in the number of deaths induced by the pandemic in some of the most affected countries. Using actual number of deaths rather than reported COVID-19 deaths may increase seven-day MUL from 6.24 to 8.96 years in Mexico City and from 2.67 to 5.49 years in Lima for instance. In Guayas (Ecuador), MUL is estimated to have reached 12.7 years for the entire month of April 2020.
Article
Keyfitz entropy index is a new indicator that measures the sensitivity of life expectancy to a change in mortality rate. Understanding the characteristics of this indicator can significantly help life table studies in survival analysis. In this paper, we take a closer look at some mathematical properties of Keyfitz entropy index. First, using theoretical studies we show that in some cases this index belongs to the interval [0, 1] and in other cases, it is greater than 1. We also provide two inequalities for Keyfitz entropy using Shannon entropy and pth central moments of random variables. Then, we present an empirical value for it. This value can be useful and provides initial information about Keyfitz entropy value to the researcher, especially before estimating the population survival function with common parametric and nonparametric methods. Second, we propose a new nonparametric method for estimating the survival function in life table using information theory which applies existing information from the population, such as average and moments. The survival function estimated by this method provides the maximum value for Keyfitz entropy indicating the maximum sensitivity of life expectancy to changes in age-specific mortality rates. We also demonstrate that the survival function estimated by this method can be a powerful competitor to its counterparts which are estimated by common parametric and nonparametric methods.
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Recent work has unearthed many empirical regularities in mortality trends, including the inverse correlation between life expectancy and life span inequality, and the compression of mortality into older age ranges. These regularities have furnished important insights into the dynamics of mortality by describing, in demographic terms, how different attributes of the life table deaths distribution interrelate and change over time. However, though empirical evidence suggests that the demographically-meaningful metrics these regularities involve (e.g., life span disparity and life table entropy) are correlated to the moments of the deaths distribution (e.g., variance), the broader theoretical connections between life span inequality and the moments of the deaths distribution have yet to be elucidated. In this article we establish such connections and leverage them to furnish new insights into mortality dynamics. We prove theoretical results linking life span disparity and life table entropy to the central moments of the deaths distribution, and use these results to empirically link statistical measures of variation of the deaths distribution (e.g., variance, index of dispersion) to life span disparity and life table entropy. We validate these results via empirical analyses using data from the Human Mortality Database and extract from them several new insights into mortality shifting and compression in human populations.
Conference Paper
Modeling mortality and longevity risks is critical to pricing longevity products. It has challenged practitioners and academics alike, because of first the existence of common stochastic trends, and second the unpredictability of an eventual mortality improvement in some age-groups. When considering cause-of-death-mortality rates, both aforementioned trends are additionally affected by the cause of death. Over the last century, the assumption usually made was that causes of death are independent, although it is well-known that dependancies exist. Recent developments in econometrics allow, through Vector Error Correction Models (VECM), to model multivariate dynamic systems including time dependency between economic variables. Common trends that exist between the variables may then be highlighted, the relation between these variables being represented by a long-run equilibrium relationship. In this work, VECM are developed for causes-of-death mortality. We analyze the five main causes of death across ten major countries representing a diversity of developed economies. The World Health Organization website provides cause-of-death information over about the last 60 years. Our analysis reveals that long-run equilibrium relationships exist between the five main causes of death, improving our understanding of the nature of dependence between these competing risks over recent years. It also highlights that countries had usually different past experience in regards to cause-of-death mortality trends and thus, applying results from one country to another may be misleading.
Article
BACKGROUND Despite much evidence that modifying risk factors for coronary heart disease can decrease morbidity and mortality, little is known about the impact of risk-factor modification on life expectancy. METHODS AND RESULTS We used the Coronary Heart Disease Policy Model, a state-transition computer simulation of the US population, to forecast potential gains in life expectancy from risk-factor modification for the cohort of Americans turning age 35 in 1990. Among 35-year-old men, we projected that the population-wide increase in life expectancy would be about 1.1 years from strict blood pressure control, 0.8 years from smoking cessation, 0.7 years from reduction of serum cholesterol to 200 mg/dl, and about 0.6 years from weight loss to ideal body weight. For women, reducing cholesterol to 200 mg/dl would have the greatest estimated impact-a gain of 0.8 years-whereas smoking cessation, blood pressure control, or weight loss would yield population-wide gains of 0.7, 0.4, and 0.4 years, respectively. Gains for 35-year-old individuals having a given risk factor are greater. We estimate that, on average, male smokers would gain 2.3 years from quitting smoking; males with hypertension would gain 1.1-5.3 years from reducing their diastolic blood pressure to 88 mm Hg; men with serum cholesterol levels exceeding 200 mg/dl would gain 0.5-4.2 years from lowering their serum cholesterol level to 200 mg/dl; and overweight men would gain an average of 0.7-1.7 years from achieving ideal body weight. Corresponding projected gains for at-risk women are 2.8 years from quitting smoking, 0.9-5.7 years from lowering blood pressure, 0.4-6.3 years from decreasing serum cholesterol, and 0.5-1.1 years from losing weight. Eliminating coronary heart disease mortality is estimated to extend the average life expectancy of a 35-year-old man by 3.1 years and a 35-year-old woman by 3.3 years. CONCLUSIONS Population-wide gains in life expectancy from single risk-factor modifications are modest, but gains to individuals at risk can be more substantial.
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Mutation accumulation is one of the major genetic theories of ageing and predicts that the frequencies of deleterious alleles that are neutral to selection until post-reproductive years are influenced by random genetic drift. The effective population size (Ne) determines the rate of drift and in age-structured populations is a function of generation time, the number of newborn individuals and reproductive value. We hypothesise that over the last 50,000 years, the human population survivorship curve has experienced a shift from one of constant mortality and no senescence (known as a Type-II population) to one of delayed, but strong senescence (known as a Type-I population). We simulate drift in age-structured populations to explore the sensitivity of different population ‘types’ to generation time and contrast our results with predictions based purely on estimates of Ne. We conclude that estimates of Ne do not always accurately predict the rates of drift between populations with different survivorship curves and that survivorship curves are useful predictors of the sensitivity of a population to generation time. We find that a shift from an ancestral Type-II to a modern Type-I population coincides with an increase in the rate of drift unless accompanied by an increase in generation time. Both population type and generation time are therefore relevant to the contribution mutation accumulation makes to the genetic underpinnings of senescence.
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Mortality rates differ across countries and years, and the country with the lowest observed mortality has changed over time. However, the classic Science paper by Oeppen and Vaupel (2002) identified a persistent linear trend over time in maximum national life expectancy. In this work, we look to exploit similar regularities in age-specific mortality by considering for any given year a hypothetical mortality ‘frontier’, which we define as the lower limit of the force of mortality at each age across all countries. Change in this frontier reflects incremental advances across the wide range of social, institutional and scientific dimensions that influence mortality. We jointly estimate frontier mortality as well as mortality rates for individual countries. Generalised additive models are used to estimate a smooth set of baseline frontier mortality rates and mortality improvements, and country-level mortality is modelled as a set of smooth, positive deviations from this, forcing the mortality estimates for individual countries to lie above the frontier. This model is fitted to data for a selection of countries from the Human Mortality Database. The efficacy of the model in forecasting over a 10-year horizon is compared to a similar model fitted to each country separately.
Article
This study examines differential mortality between immigrant and native-born populations in Canada with respect to eighteen causes of death categories encompassing chronic and external types of mortality over two census periods, 2001 and 2011. The following interrelated questions are addressed: (1) what is the magnitude of the immigrant mortality advantage relative to native-born Canadians? (2) How does it change over time? (3) Is the migrant advantage uniform across all causes of death? (4) Does the advantage for immigrants prevail across all age groups? (5) Are immigrant men and women equally advantaged across causes of death? These queries are explored with multivariate analysis guided by a conceptual framework that specifies differential mortality as a function of nativity factors, health selection, and acculturation effects. It is shown that nativity status exerts a strong independent effect, and that over time, migrants experienced larger reductions in risk than did native-born Canadians. Further analysis revealed support for both health selection and acculturative explanations. Sex differences are found, with male immigrants enjoying a small but significant relative mortality advantage compared to immigrant females. The paper discusses these findings and closes with suggestions for further study.
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To put estimates of COVID-19 mortality into perspective, we estimate age-specific mortality for an epidemic claiming for illustrative purposes 1 million US lives, with results approximately scalable over a broad range of deaths. We calculate the impact on period life expectancy (down 2.94 y) and remaining life years (11.7 y per death). Avoiding 1.75 million deaths or 20.5 trillion person years of life lost would be valued at $10.2 to $17.5 trillion. The age patterns of COVID-19 mortality in other countries are quite similar and increase at rates close to each country’s rate for all-cause mortality. The scenario of 1 million COVID-19 deaths is similar in scale to that of the decades-long HIV/AIDS and opioid-overdose epidemics but considerably smaller than that of the Spanish flu of 1918. Unlike HIV/AIDS and opioid epidemics, the COVID-19 deaths are concentrated in a period of months rather than spread out over decades.
Chapter
Die demographische Entwicklung und der Gesundheitszustand sind auf vielfache Weise miteinander verknüpft, was angesichts des knappen zur Verfügung stehenden Raums zwangsläufig eine starke Eingrenzung der Themenstellung bedingt. Besonders eng ist naturgemäß der Zusammenhang zwischen der Mortalität und der Morbidität. Aus den vielen in diesem Zusammenhang relevanten Fragen wird im weiteren zur detaillierten Behandlung ein Teilaspekt ausgewählt, der einerseits theoretisch und politisch relevant ist und andererseits zugleich mit konkreten empirischen Daten der Bundesrepublik beantwortet werden kann.
Chapter
Demography is the study of populations—viewed re­gionally, nationally, or globally—describing the numbers of people and the dynamics of population change. Demographic studies reveal the phenomenon of increasing numbers and increasing proportion of older people in the United States and in other developed countries. This phenomenon is so predictable that it has become a measure of improved economic and health status of nations in the 20th Century. Aging populations are the result of three major factors: fertility, mortality, and immigration. This discussion concerns the United States, where in the last half century immigration has not been a major influence on mortality patterns, and thus will not discuss immigration in any detail.
Chapter
The expected duration of life for a baby born in France in 1991 was 76.9 years – 72.9 years for males and 81.2 years for females (Couet and Tambay 1995). These figure are calculated from period life tables produced from age-specific death rates that prevailed in France from 1990–1992. Estimates of the duration of life based on period life tables are predicated on the assumption that babies born in a given year will experience, for the duration of their lives, the prevailing mortality risks observed at every age. When secular declines in total mortality are occurring, as they have been in France and other developed nations for most of the 20th century, estimates of life expectancy at birth using this method tend to underestimate the subsequent longevity of the birth cohort. Given the historical trend in declining death rates in France and other developed nations, and the expectation that they will continue to decline in the future, how much higher can life expectancy at birth be expected to rise beyond these period estimates? Is the measure of period life expectancy providing a reasonable estimate of future longevity, or is it possible that the actual life expectancy of babies born in France today will be considerably higher than is currently indicated by period life tables? Alternatively, how much higher can life expectancy at birth practically increase in France and other developed nations with life expectancy (for males and females combined) approaching 80 years?
Chapter
In many developed countries where mortality levels have been declining sharply it is increasingly important to study mortality differentials taking causes of death into account. In a low mortality country, the situations favouring survival to one cause and unfavourable to another cause have no chance to appear as significant variable because of compensation. Moreover, will the increase in survival be accompanied by an increase in survival free of disease?
Chapter
The parameters of the cohort-profiles are able to closely simulate the period-profiles, and the associated aggregate rates of non-communicable diseases. The mix of cohorts, by shaping the period-profiles, then shapes the aggregate rate’s long-term direction. In the second half of the nineteenth century, the aggregate had climbed as the Malthusian cohorts, whose profiles had shifted up for the worse, were the main contributors. Since the early twentieth century, the long-term rate trended down as the transition stage cohorts increasingly dominated the cohort mix. The downward shifts seem the only way to reconcile why the rates of non-communicable diseases have shrunk as the population was aging more than ever before. The link between cohort- and period-profiles suggests that children’s development in the past can echo in the period-profiles and the resulting period-life expectancies.
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Life expectancy (LE) is considered a straightforward summary measure of mortality that comes with an implicit age standardisation. Thus, it has become common to present differences in mortality across populations as differences in LE, instead of, say, relative risks. However, most of the time LE does not quite provide what the term promises. LE is based on a synthetic cohort and is therefore not the true LE of anyone. Also, the implicit age standardisation is construed in such a way that it can be questioned whether it standardises age at all. In this paper, we examine LE from the point of view of its applicability to epidemiological and public health research and provide examples on the relation between an LE difference and a relative risk. We argue that the age standardisation in estimations of LE is not straightforward since it is standardised against different age distributions and that the translation of changes in age specific mortality into change in remaining LE will depend on the level and the distribution of mortality in the population. We conclude that LE is not the measure of choice in aetiological research or in research with the aim to identify risk factors of death, but that LE may be a compelling choice in public health contexts. One cannot escape the thought that the mathematical elegance of LE has contributed to its popularity.
Chapter
The phenomenon known as the “demographic revolution” has been with us for more than 200 years. Falling birth rates, rising incomes, and declining death rates have followed industrialization. Between 1880 and 1920 the impact of industrialization on demographic profiles was dramatically enhanced by a public health revolution, during which acute infectious diseases and tuberculosis became minor causes of death for the first time in history.
Article
Timely, high‐quality mortality data have allowed for assessments of the impact of the novel coronavirus disease 2019 (COVID‐19) on life expectancies in upper‐middle‐ and high‐income countries. Extant data, though imperfect, suggest that the bulk of the pandemic‐induced mortality might have occurred elsewhere. This article reports on changes in life expectancies around the world as far as they can be estimated from the evidence available at the end of 2021. The global life expectancy appears to have declined by 0.92 years between 2019 and 2020 and by another 0.72 years between 2020 and 2021, but the decline seems to have ended during the last quarter of 2021. Uncertainty about its exact size aside, this represents the first decline in global life expectancy since 1950, the first year for which a global estimate is available from the United Nations. Annual declines in life expectancy (from a 12‐month period to the next) appear to have exceeded two years at some point before the end of 2021 in at least 50 countries. Since 1950, annual declines of that magnitude had only been observed on rare occasions, such as Cambodia in the 1970s, Rwanda in the 1990s, and possibly some sub‐Saharan African nations at the peak of the acquired immunodeficiency syndrome (AIDS) pandemic.
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Cambridge Core - Sociology: General Interest - Population and Society - by Dudley L. Poston, Jr
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The long term asymptotic behaviour of a population is evaluated where the age specific fertility behaviour is allowed to change with time. Thus in this article the behaviour of a population is determined with a time dependent net maternity function. It is shown that methods used when the net maternity function was independent of time are still applicable if the change with time is explicit only for the initial population. Further, using the fact that for realistic situations the net maternity function is non-zero over a finite interval α < x < β, it is shown that traditional methods can again be used if the time dependence is associated with ages less than α, the minimum age of childbearing. Recent extensions of Cerone and Keane to include exponential time dependence are utilized and models are presented which are piecewise defined, allowing general and exponential time dependence for the parent and new-born populations respectively. The Sharpe-Lotka single sex determinstic population model is used as the basis for the analysis.
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A lethal defect-wear model of mortality is presented which rationalizes the assumption of independent risks when death may be due to more than a single condition, Under this model, it is shown how competing risk theory and standard categorical data methods may be merged in a unified approach to the analysis of multiple-cause mortality data. The methodology is used to analyze linkages among diseases in the mortality data and evaluate the implication of the elimination of patterns of morbid states for multiple-cause mortality data from deaths occurring in 1969 in North Carolina.
Article
An expression for the entropy of a population was derived in Demetrius (1974) by using a variational principle argument. This entropy measure is precisely the information content of the distribution in the ages of reproducing individuals in a stationary population. This paper introduces another expression for the entropy by considering the variation in the ages at which offspring will be produced by newborn individuals.The relation between these two measures of entropy and their biological significance are discussed.
Article
The stable population model is used to establish formulas expressing the effects of mortality change on population growth rates, birth rates, and age composition. The change in the intrinsic growth rate is shown to be quite accurately approximated by the average decline in age-specific death rates between age zero and the mean age at childbearing in the stable population. This change is essentially independent of the initial level of fertility in the population. Changes in birth rates and age composition are shown to be simple functions of the age pattern of cumulative changes in mortality rates relative to an appropriately defined “neutral” standard.
The Assessment of Programs to Prolong Life, Recognizing their Interaction with Risk Factors. Discussion Paper 320
  • Donald Shepard
  • R Zeckhauser