Ускорение Смертности

A multistage theory of age-specific acceleration in human mortality Steven A Frank BMC Biology 2004, 2:16 doi:10.1186/1741-7007-2-16 The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1741-7007/2/16
Рис.1. \| Age-specific female mortality patterns Рис.2. \| Age-specific male mortality patterns Рис.3. \| Predicted patterns of mortality from a multistage model	Люди умирают с увеличивающейся скоростью вплоть до позднего периода жизни, когда уровень скорости смертности перестаёт расти. Причина плато смертности в поздний период жизни активно дебатируется последние годы. Я изучал картину смертности отдельно для каждой из ведущих причин смертности. Разные причины смерти обнаруживают разные паттерны смертности, это даёт некоторые указания на варьирующее ускорение смертности в разные возраста. Results Я изучал характер смертности сначала с помощью вычерчивания данных скорости смертности по отношению к возрасту на log-log шкале. Кривая скорости возраст-специфической смертности для каждого возраста является возраст-специфическим ускорением смертности. Примерно половина всех смертей вызывается сходными формами возраст-специфического ускорения смертности: постоянный рост ускорения от средины жизни вплоть до хорошо известного пика в 80 лет, сопровождаемого почти линейным уменьшением ускорения. Эта первая группа причин включает болезни сердца, cerebrovascular заболевания и случайную гибель. Вторая группа, составляющая примерно треть от всех смертей, следует разным паттернам возраст специфического ускорения. Эти смерти обнаруживают примерно линейное возрастание ускорения с пиком в 35–45 лет, сопровождаются ступенчатым и постоянным снижением ускорения в оставшийся период жизни. Эта вторая группа включает рак, хронические респираторные заболевания и болезни печени. Я разработал многоступенчатую модель прогрессирования болезней для наблюдения наблюдаемой картины ускорения смертности. Conclusions Многосутпенчатая модель прогрессирования болезней м. объяснить как увеличение в ранний период жизни, так и снижение в поздний период жизни ускорения смертности. В ранний период жизни рост ускорения м. б. вызван увеличением скорости перехода между стадиями, т.к. индивид становится старше. Снижение в поздний период жизни м.б. вызвано прохождением ранних стадий и преодолением (leaving) лишь немногих стадий, оставшихся для более старых индивидов. Humans die at an increasing rate until late in life, when mortality rates level off. The causes of the late-life mortality plateau have been debated extensively over the past few years [1-6]. Here, I examine mortality patterns separately for each of the leading causes of death. The different causes of death show distinct mortality patterns, providing some clues about the varying acceleration of mortality at different ages [2,7]. For most causes of death, the acceleration in mortality rises until middle or late life, and then declines rapidly at older ages. I interpret these patterns in light of a multistage theory of aging, developed by analogy with multistage models of cancer progression [8-11]. In the multistage model, disease develops by progression through a series of intermediate physiological or somatic conditions. I show that the late-life decline in acceleration (mortality plateau) is an inevitable consequence of multistage disease progression [12]. The midlife rise in acceleration may also be explained by a multistage theory if the rates of progression between stages rise slowly during midlife [12]. Figure 1 illustrates mortality patterns for non-Hispanic white females in the United States for the years 1999 and 2000. The top row of panels shows the age-specific death rate per 100,000 individuals on a log-log scale. The columns plot all causes of death, death by heart disease, and death by cancer. The curves for death rate in the top row have different shapes. However, the quantitative characteristics of death rate at different ages can be difficult to discern visually. The second row of panels shows the same data, but plots the age-specific acceleration of death instead of the age-specific rate of death (see Methods). The acceleration is simply the slope of the rate curve in the top panel at each age. Plots of acceleration emphasize how changes in the rate of mortality vary with age. The bottom row of panels shows one final plotting transformation to aid in visual inspection of mortality patterns. The bottom row takes the plots in the row above, transforms the age axis to a linear scale to spread the ages more evenly, and applies a mild smoothing algorithm that retains the same shape but smooths the jagged curves. These methods of plotting transformations in Figure 1 are used to plot mortality patterns for the leading causes of death in Figure 2, using the style of plot in the bottom row of Figure 1. Figure 2 illustrates the mortality patterns for non-Hispanic white males in the United States for the years 1999 and 2000. Each plot shows a different cause of death and the percentage of deaths associated with that cause. The left column of panels shows causes that account for about one-half of all deaths. Each of those causes shares two attributes of age-specific acceleration. From early life until about age 80, the acceleration in mortality increases in an approximately linear way. After age 80, acceleration declines sharply and linearly for the remainder of life. Some of the causes of death also have a lower peak between 30 and 40 years. The upper-right column of panels shows causes that account for about one-third of all deaths. These causes show steep, linear rises in mortality acceleration up to 40–50 years, and then steep, nearly linear declines in acceleration for the remainder of life. The bottom-right column of panels shows two minor causes of mortality that are intermediate between the left and upper-right columns. What can we conclude from these mortality curves? The patterns by themselves do not reveal the underlying processes. However, the patterns do constrain the possible explanations for changes in age-specific mortality and suggest some interesting hypotheses. With regard to constraint, we can rule out a single underlying cause of all human mortality acceleration because the two leading causes of death, heart disease and cancer, show markedly different patterns. In addition, any plausible explanation must satisfy the constraint of generating an early-life rise in acceleration and a late-life decline in acceleration, with the rise and fall being nearly linear in most cases. A refined explanation would also account for the minor peak in acceleration before age 40 for certain causes. One point of this paper is to reiterate the puzzles revealed by the age-specific acceleration plots for different causes of mortality [2,7]. The clarity of those patterns sets the stage for more focused work on this topic and for new hypotheses. Multistage theory of disease progression and mortality Four attributes of the mortality patterns must be explained: early-life rise in acceleration, late-life decline in acceleration, a peak near 80 for some causes and a peak near 40–50 for other causes, and a minor peak near 40 for a few causes. I favor the multistage model of disease progression that has been used widely in analyzing cancer incidence and mortality [8]. A multistage model readily explains the late-life decline in acceleration [12]. Suppose, for example, that there are n stages in progression before death, and the transitions between stages happen at constant rates. It is well known that this sort of multistage progress yields a linear increase in incidence with age when measured on a log-log scale, in the style of the plots shown in the top row of Figure 1 [8]. (I provide a full mathematical description of the multistage model and its properties of acceleration in the Methods section.) If n stages remain before death, then the predicted slope of the log-log plot is n-1. In a paper on cancer incidence [12], I pointed out that as individuals age, they tend to progress through the early stages. If there are n stages remaining at birth, then later in life the typical individual will have progressed through some of the early stages, say a of those stages. Then, at that later age, there are n-a stages remaining and the slope of the log-log plot (acceleration) is n-a-1. As time continues, a rises and the acceleration declines. Gavrilov and Gavrilova [13] made roughly the same argument for the late-life decline in acceleration of human mortality. They argued that individuals at birth have redundant systems of protection against mortality, say n redundant systems. As one ages, some of those n systems fail, say a, fail. Then with n-a systems operating, the acceleration is n-1-a. Mathematically, this is essentially the same argument that I gave for cancer. However, I emphasized a multistage model of progression based on the idea that cancer develops in stages, partly driven by the accumulation over time of key somatic mutations in cell lineages. With regard to Gavrilov and Gavrilova's argument, it is not clear biologically what sort of redundancy exists in systems that protect against mortality. The multistage model can also explain the early-life increase in acceleration. Such increase occurs when the transition rate between stages increases slowly over time [12]. In cancer, a slow clonal expansion of a precancerous population of cells increases the number of cells at risk for passage through the next stage of progression, and thus causes a slow increase in the acceleration of cancer incidence [9,10]. Any slow rise in the transition rates between stages of progression will also cause a slow rise in acceleration. Figure 3 provides some numerical illustrations of how the multistage model may explain a midlife rise in acceleration and a late-life decline in acceleration. In the multistage model, the different acceleration peaks in heart disease and cancer may arise from different numbers of stages in progression or different transition rates between stages. The minor peak in acceleration early in life for male heart disease and a few other causes could be explained by heterogeneity in predisposition. Strongly predisposed individuals would go through the same multistage process, but with perhaps fewer steps to pass. That would cause the early-predisposition group to follow the same pattern of a rise and fall in acceleration, but to do so at an early age. That group would dominate the death statistics of early life, and thus would be seen as an early-life minor peak in acceleration. The multistage model is widely used in the analysis of cancer incidence and mortality [9,10]. Could there be a different multistage progression for heart disease and other causes of death? Certainly, there are morphological and physiological stages of artery disease. First, depositions on the artery walls constrict blood flow. Second, various types of lesions may form, such as a fatty streak or fibrous plaque. Finally, lesion growth may trigger the initial stages of cardiovascular diseases. Andreassi et al. [14] have argued that plaque formation may actually develop through a process of accumulating somatic mutations in cell lineages. Stages follow as mutations accumulate sequentially in those cell lineages, just as cancer may arise by mutations accumulating in the stem cell lineages that renew epithelial tissues. Multistage models can be tested by identifying the stages in progression and measuring how many stages healthy individuals have passed at different ages. Although the stages of cancer progression have not been fully worked out yet for any particular type of cancer, much research is focusing on this problem. Within a few years, we may know more about how particular somatic mutations affect progression. Then, with high-throughput genomics, one could screen cell lineages in healthy individuals to measure how individuals of different ages pass through the early stages of progression. Those data could then be linked to the acceleration patterns for disease at different ages. Similarly, better understanding of and diagnostics for cardiovascular disease progression will allow measurement of early stage progression in individuals of different ages. Again, those measurements of progression could be used to test particular models for the acceleration of mortality at different stages in life. Conclusions The acceleration plots for the leading causes of death show several striking patterns that must be explained by any theory of aging and mortality [2,7]. The late-life decline in mortality acceleration has been widely discussed. However, the analyses here demonstrate different patterns of midlife rise and late-life decline in acceleration for different causes of death. These analyses also put the late-life decline in a broader context by emphasizing various universal and particular features of mortality acceleration at different ages and across the different major causes of death. I developed a multistage model of disease progression that can explain the observed patterns of mortality acceleration. An early-life rise in acceleration may be caused by increasing rates of transition between stages as individuals grow older. The late-life decline in acceleration may be caused by progression through earlier stages, leaving only a few stages remaining for older individuals.

Люди умирают с увеличивающейся скоростью вплоть до позднего периода жизни, когда уровень скорости смертности перестаёт расти. Причина плато смертности в поздний период жизни активно дебатируется последние годы. Я изучал картину смертности отдельно для каждой из ведущих причин смертности. Разные причины смерти обнаруживают разные паттерны смертности, это даёт некоторые указания на варьирующее ускорение смертности в разные возраста.

Results

Я изучал характер смертности сначала с помощью вычерчивания данных скорости смертности по отношению к возрасту на log-log шкале. Кривая скорости возраст-специфической смертности для каждого возраста является возраст-специфическим ускорением смертности. Примерно половина всех смертей вызывается сходными формами возраст-специфического ускорения смертности: постоянный рост ускорения от средины жизни вплоть до хорошо известного пика в 80 лет, сопровождаемого почти линейным уменьшением ускорения. Эта первая группа причин включает болезни сердца, cerebrovascular заболевания и случайную гибель. Вторая группа, составляющая примерно треть от всех смертей, следует разным паттернам возраст специфического ускорения. Эти смерти обнаруживают примерно линейное возрастание ускорения с пиком в 35–45 лет, сопровождаются ступенчатым и постоянным снижением ускорения в оставшийся период жизни. Эта вторая группа включает рак, хронические респираторные заболевания и болезни печени. Я разработал многоступенчатую модель прогрессирования болезней для наблюдения наблюдаемой картины ускорения смертности.

Conclusions

Многосутпенчатая модель прогрессирования болезней м. объяснить как увеличение в ранний период жизни, так и снижение в поздний период жизни ускорения смертности. В ранний период жизни рост ускорения м. б. вызван увеличением скорости перехода между стадиями, т.к. индивид становится старше. Снижение в поздний период жизни м.б. вызвано прохождением ранних стадий и преодолением (leaving) лишь немногих стадий, оставшихся для более старых индивидов.

Humans die at an increasing rate until late in life, when mortality rates level off. The causes of the late-life mortality plateau have been debated extensively over the past few years [1-6]. Here, I examine mortality patterns separately for each of the leading causes of death. The different causes of death show distinct mortality patterns, providing some clues about the varying acceleration of mortality at different ages [2,7].

For most causes of death, the acceleration in mortality rises until middle or late life, and then declines rapidly at older ages. I interpret these patterns in light of a multistage theory of aging, developed by analogy with multistage models of cancer progression [8-11]. In the multistage model, disease develops by progression through a series of intermediate physiological or somatic conditions. I show that the late-life decline in acceleration (mortality plateau) is an inevitable consequence of multistage disease progression [12]. The midlife rise in acceleration may also be explained by a multistage theory if the rates of progression between stages rise slowly during midlife [12].

Figure 1 illustrates mortality patterns for non-Hispanic white females in the United States for the years 1999 and 2000. The top row of panels shows the age-specific death rate per 100,000 individuals on a log-log scale. The columns plot all causes of death, death by heart disease, and death by cancer.

The curves for death rate in the top row have different shapes. However, the quantitative characteristics of death rate at different ages can be difficult to discern visually. The second row of panels shows the same data, but plots the age-specific acceleration of death instead of the age-specific rate of death (see Methods). The acceleration is simply the slope of the rate curve in the top panel at each age. Plots of acceleration emphasize how changes in the rate of mortality vary with age.

The bottom row of panels shows one final plotting transformation to aid in visual inspection of mortality patterns. The bottom row takes the plots in the row above, transforms the age axis to a linear scale to spread the ages more evenly, and applies a mild smoothing algorithm that retains the same shape but smooths the jagged curves. These methods of plotting transformations in Figure 1 are used to plot mortality patterns for the leading causes of death in Figure 2, using the style of plot in the bottom row of Figure 1.

Figure 2 illustrates the mortality patterns for non-Hispanic white males in the United States for the years 1999 and 2000. Each plot shows a different cause of death and the percentage of deaths associated with that cause.

The left column of panels shows causes that account for about one-half of all deaths. Each of those causes shares two attributes of age-specific acceleration. From early life until about age 80, the acceleration in mortality increases in an approximately linear way. After age 80, acceleration declines sharply and linearly for the remainder of life. Some of the causes of death also have a lower peak between 30 and 40 years.

The upper-right column of panels shows causes that account for about one-third of all deaths. These causes show steep, linear rises in mortality acceleration up to 40–50 years, and then steep, nearly linear declines in acceleration for the remainder of life. The bottom-right column of panels shows two minor causes of mortality that are intermediate between the left and upper-right columns.

What can we conclude from these mortality curves? The patterns by themselves do not reveal the underlying processes. However, the patterns do constrain the possible explanations for changes in age-specific mortality and suggest some interesting hypotheses. With regard to constraint, we can rule out a single underlying cause of all human mortality acceleration because the two leading causes of death, heart disease and cancer, show markedly different patterns. In addition, any plausible explanation must satisfy the constraint of generating an early-life rise in acceleration and a late-life decline in acceleration, with the rise and fall being nearly linear in most cases. A refined explanation would also account for the minor peak in acceleration before age 40 for certain causes.

One point of this paper is to reiterate the puzzles revealed by the age-specific acceleration plots for different causes of mortality [2,7]. The clarity of those patterns sets the stage for more focused work on this topic and for new hypotheses.

Multistage theory of disease progression and mortality

Four attributes of the mortality patterns must be explained: early-life rise in acceleration, late-life decline in acceleration, a peak near 80 for some causes and a peak near 40–50 for other causes, and a minor peak near 40 for a few causes.

I favor the multistage model of disease progression that has been used widely in analyzing cancer incidence and mortality [8]. A multistage model readily explains the late-life decline in acceleration [12]. Suppose, for example, that there are n stages in progression before death, and the transitions between stages happen at constant rates. It is well known that this sort of multistage progress yields a linear increase in incidence with age when measured on a log-log scale, in the style of the plots shown in the top row of Figure 1 [8]. (I provide a full mathematical description of the multistage model and its properties of acceleration in the Methods section.)

If n stages remain before death, then the predicted slope of the log-log plot is n-1. In a paper on cancer incidence [12], I pointed out that as individuals age, they tend to progress through the early stages. If there are n stages remaining at birth, then later in life the typical individual will have progressed through some of the early stages, say a of those stages. Then, at that later age, there are n-a stages remaining and the slope of the log-log plot (acceleration) is n-a-1. As time continues, a rises and the acceleration declines.

Gavrilov and Gavrilova [13] made roughly the same argument for the late-life decline in acceleration of human mortality. They argued that individuals at birth have redundant systems of protection against mortality, say n redundant systems. As one ages, some of those n systems fail, say a, fail. Then with n-a systems operating, the acceleration is n-1-a. Mathematically, this is essentially the same argument that I gave for cancer. However, I emphasized a multistage model of progression based on the idea that cancer develops in stages, partly driven by the accumulation over time of key somatic mutations in cell lineages. With regard to Gavrilov and Gavrilova's argument, it is not clear biologically what sort of redundancy exists in systems that protect against mortality.

The multistage model can also explain the early-life increase in acceleration. Such increase occurs when the transition rate between stages increases slowly over time [12]. In cancer, a slow clonal expansion of a precancerous population of cells increases the number of cells at risk for passage through the next stage of progression, and thus causes a slow increase in the acceleration of cancer incidence [9,10]. Any slow rise in the transition rates between stages of progression will also cause a slow rise in acceleration. Figure 3 provides some numerical illustrations of how the multistage model may explain a midlife rise in acceleration and a late-life decline in acceleration.

In the multistage model, the different acceleration peaks in heart disease and cancer may arise from different numbers of stages in progression or different transition rates between stages.

The minor peak in acceleration early in life for male heart disease and a few other causes could be explained by heterogeneity in predisposition. Strongly predisposed individuals would go through the same multistage process, but with perhaps fewer steps to pass. That would cause the early-predisposition group to follow the same pattern of a rise and fall in acceleration, but to do so at an early age. That group would dominate the death statistics of early life, and thus would be seen as an early-life minor peak in acceleration.

The multistage model is widely used in the analysis of cancer incidence and mortality [9,10]. Could there be a different multistage progression for heart disease and other causes of death? Certainly, there are morphological and physiological stages of artery disease. First, depositions on the artery walls constrict blood flow. Second, various types of lesions may form, such as a fatty streak or fibrous plaque. Finally, lesion growth may trigger the initial stages of cardiovascular diseases. Andreassi et al. [14] have argued that plaque formation may actually develop through a process of accumulating somatic mutations in cell lineages. Stages follow as mutations accumulate sequentially in those cell lineages, just as cancer may arise by mutations accumulating in the stem cell lineages that renew epithelial tissues.

Multistage models can be tested by identifying the stages in progression and measuring how many stages healthy individuals have passed at different ages. Although the stages of cancer progression have not been fully worked out yet for any particular type of cancer, much research is focusing on this problem. Within a few years, we may know more about how particular somatic mutations affect progression. Then, with high-throughput genomics, one could screen cell lineages in healthy individuals to measure how individuals of different ages pass through the early stages of progression. Those data could then be linked to the acceleration patterns for disease at different ages. Similarly, better understanding of and diagnostics for cardiovascular disease progression will allow measurement of early stage progression in individuals of different ages. Again, those measurements of progression could be used to test particular models for the acceleration of mortality at different stages in life.

Conclusions

The acceleration plots for the leading causes of death show several striking patterns that must be explained by any theory of aging and mortality [2,7]. The late-life decline in mortality acceleration has been widely discussed. However, the analyses here demonstrate different patterns of midlife rise and late-life decline in acceleration for different causes of death. These analyses also put the late-life decline in a broader context by emphasizing various universal and particular features of mortality acceleration at different ages and across the different major causes of death.

I developed a multistage model of disease progression that can explain the observed patterns of mortality acceleration. An early-life rise in acceleration may be caused by increasing rates of transition between stages as individuals grow older. The late-life decline in acceleration may be caused by progression through earlier stages, leaving only a few stages remaining for older individuals.