Quantity of Life

Like other life forms, humans have a characteristic life span, a maximum number of years over which individuals might survive if protected from all hazards. The span is currently unknown. Our only direct evidence about it derives from the age at death of exceptionally long-lived people, and the reliability of this evidence is often marred by poor memory, poor records, and misrepresentation. A few people have lived longer than 110 years, and the number of people surviving to extreme ages has increased over time. But it is not clear - because the evidence is inadequate - whether there has been a change in the maximum age to which individual members of the species survive. Given the very small number of

Age (years)

Figure IV.4.1. Survival curves. (From Acsadi and Nemeskeri 1970; Commons Sessional Papers 1884-5; U.S. Decennial Life Tables for 1979-81.)

Age (years)

Figure IV.4.1. Survival curves. (From Acsadi and Nemeskeri 1970; Commons Sessional Papers 1884-5; U.S. Decennial Life Tables for 1979-81.)

people who survive to even older ages, the life span is often estimated at 110 and sometimes at a lower round number, 100 (Preston 1982).

An alternative procedure for estimating longevity is based on the attempt to measure the most advanced age to which people survive in significant numbers. It can safely be suggested that over most of human existence the modal age at death - the age at which more individuals died than at any other - was during the first year. Among people surviving early childhood, however, the modal age at death occurred in adulthood. Apparently it has advanced over time. A life table based on skeletal evidence for a Copper Age population indicates that the number of postinfant deaths peaked at age 46, but late-twentieth-century life tables show a much later peak. For example, a U.S. life table for 1979-81 indicates a postinfant modal age at death of 83 (Acs&di and Nemeskeri 1970; U.S. National Center for Health Statistics 1985). Estimates of the species-specific life span or values for the modal age at death are used to show capacity for survival. Often expressed as a rectangle, this capacity is a statement about how many years of life individuals born at the same time might accumulate if they avoided hazards.

These estimates have been less important in measuring and comparing health experience than they will become. The transition can be attributed to a major change in the pattern of human survival. For most of the history of the species, the space of life -the area represented by the survival rectangle-contained more years of life lost to premature death than years survived. Figure IV.4.1 illustrates this history with survival curves for some populations, the curves showing the number of individuals who lived at each age.

For most of human history most deaths were premature, and the survival curve remained concave. It first became convex in a few advantaged societies in the nineteenth century. Since then, it has bowed out in these and some other societies, approaching a rectangular form. The concave curve can be identified with the traditional mortality regime, a regime in which the risk of death was high at every age. The convex curve is a characteristic of the modern mortality regime. And the convexity itself indicates how the transition from one mortality regime to the other has altered the problems associated with measuring mortality. For most of human history, expectations or hopes about survival have been expressed by reference to birth. The rectangularized survival curve directs attention instead toward life span, modal age at death, or another value intended to represent a survival goal. In other words, how many of the people living at the same time can be protected from premature death, and how long can they be protected?

The survival curve captures the concepts needed to compare mortality experiences. The data necessary to plot it are drawn from the life table, initially developed as a way to set insurance premiums, but subsequently put to use in epidemiology, biology, and demography. The estimation of survival curves and other elements of the life table are commonplace in historical discussion, although they are more often implicit than explicit because historians seldom work with periods and populations for which life tables exist.

One useful estimate of mortality experience is the crude death rate, the ratio of deaths in a given year to the mean population during that year. This rate is a function of the age distribution as well as the number of deaths at each age. Consider, for example, the crude death rates for the United States and Costa Rica in 1977 - 8.6 and 4.3, respectively. The lower rate for Costa Rica means a lower probability of death, but it is lower because the age structure was different in the United States rather than because the risk of death was lower at each age. In fact, Costa Ricans faced a higher mortality risk at most ages, but the younger average age offset the difference in risk of death.

The crude death rate is also influenced by migration. For example, populations receiving immigrants of a certain age group, say young adults, will appear to have higher life expectancies based on the record

Table IV.4.1. Abridged life table for Sweden, 1751-90

Proportion

Number living

dying in

at beginning

Number dying

Years lived

Accumulated

Life

Age interval,

interval,

of age interval,

in age interval,

in age interval,

years lived,

expectation,

x to x + 1

Qx

h

dx

Lz

x

«X

0

0.20825

10,000

2,082

8,314

351,935

35.19

1

0.10406

7,918

824

14,884

343,621

43.40

3

0.05642

7,094

400

13,788

328,737

46.34

5

0.06700

6,694

448

32,350

314,949

47.05

10

0.03621

6,246

226

30,663

282,599

45.24

15

0.03527

6,020

213

29,567

251,936

41.85

20

0.04270

5,807

248

28,417

222,369

38.29

25

0.05065

5,559

281

27,092

193,952

34.89

30

0.05957

5,278

315

25,605

166,860

31.61

35

0.06056

4,963

300

24,065

141,255

28.46

40

0.07947

4,663

371

22,387

117,190

25.13

45

0.08611

4,292

369

20,537

94,803

22.09

50

0.10820

3,923

425

18,552

74,266

18.93

55

0.12935

3,498

452

16,359

55,714

15.93

60

0.18615

3,046

567

13,811

39,355

12.92

65

0.25879

2,479

642

10,790

25,544

10.30

70

0.36860

1,837

677

7,463

14,754

8.03

75

0.47839

1,160

555

4,443

7,291

6.29

80

0.63916

605

387

2,059

2,848

4.71

85

0.77971

218

170

789

789

3.62

90+

1.0

48

48

(123)°

(123)°

2.56

"The adaptation supplies the sum of years lived at 90 and higher ages. Source: Adapted from Fritzell (1953).

"The adaptation supplies the sum of years lived at 90 and higher ages. Source: Adapted from Fritzell (1953).

of deaths than will more stable societies. Although there is often no more than fragmentary information about age structure or migration, the effects of these variables may require that the crude death rate be qualified by a statement concerning its possible distortion. In addition to reasons already mentioned, the crude rate may be misleading if, in a regime prone to epidemics, it is not averaged over several years.

Age-specific death rates can be compared (over time and space) in the form of the survival curves in Figure IV.4.1. Comparisons can also be made on the basis of age-standardized death rates, which adjust age-specific rates for a standardized population (this procedure and others are explained by Shryock et al. 1973). The reason for making these calculations of death rates is to compare two or more populations on the same terms, eliminating the effects of differences in age structure. (This procedure can also be applied to other characteristics according to which mortality or morbidity rates may differ, such as sex, residence, occupation, and marital status.)

With information about the size of a population, the age of its members, and the number who die at each age - or plausible estimates of these quantities - it is possible to build a life table such as the one for Sweden during 1751-90 presented in Table IV.4.1. The table begins with a radix, or base population - in this case 10,000. The probabilities of death at each age, the basic quantities of the life table, are derived from age-specific death rates. Both the death rate and the probability of death at an age have the same numerator - the number of deaths at that age within a specific time period. But their denominators differ. For the death rate, the denominator is the mean population at that age over the period studied, and for the probability of dying, it is the population at that age at the beginning of the period under study. This difference is usually minor, except when one is considering the probability of death between two ages that are separated by a number of years (e.g., from 5 to 10) and except for infants.

A current, or period, life table makes use of death rates for all ages at a given time to provide a cross-sectional picture of a stationary population. Its val ues for life expectancy and other quantities are termed hypothetical because the death rates used to construct it apply to people at each age in the current population; the history it relates refers to a hypothetical cohort, because the people alive at this time may have been subject to different death rates in past years and may be subject to differences again in the future. A cohort, or generation, life table follows the experience of one cohort from birth to death. Its values are not hypothetical, but a cohort table cannot be constructed until all members of a cohort have died. Thus, a current table, like that in Table IV.4.1, is preferred for many uses.

When populations are small, as Sweden's population was in the eighteenth century, and when death rates fluctuate from year to year, it is customary to average experience over several years. Table IV.4.1 is also an abridged table, meaning that it provides values only for benchmark ages. Those in between can be interpolated. Because the number of years lived by the cohort at high ages is so small, the custom is to close the life table at an age that is lower than that of the oldest survivor and to sum the years lived at all higher ages. The accumulated years lived by the actual or hypothetical cohort, which is the sum of years lived in each interval, provides the information necessary to calculate life expectancy. From Table IV.4.1 life expectancy at birth (35.2) is the sum of all years lived by the hypothetical cohort (351,935) divided by the radix population (10,000); life expectancy at age 20 (38.3) is the sum of years lived after 20 (222,369) divided by the number surviving to 20 (5,807).

What makes the life table so useful for historical investigation is its capacity to represent a sequence of events over a long span. Thus, the life table has been used to estimate changes in the prevalence of specific diseases over time. Although the events of interest in this essay are mortality and episodes of morbidity, other events, such as marriage and divorce, can also be followed, as can conditional events, such as deaths among people already ill. Age-specific death rates are conditional because they depend on survival to each age. The population whose experience is followed over time may be select in the sense that its members differ in significant ways from the general population. The life table need not begin at birth or be limited to single events. More complex models treat contingent events that occur in stages, such as the evolution of cancer, with its various outcomes and probabilities at each stage. The concept can also be applied to the longevity of political regimes or credit instruments.

Because historians often know or can reliably estimate the death rate at a few ages but not throughout the life course, it is helpful to employ model life tables to make inferences about other ages or to estimate the overall structure of mortality. Model tables are based on the observation that mortality risks show some regularities over time. Populations that have low death rates at one age are likely to have low death rates at other ages, and vice versa. The regularities can be seen by plotting the mortality schedule, which consists of a line linking age-specific probabilities of death. (When the change from one benchmark to another is high, it is convenient to plot values on paper with a vertical logarithmic scale. On this scale an exponential rate of change appears as a straight line.) Figure IV.4.2 shows that the form of the mortality schedule resembles a misshapen W across the survival rectangle. Over time the W-curve has usually shifted down, so that at each age lower mortality rates are reported for recent, as opposed to past, populations.

Close scrutiny of life tables from a variety of populations shows that the W-shape is preserved across time, but that it displays some irregularities. In some populations the risk of death is greater at some ages than it is in other populations. In Figure IV.4.2, for instance, the angle of change in the mortality risk varies among the three populations, most evidently at adult ages. As can be seen, the U.S. 1979-81 schedule is lower than the other two, yet its rate of increase between ages 40 and 80 is steeper. But for these variations, model life tables would suggest all other age-specific mortality rates when only one was known. Because of these variations, demographers have fashioned groups or "families" of model life tables, each representing a variation on the basic form. One widely used collection of model tables provides four families, styled West, North, South, and East, and a variety of mortality schedules or levels (Coale and Demeny 1966; McCann 1976). With model tables, which are most readily conceived from their survival curves, incomplete information about mortality experience in a given population can provide the basis for a plausible estimate of complete experience.

Life expectancy, which incorporates age-specific death risks, is a convenient value for making historical comparisons. Over time, life expectancy at birth has advanced, and the story of that advance is part of the history of mortality and the mortality revolution. Whereas life expectancy is most commonly used as an estimate of the average remaining lifetime at birth, it also captures changes in death rates

10,000 6,000 4,000

1,000

Figure IV.4.2. Mortality risk for medieval Hungary, England (1871-80), and the United States (1979-81). (From Acsadi and Nemesk6ri 1970; Commons Sessional Papers 1884-5; U.S. Decennial Life Tables for 1979-81.)

at different ages. During the modern period of mortality decline, which began in the eighteenth century and has not yet ended, the risk of death did not decline in a uniform way across the age spectrum (Perrenoud 1979, 1985; Imhof 1985). In northwestern Europe, for example, the decline during the eighteenth century was concentrated among infants, youths, and young adults. Other age groups joined the shift toward declining risks later.

Life expectancy commonly appears to increase to a greater extent when measured at birth than when measured at higher ages. That is, the risk of death has declined more in infancy (up to age 1) than at any later age. It is often reported that life expectancy at higher ages, especially in adulthood, has changed relatively little over time. In some ways this is misleading. Thinking once more in terms of the survival rectangle, a disproportion is apparent in the time at risk. At birth some members of a population might be expected to live 110 years. But at each higher age their potential survival time is bounded by the human life span; it diminishes as age rises. In short, life expectancy can also be construed as an indication of how much of the available space of life has been used.

By turning our attention toward both birth and some representation of maximum survival and by reporting an age-specific measure of mortality at several points within the life course, we obtain means of detecting more subtle changes in mortality experience. Whereas life expectancy represents the average remaining lifetime, another measure, years of potential life lost (YPLL), compares the average span achieved with the number of years that it can plausibly be supposed a population might survive. Because that value is indefinite, no convention yet exists for measuring YPLL. The U.S. National Center for Health Statistics presently uses a base of 65 years. That gauge assigns greater weight to causes of death the earlier those causes intervene, and no weight to causes that intervene at ages above 65.

Although not yet applied extensively to historical investigations, the YPLL provides a way to think about the degree to which different societies succeed in controlling mortality. If the YPLL is not adjusted for changes over time, more modern societies will systematically appear more successful than earlier societies because they have higher life expectancies. But judgments about success need not depend on the assumption implicit in this comparison, the assumption that all societies have the same potential for increasing the years its members can expect, on average, to live. If the ceiling is adjusted - perhaps using changing modal age at death - different interpretations of changes in survival may emerge. If the ceiling is adjusted with an eye on one or a few causes of death of particular interest, societies can be compared according to the efficacy of their control over leading diseases (see Preston, Keyfitz, and Schoen 1971).

How To Add Ten Years To Your Life

How To Add Ten Years To Your Life

When over eighty years of age, the poet Bryant said that he had added more than ten years to his life by taking a simple exercise while dressing in the morning. Those who knew Bryant and the facts of his life never doubted the truth of this statement.

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