 |
 |
 |
 |
 |
|
|
|
|
|
|
|
Tables 6 and 7 show values for the functions qx, lx, dx, Lx, Tx, and 
by age and sex for selected years. Table 6, the period table (by calendar year), presents values for every tenth year from 1900 through 2100. Table 7, the cohort table (by year of birth), includes every tenth year 1900 through 2000. The methods used to produce the values shown in these tables have been described in Section IV of this actuarial study.
For each calendar year, or cohort, death rates are relatively high in the first year after birth, decline very rapidly to a low point around age 10, and thereafter rise, in a roughly exponential fashion, before decelerating (or slowing their rate of increase) at the end of the life span. Cohort tables show less rapid increase in the death rate with advancing age than do period tables because cohort tables reflect in succeeding ages the general improvement in health and safety conditions that occur over time. Conversely, period tables show more rapid increase in death rates with increasing age because calendar year experience for each higher age does not reflect the improved mortality of the succeeding years.
Table 8 presents a summary comparison of one-year probabilities of death for selected ages, by sex and calendar year. This allows a more detailed year-by-year analysis of the improvement in age specific death rates over time than was presented in Table 6. The greatest relative improvement in mortality during the twentieth century occurred at the young ages, resulting largely from the control of infectious diseases. For each sex, the probability of death at age 0 decreased 95 percent between 1900 and 1999 and a further reduction of about 83 percent is projected between 2000 and 2100. At age 30, the decrease between 1900 and 1999 was 82 percent for males and 92 percent for females, reflecting the rapid decline in childbearing mortality experience for females. Over the period 1999-2100, further decreases of 55 and 51 percent for males and females respectively, are projected.
At ages 60, 65, and 70, shown in Table 8, the probability of death decreased by about 50 percent for males and by over 60 percent for females between 1900 and 1999. This large sex differential in mortality improvement is attributed partly to genetic factors and partly to environmental factors. If the genetic factors are more important, then the sex gap in mortality can be expected to remain large or even widen. If the environmental factors are more important, then the sex gap can be expected to close somewhat as women become increasingly subject to the same pressures and hazards as men. For example, during the period 1970 through 1980 when great strides were made in treating degenerative diseases affecting the cardiovascular system, male mortality at age 65 decreased 16 percent while female mortality decreased only 9 percent. Over the following 20-year period, from 1980-1999, male mortality at age 65 continued to decrease faster than female mortality, with male mortality decreasing 26 percent and female mortality decreasing only 9 percent. Increasing levels of tobacco use and job stress for women are expected to tend to narrow the gap in the future. Death rates are projected to decrease by about 55 percent for males and 50 percent for females in the 1999-2100 period.
At age 100, probability of death decreased by only about 17 percent for males and 28 percent for females in the last century. Between 2000 and 2100 decreases are projected to be somewhat greater at 40 percent for males and 42 percent for females reflecting expected increased future emphasis on those causes of death that most affect the aged.
Table 9 presents a s ummary comparison of cohort qx's, one year probabilities of death at selected ages by sex and year of birth. The values in this table are the same as those in Table 8; however, they are organized so that relative levels of death probability at each age can be conveniently compared across cohorts rather than across calendar years of experience.
Table 10 presents life expectancy at selected ages, by sex and calendar year on a period basis. That is, life expectancy at a particular age for a specific year is based on the death rates for that and all higher ages that were, or are projected to be, experienced in that specific year. Life expectancy at age 0 for males increased 27.22 years from 46.41 years in 1900 to 73.63 years in 1999. During the same period, life expectancy at age 0 for females increased 30.26 years from 48.96 years to 79.22 years. Thus the sex gap in life expectancy at birth has increased from 2.55 years in 1900 to 5.59 years in 1999. However, the sex gap has declined from a level of 7.83 years for 1973 and is projected to continue declining at a slow rate reaching a difference of 5 years in 2025.
Rapid gains in life expectancy at age 0 occurred from 1900 through the mid 1950's for both males and females. From the mid 1950's through the early 1970's, male life expectancy at age 0 remained level, while female life expectancy at age 0 increased moderately. During the 1970's faster improvement resumed for both males and females. Life expectancy for males and females in the 1980's improved only slightly with males improving more than females. In the 1990's, life expectancy has remained fairly constant for females, increasing only slightly for males.
Figure 2a shows life expectancy at age 0, by sex and calendar year, based on period life tables.
Based on period life tables, life expectancy at age 65 for males increased from 11.3 years in 1900 to 15.7 years in 1999, while for females the increase was from 12.0 years to 18.9 years. Thus, the sex gap in life expectancy at age 65 has increased from 0.7 years to 3.2 years between 1900 and 1999. However, this sex gap diminished during the 1980's and 1990's and is projected to decrease only slightly in the future.
Figure 2b shows life expectancy at age 65, by sex and calendar year, based on period life tables.
Little increase was experienced from 1900 to 1930. Since then, rapid gains occurred for females until the significant slowdown of the 1980's. The 1990's have been stable for females. For males, improvement has been rapid since the 1930's, but with a stable period during the 1950's and 1960's.
Table 11 shows, on a cohort basis, life expectancies at selected ages, by sex and year of birth. That is, life expectancy at a particular age for a specific year is based on death rates for that age in the specific year and for each higher age in each succeeding year. Life expectancies on a cohort basis tend to fluctuate less from year to year than do period-based life expectancies because of sudden and temporary events, such as a flu epidemic, which may affect the entire population, for a brief period of one or two years, but affect only one or two years of mortality experience for each of the cohorts alive during the period. Therefore, cohort life expectancies are more useful in analyzing subtle and gradual generational trends in mortality.
Figure 3 shows life expectancy at age 0, by sex and year of birth, based on cohort life tables.
Based on cohort life tables, life expectancy at age 0 for m ales increased 28.1 years from 51.5 years for births in 1900 to 79.6 years for births in 1999. During the same period, life expectancy at age 0 for females increased 26.2 years from 58.3 years to 84.5 years. Thus the sex gap in life expectancy at birth in a cohort has decreases from 6.8 years for births in 1900 to 4.9 years for births in 1999. However, substantial increases in the sex gap in life expectancy at birth were experienced during this period, reaching eight years for births in 1920, followed by a gradual decline to the projected gap for births in 1999.
Table 12 presents ratios of female to male values for life expectancies and for one-year probabilities of death, for selected ages and calendar years, based on period life tables. These ratios provide another perspective from which to consider sex differences.
Table 12 shows that the ratio of female to male life expectancy generally rose fairly steadily from 1900 through 1979 at ages 0 through 70. This ratio has declined since 1979 and is expected to continue to decline at a slow rate in the future. This trend reflects the general decline through 1970 in the ratio of female to male death probabilities at the important ages 60 through 70, and the actual and projected increase, thereafter, in this ratio for these ages.
Table 12 also shows that the ratio of female to male life expectancy at age 100 was constant from 1900 through 1959 reflecting the fact that male and female death probabilities are estimated to have been essentially the same at this and higher ages throughout this period. Since 1959, however, the ratio of female to male life expectancy at age 100 has increased, and is projected to be around 1.14 after 1999.
Table 13 presents ratios of female to male values similar to those in Table 12, but based on cohort life tables. The ratio of female to male life expectancy declines steadily at ages 0 through 70, for cohorts born after 1906. This again reflects the increase throughout that period in the ratio of female to male death probabilities at the important early-elderly ages. Declines in the ratio of female to male life expectancy at age 100 reflect the past and projected increases in the ratio of female to male death probabilities at very high ages.
Table 14 presents the age for three selected survival rates, by sex and calendar year on a period basis. The median of the inverse survival distribution increased 22.0 years, from 55.1 years for males in 1900 to 77.1 in 1999. For females the increase was 24.4 years, from 58.2 years in 1900 to 82.6 years in 1999. Increases in future lifetime between 1999 and 2100 are projected to be 8.7 years for males and 6.9 years for females.
Figure 4a shows median lifetime by sex and calendar year, based on period life tables. The shapes of the survival function at S(x) = .5 are similar to the shapes of the life expectancy curves at age 0, except that increases are smaller.
Table 14 shows that for the survival rate = .00001, the corresponding age for males increased from 104.4 years in 1900 to 109.8 years in 1999, while for females it increased from 104.9 years to 112.0 years. From 1999 to 2100, the age for males is expected to increase by 9.8 years and for females by 9.1 years. This trend runs counter to the widely held belief that the age attained by the oldest survivors in the population has risen little, if at all, during the twentieth century.
Figure 4b shows the extreme old age, age x such that S(x) = .00001, by sex and calendar year, based on period life tables. X, such that S(x) = .00001 increased very little from 1900 through 1930. Between 1930 and 1954, and again between 1963 and 1982, saw a rapid increase in age. Since 1982, age x for S(x) = .00001 has decreased for both males and females. For the period 1999, x such that S(x) = .00001 is projected to rise steadily and slowly at about .1 year per year for males and .05 year per year for females.
Figure 5 presents the population survival curves based on period life tables for selected calendar years. Great strides were made in the twentieth century toward eliminating the hazards to survival which existed at the young ages in the early 1900's. Very little additional improvement to survival rates is possible at these young ages. Survival rates at the older ages are projected to continue to improve steadily. Projected gains in the probability of surviving to age 90 during the next 50 years are about the same as experienced during the past 50 years. For age 100, projected gains are much greater than for the past. Figure 5 shows population survival curves based on period life tables for, from left to right, 1900, 1950, 2000 and projected years 2050 and 2100.
Although the shape of the survivorship curve has become somewhat more rectangular (less diagonal) through time, it appears that very little additional rectangularization will occur because survival rates are already so high at the young ages and are expected to continue increasing at older ages. The so-called "curve squaring" concept, though appealing to many, simply cannot be supported by the mathematics of mortality. The age at which the survivorship curve comes close to zero, through the compounding of single-year probabilities of survival, has increased greatly during the twentieth century and will continue to increase, as further strides are made against degenerative diseases. That mortality rates are found to continue to decline, at every age for which adequate data is available, demonstrates that no absolute limit to the biological life span for humans has yet been reached, and that such a limit is unlikely to exist.
|
|
|
|
|
