Estimating mean lifetime

Abstract

The life expectancy implied by current age-specific mortality rates is calculated with life table methods that are among the oldest and most fundamental tools of demography. We demonstrate that these conventional estimates of period life expectancy are affected by an undesirable ''tempo effect.'' The tempo effect is positive when the mean age at death is rising and negative when the mean is declining. Estimates of the effect for females in three countries with high and rising life expectancy range from 1.6 yr in the U.S. and Sweden to 2.4 yr in France for the period 1980 -1995.W hen a group of persons is observed from birth to death, mean lifetime may be calculated simply and directly as mean age at death. This statistic is problematic, however, for studying trends in mean lifetime. Mean lifetime for Swedish females born in 1850, for example, reflects mortality conditions from the mid-19th to the mid-20th centuries, a period of historically unprecedented increases in human survival. The study of these changes requires a different approach.Period life expectancy at birth calculated by life table methods has been the standard solution to this problem since the mid-19th century (1). This paper argues that it is an imperfect solution, because life expectancy at birth calculated in this way is distorted whenever it is changing.Conventional life expectancy depends solely on the force of mortality function for time t. We propose an alternative measure that depends both on the force of mortality function and on the rate of change in the standardized mean age at death. Our alternative is based on the assumption that the observed force of mortality function at any given time has the same shape as the force of mortality function inherent in the standardized population age distribution at time t, which reflects the history of mortality in the population. We demonstrate that this assumption is realistic in contemporary societies with high life expectancy and also that the proposed measure is consistent with well-established measures used in other demographic contexts. MethodsCohort Mean Lifetime. The distribution of lifetimes for a group of persons born during any given time period (a ''birth cohort'') may be described in three different ways. The survival function,gives the proportion of individuals who survive to exact age a. It is nonincreasing, with l(0) ϭ 1.0 and l( ) ϭ 0 for some advanced age . The death density function,gives the distribution of deaths by age. The force of mortality function,gives the risk of dying at each age. These functions are formally equivalent in the sense that any two may be derived from the third. The force of mortality function (a) may be derived from d(a) or l(a) by using Eq. 1c, for example, and l(a) may be derived from (a) or d(a) by using Fig. 1 plots l(a), d(a), and (a) for the cohort of females born in Sweden in 1850. The survival function declines to zero at around age 100 yr. The density function is broadly bimodal with peaks at age 0 and Ϸ80 yr. The force of mortality exhibits a U-s...

The modal age at death and the shifting mortality hypothesis

“…Bongaarts and Feeney (2002Feeney ( , 2003 showed that the value of µ(0, t) declines over time. When the reduction in mortality is almost negligible, and the value of µ(0, t) approaches zero, equations (6) and (7) decrease to a constant number of survivors…”

Found in translation?

“…The story of the "life extension" pill discussed by Bongaarts and Feeney (2003) illustrates the potential advantages of tempo-adjustment in the case of a sudden shift in survival. (See Figure 1a.) On January 1, everyone in a previously stationary population takes a pill postponing their previously programmed date of death by 3 months.…”

“…Here there is no debate. Bongaarts andFeeney (2002 and2003) Bongaarts & Feeney (2003) figure 6 shows the last 15 years of this series. Linearity in CAL implies linear shifts.…”

On the relationship between period and cohort mortality

“…As shown here, CAL is also approximately equal to certain measures of mean lifespan for the population in question. For example, it is quite similar in form to 0 e′ , defined to be the mean age at death (MAD) that would be observed in a given time period for a population with an identical historical mortality pattern and a constant annual number of births (Bongaarts and Feeney, 2003). However, such measures describe population dynamics, not the life course of a synthetic cohort based exclusively on the mortality risks of a given period.…”