0

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40

60

80

1850 1900 1950 2000

0

20

40

60

80

e0e11/1m0

Life expectancies at birth (e0) and at age one (e1) are the same when they are equal to the inverse of the infant mortality death rate, or age-specific death rate at age one (1m0).

The Crossover Between Life Expectancies at Birth and at Age OneVladimir Canudas-Romo & Stan Becker

Department of Population Family and Reproductive Health. Johns Hopkins Bloomberg School of Public Health

Life expectancy at age “x” is defined as the average number of additional years that a survivor to age x will live beyond that age. Life expectancy at birth is the most frequently used and best known measure of the length of life of a population. “As a rule, the expectation of life decreases as age increases, with the exception of the first year of life where the reverse is true because of the high mortality during the first year.” Chiang (1984: 118). However, during the second half of the twentieth century most developed countries experienced a crossover of these two life expectancies (Figure 1).

The relation between mortality in the first year of life and of life expectancies can be observed in the trend of these three measures over time. Figure 2 shows the pattern from 1850 to 2000 for the total population of Sweden. In 1850 e0-e1 = -6.7 and changes to e0-e1 = 0.8 of a year by 2000, with the crossing in life expectancies in 1965.

For industrialized countries Figure 3 shows the timing of the crossing of e0 and e1. The first crossing in the world occurred in Iceland and a clear regional clustering of the crossing of the life expectancies is observed (similar timing and level of life expectancy at the crossing).

A simple relation between infant mortality and life expectancies at birth and age one is central in explicating the mechanisms of the crossover between the life expectancies.  The timing and mortality level at which a population transitions to a life table where life expectancy by age decreases with age depends on the specific characteristics of each country, but also on regional characteristics (Fig 3).

This analysis can be considered as a within-population examination of infant mortality versus mortality after age one, e.g. the black population in the USA lags behind its white counterpart not only on levels of survivorship but also on the timing of the crossover between life expectancies at birth and age one (Fig 4). 

As shown in Figure 5, the world is highly heterogeneous in terms of the current situation of crossing in life expectancies. This division is mainly due to the high levels of infant mortality still remaining in most of the world.

DISCUSSION

INTRODUCTION

DATA AND METHOD

RESULTS

To study the trend over time in life expectancies at birth and at age one five databases are used:  i) The HMD is used to study the timing of the crossing in industrialized countries; ii) The UN and WHO databases are used to find the current situation with respect to the for the different regions of the world and iii) to address the timing in the crossing for the black and white USA subpopulations the data from CDC and the Berkeley MD are used.

e0

e0, e1 & 1/1m0

Figure 4. Infant Mortality (IM=1m0) and Life Expectancy at Birth for American Females and Males by Race (White & Black), 1968-2003.

Figure 5. Infant Mortality Rate (IMR) and Life Expectancy at Birth (e0) for Countries Members of the WHO and UN.

Figure 2. Life Expectancies at Birth (e0) and at Age One (e1) and the Inverse of the Infant Mortality (1/1m0) for the Swedish Total Population

from 1850 to 2005.

Figure 1. Life Expectancy by Age (ex) for the Icelandic Total Population in 1860, 1900, 1950 and 2000.

IMAIM OF STUDY

Assess the timing and the relations of the life table functions at the crossing of life expectancies at birth and at age one.

Age

ex

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1860

1900

1950

2000

01110

1

m)t(e)t(e)t(e

40

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60

70

80

0 10 20 30 40 50

White FemalesBlack FemalesWhite MalesBlack MalesLife expectancy crossing (e0=e1)

e0

10

30

50

70

0 30 60 90 120 150 180

AFRICAAMERICAASIAEUROPELife expectancy crossing (e0=e1)

IMR

e0

Figure 3. Life Expectancy at Birth (e0) at Year of the First Crossing with Life Expectancy at Age One, Total Population by Country.

ISL

FIN

JPN

LUX

CHE

TWN

FRG

USA

AUT

RUS

SWE NLD

NOR

DNK FRA

AUS

CAN

BEL

ENW

NZLGDR

ESPITA

LVA

LTU

SVN

CZE

EST

BLRSVKBGR

PRT

UKR

HUN

65

68

71

74

77

1955 1965 1975 1985 1995 2005

Year

All the US subpopulations, by sex and race, have experienced an increase in life expectancy and decline in infant mortality over time, moving from right to left in Figure 4. However, the white population experiences the crossover during this period while the male black population is still transitioning. Figure 5 presents the current situation of the countries of the world with respect to their life expectancy at birth and infant mortality. In Asia and the Americas some of the countries are still experiencing the crossing in life expectancies, and only two countries have achieved this in Africa.

Year