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Vladimir Canudas-Romo
Stan Becker Michal Engelman
The Crossover Between Life Expectancies
and Their Record Values
Life expectancy
• Life expectancy at birth is the most frequently used and best-known measure of the length of life of a population.
• Its use as a summary indicator of population health was propagated in the 1920s and 1930s.
(Dublin 1923; Dublin and Lotka 1934)
Life expectancy
1750 1800 1850 1900 1950 2000
020
4060
80
Year
Life
Exp
ecta
ncy
Life Expectancy for Countries Included in the HMD, 1751−2007.
1750 1800 1850 1900 1950 2000
020
4060
80
Year
Life
Exp
ecta
ncy
Life Expectancy for Countries Included in the HMD, 1751−2007.
Life expectancy
• However:
Life expectancy at birth is heavily dependent on events in early life. Its time series alone is not well suited for studying the length of life for aging populations, because potentially important stages of mortality change can not be distinguish.
Kannisto (2001)
Life expectancy
Life expectancy at other ages
• But it is not alone:
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”.
(Preston et al. 2001)
Life expectancy by age
Figure 1. Life Expectancy by Age for the Icelandic Total Population in 2000.
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50 60 70 80 90 100 110Age
Life
exp
ecta
ncy
by a
ge
2000
Source: Human Mortality Database (2008).
Life expectancy
“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)
Life expectancy
Figure 1. Life Expectancy by Age for the Icelandic Total Population in 1860, 1900, 1950 and 2000.
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50 60 70 80 90 100 110Age
Life
exp
ecta
ncy
by a
ge
1860190019502000
Source: Human Mortality Database (2008).
Research Interests
1. Relation between the functions of the life table at the crossing in life expectancies.
2. The timing of the crossing in life expectancies: comparison between and within populations.
Research Interest
Data
Five data bases:
1. Human Mortality Database 2. Berkeley Mortality Database3. United Nations, yearbook for 20084. WHO, mortality data for 2008 5. CDC, USA life tables 1980-2006
Data
Life expectancy
?)()( 10 tete =
Figure 2. Life Expectancies at Birth (e0) and at Age One (e1) for the Swedish Total Population from 1850 to 2005.
0
10
20
30
40
50
60
70
80
90
1850 1875 1900 1925 1950 1975 2000Year
e0 a
nd e
1
e0e1
Source: Human Mortality Database (2008).
Life expectancy
)()(
11 te
tmo
=
)t(e)t(e 10 =
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.
0
10
20
30
40
50
60
70
80
90
1850 1875 1900 1925 1950 1975 2000Year
e0 a
nd e
1
0
10
20
30
40
50
60
70
80
90
1/1m
0
e0e11/1m0
Source: Human Mortality Database (2008). Only values of inverse infant mortality below 90 are shown.
Research Interests
2. The timing of the crossing in life expectancies: comparison between and within populations.
Results 1) Common trends in crossing in life expectancies
2) Current situation in the world3) Record maximum remaining life expectancy4) Subpopulations comparison in the USA
Research Interest
Figure 3. Life Expectancy at Birth at Year of the First Crossing with Life Expectancy at Age One, Total Population by Country.
ISL
FIN
JPN
DNK
LUX
CHE
TWN
CANENW
NZL
FRG
ESP
USA
AUT
EST
BLR
RUS
SWENLDNOR
FRAAUS
BEL
GDR
ITA
LVA
LTUSVN
CZE SVKBGR
PRT
UKR
HUN
65
67
69
71
73
75
77
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005Year
Life
exp
ecta
ncy
at b
irth
& a
t age
one
Source: Human Mortality Database (2008); Table 1 has the countries 3-letter digits.
Figure 3. Life Expectancy at Birth at Year of the First Crossing with Life Expectancy at Age One, Total Population by Country.
ISL
FIN
JPN
DNK
LUX
CHE
TWN
CANENW
NZL
FRG
ESP
USA
AUT
EST
BLR
RUS
SWENLDNOR
FRAAUS
BEL
GDR
ITA
LVA
LTUSVN
CZE SVKBGR
PRT
UKR
HUN
65
67
69
71
73
75
77
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005Year
Life
exp
ecta
ncy
at b
irth
& a
t age
one
Source: Human Mortality Database (2008); Table 1 has the countries 3-letter digits.
Research Interests
2. The timing of the crossing in life expectancies: comparison between and within populations.
Results 1) Common trends in crossing in life expectancies
2) Current situation in the world3) Record maximum remaining life expectancy4) Subpopulations comparison in the USA
Research Interest
Figure 5a. Infant Mortality Rate and Life Expectancy at Birth for Countries Members of the WHO and UN, and Not Included in the HMD, Latest Available
Information from WHO and UN.
10
20
30
40
50
60
70
80
0 20 40 60 80 100 120 140 160 180Infant Mortality Rate
Life
exp
ecta
ncy
at b
irth
Life expectancy crossing (e0=e1)EUROPE
Source: United Nations (2008) and World Health
Figure 5a. Infant Mortality Rate and Life Expectancy at Birth for Countries Members of the WHO and UN, and Not Included in the HMD, Latest
Available Information from WHO and UN.
10
20
30
40
50
60
70
80
0 20 40 60 80 100 120 140 160 180
Infant Mortality Rate
Life
exp
ecta
ncy
at b
irth
Life expectancy crossing (e0=e1)AFRICAAMERICAASIAEUROPE
Source: United Nations (2008) and World Health
Research Interests
2. The timing of the crossing in life expectancies: comparison between and within populations.
Results 1) Common trends in crossing in life expectancies
2) Current situation in the world3) Record maximum remaining life expectancy4) Subpopulations comparison in the USA
Research Interest
Figure. Country Holders of the Female Record Life Expectancy at Birth and the Best Fitting Line from 1840-2005.
40
50
60
70
80
90
1840 1860 1880 1900 1920 1940 1960 1980 2000Years
Mod
al, m
edia
n an
d lif
e ex
pect
ancy
40
50
60
70
80
90
AUS BLR ISL DNK NOR
SWE CHE CAN NZL JPN
Source: Human Mortality Database; Note: AUS=Australia, BLR=Belarus, Can=Canada, DNK=Denmark, ISL=Iceland, JPN=Japan, NOR=Norway, NZL= New Zealand, SWE=Sweden, CHE=Switzerland.
Figure 1. Life Expectancy by Age for the Icelandic Total Population in 1860, 1900, 1950 and 2000.
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50 60 70 80 90 100 110Age
Life
exp
ecta
ncy
by a
ge
1860190019502000
Source: Human Mortality Database (2008).
Life expectancyRecord LE, e0
)(max)( 00 tete i
i=
Life expectancyMaximum remaining LE, em
)(max)( tete imim =
1850 1900 1950 2000
02
46
810
Year
Diff
eren
ce b
etw
een
reco
rd e
xpec
tanc
ies (e
rx−
e 0)
Figure 4. Difference between record life expectancy at birth (e0)and record remaining life expectancy (erx)
Age of erx
AGE 0AGE 1AGE 2AGE 3AGE 4AGE 5AGE 6
1850 1900 1950 2000
4050
6070
80
Year
Life
exp
ecta
ncy
Figure 5. Countries holding the record life expectancy at birth (e0)and the record total expected longevity (eT) for the total population
AUSTRALIADENMARKICELANDJAPANNETHERLANDSNEW−ZEALANDNORWAYSWEDEN
eT
e0
Research Interests
2. The timing of the crossing in life expectancies: comparison between and within populations.
Results 1) Common trends in crossing in life expectancies
2) Current situation in the world3) Record maximum remaining life expectancy4) Subpopulations comparison in the USA
Research Interest
Figure 6. Infant Mortality and Life Expectancy at Birth for American Females and Males by Race (White & Black), 1968.
40
45
50
55
60
65
70
75
80
85
0
Life
exp
ecta
ncy
(e0)
White Females
White Males
Black Females
Black Males
Source: BMDB(2009) & CDC (1984-2006).
Figure 6. Infant Mortality and Life Expectancy at Birth for American Females and Males by Race (White & Black), 1968.
40
45
50
55
60
65
70
75
80
85
0 10 20 30 40 50
Infant Mortality
Life
exp
ecta
ncy
(e0)
White FemalesWhite MalesBlack FemalesBlack MalesLife expectancy crossing (e0=e1)
Source: BMDB(2009) & CDC (1984-2006).
Figure 6. Infant Mortality and Life Expectancy at Birth for American Females and Males by Race (White & Black), 1968-1973.
40
45
50
55
60
65
70
75
80
85
0 10 20 30 40 50
Infant Mortality
Life
exp
ecta
ncy
(e0)
White FemalesBlack FemalesWhite MalesBlack MalesLife expectancy crossing (e0=e1)
Source: BMDB(2009) & CDC (1984-2006).
Figure 6. Infant Mortality and Life Expectancy at Birth for American Females and Males by Race (White & Black), 1968-1977.
40
45
50
55
60
65
70
75
80
85
0 10 20 30 40 50
Infant Mortality
Life
exp
ecta
ncy
(e0)
White FemalesBlack FemalesWhite MalesBlack MalesLife expectancy crossing (e0=e1)
Source: BMDB(2009) & CDC (1984-2006).
Figure 6. Infant Mortality and Life Expectancy at Birth for American Females and Males by Race (White & Black), 1968-1996.
40
45
50
55
60
65
70
75
80
85
0 10 20 30 40 50
Infant Mortality
Life
exp
ecta
ncy
(e0)
White FemalesBlack FemalesWhite MalesBlack MalesLife expectancy crossing (e0=e1)
Source: BMDB(2009) & CDC (1984-2006).
Figure 6. Infant Mortality and Life Expectancy at Birth for American Females and Males by Race (White & Black), 1968-2003.
40
45
50
55
60
65
70
75
80
85
0 10 20 30 40 50
Infant Mortality
Life
exp
ecta
ncy
(e0)
White FemalesBlack FemalesWhite MalesBlack MalesLife expectancy crossing (e0=e1)
Source: BMDB(2009) & CDC (1984-2006).
Discussion
To assess the mortality situation of a population it is
important to consider several measures of mortality in
conjunction, e.g. the level of e0 respect to e1 or with
infant mortality. Following the latter relationship the
physical quality-of-life index (infant mortality, e1 and
education) is more suited for comparison than the
more popular Human Development Index (e0,
education and GDP).
During the demographic transition mortality between
ages one and five declined before mortality in the first
year of life, followed by a second phase of decline
where mortality in infancy declined faster than in the
later childhood years (Hill 1995). This historical
process of mortality reductions, is well captured in this
research of life expectancies at different ages and the
convergence of the two record expectancy measures.
Discussion
Our findings show that a substantial difference
between and the maximum lifespan (e0 and at other
ages) existed throughout most of the 19th and 20th
centuries both in individual countries and for the
global record holders.
Discussion
Basing the “best-practice” designation on a measure
so dependent on mortality in the first year of life as life
expectancy may be problematic. However, the fact
that the same group of countries also holds the record
remaining life expectancy offers some support to the
“best-practice” idea originated by Oeppen and Vaupel
(2002).
Discussion
The Crossover BetweenLife Expectancies
and Their Record Values
Thank you!