Samuel Clark Department of Sociology, University of Washington Institute of Behavioral Science, University of Colorado at Boulder Agincourt Health and Population Unit, University of the Witwatersrand Using & Interpreting the Single Decrement Life Table Examples
Using & Interpreting the Single Decrement Life Table
Jan 16, 2016
Using & Interpreting the Single Decrement Life Table. Examples. Plan. Review Period Life Table Construction Ways of using the life table The life table as a Stationary Population Examples Life tables from South Africa Life tables from Zambia Life tables from the USA. - PowerPoint PPT Presentation
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Samuel Clark
Department of Sociology, University of WashingtonInstitute of Behavioral Science, University of Colorado at Boulder
Agincourt Health and Population Unit, University of the Witwatersrand
Using & Interpreting the Single Decrement Life Table
Examples
2
Plan
Review Period Life Table Construction Ways of using the life table The life table as a Stationary Population Examples
– Life tables from South Africa– Life tables from Zambia– Life tables from the USA
3
Creating a Period Life Table
The data available are usually observed age-specific mortality rates, nMx
Critical assumption is that nMx~ nmx
The trick then is to convert these observed age-specific mortality rates into one of the columns of a life table
The most convenient choice is to convert to nqx
nMx to nqx conversion:
1
n xn x
n x n x
n mq
n a m
4
Strategies for Choosing nax
nmx nqx requires nax … where do we get nax ?
From calculating it directly From smoothing (graduating) the death distribution within
each age interval Borrowing values from another population Making one of two assumptions:
– nax is half the length of the age interval (n/2), or
– nmx is constant in the interval which negates the necessity of using nax because there is a direct formula to calculate
npx: n xn mn xp e
5
nax in Practice
Usually use n/2 for all age groups except the first Mortality rate between ages 0 and 5 changes very
rapidly, falling very quickly at first and then flattening out Consequently most deaths early in life occur closer to 0
than to 5 and hence nax is significantly less than n/2 in the first two age groups (0, 1-4)
In general in other age groups where mortality is changing less rapidly, the overall life table is very insensitive to the exact choice of nax
6
nax for Very Young Ages
Males Females
Value of 1a0
I f 1m0 >= 0.107 0.330 0.350I f 1m0 < 0.107 0.045+2.684(1m0) 0.053+2.800(1m0)
Value of 4a1
I f 1m0 >= 0.107 1.352 1.361I f 1m0 < 0.107 1.651-2.816(1m0) 1.522-1.518(1m0)
7
Example Sensitivity of ex to nax
Age Suggested All 50% All 25% All 75%
0 0.330 0.500 0.250 0.7501-4 1.332 2.000 1.000 3.0005-9 2.500 2.500 1.250 3.750
10-14 2.500 2.500 1.250 3.75015-19 2.500 2.500 1.250 3.75020-24 2.500 2.500 1.250 3.75025-29 2.500 2.500 1.250 3.75030-34 2.500 2.500 1.250 3.75035-39 2.500 2.500 1.250 3.75040-44 2.500 2.500 1.250 3.75045-49 2.500 2.500 1.250 3.75050-54 2.500 2.500 1.250 3.75055-59 2.500 2.500 1.250 3.75060-64 2.500 2.500 1.250 3.75065-69 2.500 2.500 1.250 3.75070-74 2.500 2.500 1.250 3.75075-79 2.500 2.500 1.250 3.75080-84 2.500 2.500 1.250 3.750
e(0) 44.443219 44.3598 44.00779 44.714498error (% ) -na- -0.19% -0.79% 1.61%
nax value
8
Life Table Columns: nmx
Death rate in the cohort between ages x and x+n
In constructing a period life table, we usually start by assuming that the observed mortality rates are equal to the life table mortality rates: nmx ~nMx
n xn x
n x
dm
L
9
Life Table Columns: nax
Average number of years lived in the age interval by those dying in the age interval
We must acquire the nax values from somewhere, discussed previously
n xa
10
Life Table Columns: nqx
n xn x
x
dq
l
Probability of dying between ages x and x+n
This is where we usually start constructing the life table:
1
n xn x
n x n x
n Mq
n a M
11
Life Table Columns: npx
Probability of surviving from ages x to x+n
1x n x n xn x n x
x x
l l dp q
l l
12
Life Table Columns: lx
x n x n xl l p Survivors, number left alive at age x+n
13
Life Table Columns: ndx
Number dying between ages x and x+n
n x x x nd l l
14
Life Table Columns: nLx
Person-years lived between ages x and x+n
Because n is effectively infinite for the open (last) age interval, we cannot calculate nLx given the formulas we have:
n x x n n x n xL n l a d
xx
x
lL
m
15
Life Table Columns: Tx
Person-years lived at ages older than x
x n aa x
T L
16
Life Table Columns: ex
Expectation of life at age x; average additional years of life that someone who survives to age x can expect to live
Single-Life-Table-Template.xls
0 xx
x
Te
l
17
Additional Ways of Using a Life Table
Probability of surviving from age x to age y
Probability of dying between ages x and y
Number of people dying between ages x and y
Number of person years lived between ages x and y
Probability that a newborn will die between ages x and x+n
yy x x
x
lp
l
x y y x xl l d
1 1 y x y y x x
y x x y x xx x x
l l l dq p
l l l
x y y x xT T L
0
n xdl
18
Additional Ways of Using a Life Table
Probability that a newborn will experience their death between ages x and y
Number of years that a newborn can expect to live between ages x and y
Probability that newborn will survive to age x
Probability that a newborn will die before age x
0
( ) xlp xl
0 0
0 0 0
( ) 1 ( ) 1 x xx l l dlq x p x
l l l
0 0
x y y x xl l d
l l
0
x yT T
l
19
The Life Table as Stationary Population
A stationary population has:– Age-specific mortality constant through time– The number of births constant through time– Net migration = 0 at all ages
size and age structure that are constant through time
x xp0 Jan. 1 Jan. 2 Jan. 3 Jan. 4 Jan. 5 Jan. 6 Jan. 7 Jan. 8 Jan. 9 Jan. 10 . Dec. 31
0 1.000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 . 10001 0.970 970 970 970 970 970 970 970 970 970 . 9702 0.950 950 950 950 950 950 950 950 950 . 9503 0.946 946 946 946 946 946 946 946 . 9464 0.942 942 942 942 942 942 942 . 9425 0.938 938 938 938 938 938 . 9386 0.935 935 935 935 935 . 9357 0.932 932 932 932 . 9328 0.930 930 930 . 9309 0.928 928 . 928
. . . .364 0.900 900
Population alive on:Age in days
Probability of surviving to age x
20
Stationary Population Life Table Columns
is the number of births each year
is the number at age x in each year
is the number between age x and x+n in each year
is the number above age x in each year
is the population size
is the number dying between age x and x+n each year
is the mean age at death
xl
xTn xL
0T
n xd00e
0l
21
Stationary Population Relationships
0
00 0
0
1 1lBCBR
TPY T el
0
1CBR CDR
e
1 1x
xxx x
x
lm
TT el
101 1 1 2
10 0 0 0
10
1x
x x xx
aa
llL L L
C CBRT l T lL
2 2
0 0
n nx x
n x
n l l
C CBR n CBRl l
22
Simple Examples
Constant graduate student population of size 40 with 10 new and 10 graduating each year:
Constant number of employees, average time spent in a job is five years:
0
1 10.2 20% attrition rate
5CDR CBR
e
23
LIFE TABLES FROM SOUTH AFRICA
Life-Tables_South-Africa.xls
24
nqxAgincourt, Male
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
01-
45-
9
10-1
4
15-1
9
20-2
4
25-2
9
30-3
4
35-3
9
40-4
4
45-4
9
50-5
4
55-5
9
60-6
4
65-6
9
70-7
4
75-7
9
80-8
4
85-8
9
90-9
4
95-9
9
Age (Years)
nq
x
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 92-04
25
nqxAgincourt, Female
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
01-
45-
9
10-1
4
15-1
9
20-2
4
25-2
9
30-3
4
35-3
9
40-4
4
45-4
9
50-5
4
55-5
9
60-6
4
65-6
9
70-7
4
75-7
9
80-8
4
85-8
9
90-9
4
95-9
9
Age (Years)
nq
x
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 92-04
26
lxAgincourt, Male
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
110,000
01-
45-
9
10-1
4
15-1
9
20-2
4
25-2
9
30-3
4
35-3
9
40-4
4
45-4
9
50-5
4
55-5
9
60-6
4
65-6
9
70-7
4
75-7
9
80-8
4
85-8
9
90-9
4
95-9
9
Age (Years)
l x
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 92-04
27
lxAgincourt, Female
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
110,000
01-
45-
9
10-1
4
15-1
9
20-2
4
25-2
9
30-3
4
35-3
9
40-4
4
45-4
9
50-5
4
55-5
9
60-6
4
65-6
9
70-7
4
75-7
9
80-8
4
85-8
9
90-9
4
95-9
9
Age (Years)
l x
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 92-04
28
ndxAgincourt, Male
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
22,000
24,000
01-
45-
9
10-1
4
15-1
9
20-2
4
25-2
9
30-3
4
35-3
9
40-4
4
45-4
9
50-5
4
55-5
9
60-6
4
65-6
9
70-7
4
75-7
9
80-8
4
85-8
9
90-9
4
95-9
9
Age (Years)
nd
x
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 92-04
29
ndxAgincourt, Female
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
22,000
24,000
01-
45-
9
10-1
4
15-1
9
20-2
4
25-2
9
30-3
4
35-3
9
40-4
4
45-4
9
50-5
4
55-5
9
60-6
4
65-6
9
70-7
4
75-7
9
80-8
4
85-8
9
90-9
4
95-9
9
Age (Years)
nd
x
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 92-04
30
TxAgincourt, Male
0
1,000,000
2,000,000
3,000,000
4,000,000
5,000,000
6,000,000
7,000,000
8,000,000
01-
45-
9
10-1
4
15-1
9
20-2
4
25-2
9
30-3
4
35-3
9
40-4
4
45-4
9
50-5
4
55-5
9
60-6
4
65-6
9
70-7
4
75-7
9
80-8
4
85-8
9
90-9
4
95-9
9
Age (Years)
Tx
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 92-04
31
TxAgincourt, Female
0
1,000,000
2,000,000
3,000,000
4,000,000
5,000,000
6,000,000
7,000,000
8,000,000
9,000,000
01-
45-
9
10-1
4
15-1
9
20-2
4
25-2
9
30-3
4
35-3
9
40-4
4
45-4
9
50-5
4
55-5
9
60-6
4
65-6
9
70-7
4
75-7
9
80-8
4
85-8
9
90-9
4
95-9
9
Age (Years)
Tx
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 92-04
32
exAgincourt, Male
0
10
20
30
40
50
60
70
80
01-
45-
9
10-1
4
15-1
9
20-2
4
25-2
9
30-3
4
35-3
9
40-4
4
45-4
9
50-5
4
55-5
9
60-6
4
65-6
9
70-7
4
75-7
9
80-8
4
85-8
9
90-9
4
95-9
9
Age (Years)
e x
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 92-04
33
exAgincourt, Female
0
10
20
30
40
50
60
70
80
90
01-
45-
9
10-1
4
15-1
9
20-2
4
25-2
9
30-3
4
35-3
9
40-4
4
45-4
9
50-5
4
55-5
9
60-6
4
65-6
9
70-7
4
75-7
9
80-8
4
85-8
9
90-9
4
95-9
9
Age (Years)
e x
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 92-04
34
Male Proportional Age StructureAgincourt 1992-2004
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
0-5
5-9
10-1
4
15-1
9
20-2
4
25-2
9
30-3
4
35-3
9
40-4
4
45-4
9
50-5
4
55-5
9
60-6
4
65-6
9
70-7
4
75-7
9
80-8
4
85-8
9
90-9
4
95-9
910
0+
Age (years)
Pro
po
rtio
n (
per
cen
t)
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
92-04
35
Female Proportional Age StructureAgincourt 1992-2004
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
0-5
5-9
10-1
4
15-1
9
20-2
4
25-2
9
30-3
4
35-3
9
40-4
4
45-4
9
50-5
4
55-5
9
60-6
4
65-6
9
70-7
4
75-7
9
80-8
4
85-8
9
90-9
4
95-9
910
0+
Age (years)
Pro
po
rtio
n (
per
cen
t)
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
92-04
36
1992199319941995199619971998199920002001200220032004
01-
45-
9
10-1
4
15-1
9
20-2
4
25-2
9
30-3
4
35-3
9
40-4
4
45-4
9
50-5
4
55-5
9
60-6
4
65-6
9
70-7
4
75-7
9
80-8
4
85-8
9
90-9
4
95-9
910
0+
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
lx
Year
Age (Years)
Trend in Male Survival CurvesAgincourt 1992-2004
37
1992199319941995199619971998199920002001200220032004
01-
45-
9
10-1
4
15-1
9
20-2
4
25-2
9
30-3
4
35-3
9
40-4
4
45-4
9
50-5
4
55-5
9
60-6
4
65-6
9
70-7
4
75-7
9
80-8
4
85-8
9
90-9
4
95-9
910
0+
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
lx
Year
Age (Years)
Trend in Female Survival CurvesAgincourt 1992-2004
38
Life Table Template
Examine life table template It is possible to calculate standard errors around life
table values See:
Chiang, C.L. 1984. The Life Table and Its Applications. Malabar, FL: Robert E. Krieger Publishing Company.
Single-Life-Table-Template.xls
39
CHILD MORTALITYTrend in Probability of Dying between Ages 0 and 5, 5q0
Agincourt 1992-2004
0
20
40
60
80
100
120
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Year
5q0
per
1,0
00
Female
Male
Male (2nd Poly.)
Female (2nd Poly.)
40
ADOLESCENT MORTALITYTrend in Probability of Dying between Ages 5 and 15, 10q5
Agincourt 1992-2004
0
2
4
6
8
10
12
14
16
18
20
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Year
10q
5 p
er 1
,000
FemaleMaleMale (linear)Female (linear)
41
ADULT MORTALITYTrend in Probability of Dying between Ages 15 and 60, 45q15
Agincourt 1992-2004
0
100
200
300
400
500
600
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Year
45q
15 p
er 1
,000
Female
Male
Male (2nd Poly.)
Female (2nd Poly.)
42
OLDER ADULT MORTALITYTrend in Probability of Dying between Ages 60 and 90, 30q60
Agincourt 1992-2004
200
300
400
500
600
700
800
900
1000
1100
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Year
30q
60 p
er 1
,000
Female
Male
Male (linear)
Female (linear)
43
OLDER ADULT MORTALITYTrend in Probability of Dying between Ages 50 and 65, 15q50
Agincourt 1992-2004
0
100
200
300
400
500
600
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Year
15q
50 p
er 1
,000
Female
Male
Male (3rd Poly.)
Female (2nd Poly.)
InflectionPoint
Converging Trend
Diverging Trend
44
Trend in Expectation of Life at Birth, e0
Agincourt 1992-2004
50.0
52.5
55.0
57.5
60.0
62.5
65.0
67.5
70.0
72.5
75.0
77.5
80.0
82.5
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Year
e0 (
Yea
rs)
Female
Male
Male fit (2nd Poly.)
Female fit (2nd Poly.)
45
LIFE TABLES FROM ZAMBIA
Life-Tables_Zambia.xls
46
Life Table Probability of Dying nqx 1957-1995
0
50
100
150
200
250
300
350
Age
per 1,00
0
Female Male
47
Life Table Survivors lx 1957-1995
0
20,000
40,000
60,000
80,000
100,000
120,000
Age
Female Male
48
Life Table Probability of Dying nqx 1957-1961
0
100
200
300
400
500
600
700
0 1-4 5-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79
Age
per 1,00
0
Female Male
49
Life Table Survivors lx 1957-1961
0
20,000
40,000
60,000
80,000
100,000
120,000
0 1-4 5-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79
Age
Female Male
50
Life Table Probability of Dying nqx 1992-1995
0
50
100
150
200
250
300
350
400
450
500
0 1-4 5-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79
Age
per 1,00
0
Female Male
51
Life Table Survivors lx 1992-1995
0
20,000
40,000
60,000
80,000
100,000
120,000
0 1-4 5-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79
Female Male
52
LIFE TABLES FROM USA
Male-USA-LTs-1959-2002.xls
Human-Mortality-Database-1x1.mdb
53
nMxUSA, Male
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0
2
4
6
8
1
0
12
1
4
16
1
8
20
2
2
24
2
6
28
3
0
32
3
4
36
3
8
40
4
2
44
4
6
48
5
0
52
5
4
56
5
8
60
6
2
64
6
6
68
7
0
72
7
4
76
7
8
80
8
2
84
8
6
88
9
0
92
9
4
96
9
8
100
10
2
104
10
6
108
11
0+
Age (Year)
nM
x
1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971
1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
1998 1999 2000 2001 2002
54
naxUSA, Male
0
0.1
0.2
0.3
0.4
0.5
0.6
0
2
4
6
8
1
0
12
1
4
16
1
8
20
2
2
24
2
6
28
3
0
32
3
4
36
3
8
40
4
2
44
4
6
48
5
0
52
5
4
56
5
8
60
6
2
64
6
6
68
7
0
72
7
4
76
7
8
80
8
2
84
8
6
88
9
0
92
9
4
96
9
8
100
10
2
104
10
6
108
Age (Year)
na x
1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971
1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
1998 1999 2000 2001 2002
55
nqxUSA, Male
0
0.1
0.2
0.3
0.4
0.5
0.6
0
2
4
6
8
1
0
12
1
4
16
1
8
20
2
2
24
2
6
28
3
0
32
3
4
36
3
8
40
4
2
44
4
6
48
5
0
52
5
4
56
5
8
60
6
2
64
6
6
68
7
0
72
7
4
76
7
8
80
8
2
84
8
6
88
9
0
92
9
4
96
9
8
100
10
2
104
10
6
108
Age (Year)
nq
x
1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971
1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
1998 1999 2000 2001 2002
56
nqxUSA, Male
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0
2
4
6
8
1
0
12
1
4
16
1
8
20
2
2
24
2
6
28
3
0
32
3
4
36
3
8
40
4
2
44
4
6
48
5
0
52
5
4
56
5
8
60
6
2
64
6
6
68
7
0
72
7
4
76
7
8
80
8
2
84
8
6
88
9
0
92
9
4
96
9
8
100
10
2
104
10
6
108
Age (Year)
nq
x
1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971
1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
1998 1999 2000 2001 2002
57
lxUSA, Male
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
110,000
0
2
4
6
8
1
0
12
1
4
16
1
8
20
2
2
24
2
6
28
3
0
32
3
4
36
3
8
40
4
2
44
4
6
48
5
0
52
5
4
56
5
8
60
6
2
64
6
6
68
7
0
72
7
4
76
7
8
80
8
2
84
8
6
88
9
0
92
9
4
96
9
8
100
10
2
104
10
6
108
Age (Year)
l x
1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971
1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
1998 1999 2000 2001 2002
58
ndxUSA, Male
0
500
1,000
1,500
2,000
2,500
3,000
3,500
0
2
4
6
8
1
0
12
1
4
16
1
8
20
2
2
24
2
6
28
3
0
32
3
4
36
3
8
40
4
2
44
4
6
48
5
0
52
5
4
56
5
8
60
6
2
64
6
6
68
7
0
72
7
4
76
7
8
80
8
2
84
8
6
88
9
0
92
9
4
96
9
8
100
10
2
104
10
6
108
Age (Year)
nd
x
1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971
1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
1998 1999 2000 2001 2002
59
nLxUSA, Male
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
110,000
0
2
4
6
8
1
0
12
1
4
16
1
8
20
2
2
24
2
6
28
3
0
32
3
4
36
3
8
40
4
2
44
4
6
48
5
0
52
5
4
56
5
8
60
6
2
64
6
6
68
7
0
72
7
4
76
7
8
80
8
2
84
8
6
88
9
0
92
9
4
96
9
8
100
10
2
104
10
6
108
Age (Year)
nL
x
1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971
1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
1998 1999 2000 2001 2002
60
TxUSA, Male
0
1,000,000
2,000,000
3,000,000
4,000,000
5,000,000
6,000,000
7,000,000
8,000,000
0
2
4
6
8
1
0
12
1
4
16
1
8
20
2
2
24
2
6
28
3
0
32
3
4
36
3
8
40
4
2
44
4
6
48
5
0
52
5
4
56
5
8
60
6
2
64
6
6
68
7
0
72
7
4
76
7
8
80
8
2
84
8
6
88
9
0
92
9
4
96
9
8
100
10
2
104
10
6
108
Age (Year)
Tx
1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971
1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
1998 1999 2000 2001 2002
61
exUSA, Male
0
10
20
30
40
50
60
70
80
0
2
4
6
8
1
0
12
1
4
16
1
8
20
2
2
24
2
6
28
3
0
32
3
4
36
3
8
40
4
2
44
4
6
48
5
0
52
5
4
56
5
8
60
6
2
64
6
6
68
7
0
72
7
4
76
7
8
80
8
2
84
8
6
88
9
0
92
9
4
96
9
8
100
10
2
104
10
6
108
Age (Year)
e x (
Yea
r)
1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971
1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
1998 1999 2000 2001 2002
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