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Copyright 2008, The Johns Hopkins University and Stan Becker. All rights reserved. Use of these materials permitted only in accordance with license rights granted. Materials provided “AS IS”; no representations or warranties provided. User assumes all responsibility for use, and all liability related thereto, and must independently review all materials for accuracy and efficacy. May contain materials owned by others. User is responsible for obtaining permissions for use from third parties as needed.
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Fertility and Its Measurement
Stan Becker, PhD Bloomberg School of Public Health
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Section A
Indicators of Fertility Based on Vital Statistics
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4
Definitions
Fecundity—Physiological capacity to conceiveInfecundity (sterility)—Lack of the capacity to conceive– Primary sterility—Never able to produce
a child– Secondary sterility—Sterility after one or
more children have been born
Continued
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5
Definitions
Fecundability—Probability that a woman will conceive during a menstrual cycleFertility (natality)—Manifestation of fecundityInfertility—Inability to bear a live birthNatural fertility—Fertility in the absence of deliberate parity-specific control
Continued
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6Continued
Definitions
Reproductivity—Extent to which a group is replacing its own numbers by natural processesGravidity—Number of pregnancies a woman has hadParity—Number of children born alive to a woman
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7
Definitions
Birth interval—Time between successive live birthsPregnancy interval—Time between successive pregnancies of a woman
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8
Crude Birth Rate (CBR)
Let B = Number of birthsLet P = Mid-year populationLet W15-44 = Number of women of
reproductive ages
Continued
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9
Crude Birth Rate (CBR)
Crude Birth Rate—Number of births per 1,000 population
1000PB∗=
1000P
4415W
44-15W B
∗−∗=
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10
Exercise Crude Birth Rate (CBR)
Use the following data to calculate the CBR per 1,000
You have 15 seconds to calculate the answer. You may pause the presentation if you need more time.
Island of Mauritius, 1985
Total Births: 18,247Total female population: 491,310Total male population: 493,900
Source: U.N. Demographic Yearbook, 1986
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11
Exercise Answer Crude Birth Rate (CBR)
The correct answer is as follows: – 18.5 births per 1,000 population
Island of Mauritius, 1985
Total Births: 18,247Total female population: 491,310Total male population: 493,900
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12
Crude Birth Rate (CBR)
Crude birth rates can be standardized using the direct or the indirect methodExample: Direct (DSBR) and indirect (ISBR) standardization of the Island of Mauritius (I.M.) 1985 crude birth rate using Mali's 1987 data as standard
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13
Direct Standardization of Birth Rate for Mauritius Island
(Study) (Standard)
15-19 18 725719 1306320-24 58 574357 3331325-29 57 536226 3056530-34 36 443702 1597335-39 19 379184 720440-44 6 325824 1955Total 2985012 102073
37511718247
CBR Mali: 48.7CBR I.M. 18.5
Age group Rates I.M. per 1000
Expected number of births, I.M.
Population Mali
Total number of births, Mali:Total number of births, I.M.:
Source: U.N. Demographic Yearbook, 1986, 1992, 1996
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14
Indirect Standardization of Birth Rate for Mauritius Island
(Standard) (Study)
15-19 79 105764 835520-24 159 109914 1747625-29 171 94576 1617230-34 140 81144 1136035-39 107 60063 642740-44 50 45825 2291Total 497286 62082
Total number of births, Mali: 375117Total number of births, I.M.: 18247
CBR Mali: 48.7CBR I.M. 18.5
Expected number of births, I.M.
Rates Mali per 1000
Age group Population I.M.
Source: U.N. Demographic Yearbook, 1986, 1992, 1996
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15
3.1348.7 375117102073
MaliCBRMaliin births Actual
I.M.in births ExpectedI.M.DSBR
=∗=
∗=
3.147.486208218247
MaliCBR.I.Min births Expected
I.M.in births ObservedI.M.ISBR
=∗=
∗=
CBR I.M. = 18.5Source: U.N. Demographic Yearbook, 1986, 1996
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16
General Fertility Rate (GFR)
General Fertility Rate—Number of births per 1,000 women of reproductive ages
100044-15W
B∗=
CBR4GFR ∗≈
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17
Exercise General Fertility Rate (GFR)
Use the following data to calculate the GFR per 1,000 women aged 15–44:
You have 15 seconds to calculate the answer. You may pause the presentation if you need more time.
Source: U.N. Demographic Yearbook, 1986 Continued
Island of Mauritius, 1985
Age Group Women 15-19 52 013 20-24 54 307 25-29 46 990 30-34 40 211 35-39 30 401 40-44 23 496
Total births: 18 247
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18
Exercise General Fertility Rate (GFR)
The correct answer is: – 73.7 births per 1,000 women aged
15-44Island of Mauritius, 1985
Age Group Women 15-19 52 013 20-24 54 307 25-29 46 990 30-34 40 211 35-39 30 401 40-44 23 496
Total births: 18 247
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19
Age-Specific Fertility Rate (ASFR)
Let Ba = Number of births to women of age (group) “a”
Wa = Number of women of age (group) “a”
n = Number of years in age group
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20
Age-Specific Fertility Rate (ASFR[a, n])
ASFR(a, n)—Number of births per 1,000 women of a specific age (group)
If n = 1 , then write ASFR(a)Example: ASFR Poland 1984
1000aWaB
aF ∗==
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21
Age-Specific Fertility RatesPoland, 1984
0
50
100
150
200
15-19 20-24 25-29 30-34 35-39 40-44 45-49Age Group
Rat
e (p
er
thou
sand
)
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22
Exercise Age-Specific Fertility Rate (ASFR[a, n])
Use the following data to calculate the ASFR per 1,000 for women age 20–24 and 25–29
Source: U.N. Demographic Yearbook, 1986
Island of Mauritius, 1985
Age Group of Mother Women Births
15-19 52 013 188420-24 54 307 637125-29 46 990 536230-34 40 211 290135-39 30 401 117040-44 23 496 268
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23
Exercise Answer Age-Specific Fertility Rate (ASFR)
The correct answers are: – ASFR(20,5) = 117.3 births per 1,000 women 20–24– ASFR(25,5) = 114.1 births per 1,000 women 25–29
Island of Mauritius, 1985
Age Group of Mother Women Births
15-19 52 013 188420-24 54 307 637125-29 46 990 536230-34 40 211 290135-39 30 401 117040-44 23 496 268
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24
Total Fertility Rate (TFR)
Total Fertility Rate—Number of children a woman will have if she lives through all the reproductive ages and follows the age-specific fertility rates of a given time period (usually one year)
Continued
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25
Total Fertility Rate (TFR)
For single-year age groups
For five-year age groups
aF ASFR(a) 100044
15a aWaB
TFR ∑=∑=∗∑=
=
∑=
−
−==∗∑∗=
44-40
19-15a
4440
1915aASFR(a,5)*5 1000
aWaB
5 TFR
Continued
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26
Total Fertility Rate (TFR)
Example: ASFR and TFR—Poland, 1984
Age group Ba Wa ASFR15-19 43807 1230396 35.6020-24 257872 1390077 185.5125-29 236088 1653183 142.8130-34 115566 1608925 71.8335-39 38450 1241967 30.9640-44 6627 941963 7.04
473.74TFR= (5 * 473.74) / 1000 = 2.4
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27
Exercise Total Fertility Rate (TFR)
Use the following data to calculate the TFR per 1,000
Source: U.N. Demographic Yearbook, 1986
Island of Mauritius, 1985
Age Group of Mother Women Births
15–19 52,013 1,884 20–24 54,307 6,371 25–29 46,990 5,362 30–34 40,211 2,901 35–39 30,401 1,170 40–44 23,496 268
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28
Exercise Answer Total Fertility Rate (TFR)
The correct answer is as follows: – TFR = 1.9 children per woman
Island of Mauritius, 1985
Age Group of Mother Women Births
15–19 52,013 1,884 20–24 54,307 6,371 25–29 46,990 5,362 30–34 40,211 2,901 35–39 30,401 1,170 40–44 23,496 268
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29
Mean of Age of Childbearing
For single-year groups
For five-year age groups
( )
∑
∑ +=
=
=44
15
44
1521
a
a_
aF
aF aa
( )
∑
∑ +=
aF
aF aa_ 5.2
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30
Variance of Age of Childbearing
∑
∑ ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−
=
=
=
44
15a
44
15a
2
2
aF
aF _aa
s
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31
Exercise Mean and Variance of Age of Childbearing
Use the following data to calculate the mean and variance of age of childbearing
Source: U.N. Demographic Yearbook, 1986
Island of Mauritius, 1985Age Groupof Mother Women Births
15Ğ19 52,013 1,88420Ğ24 54,307 6,37125Ğ29 46,990 5,36230Ğ34 40,211 2,90135Ğ39 30,401 1,17040Ğ44 23,496 268
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32
Exercise Answer Mean and Variance of Age of Childbearing
The correct answers are as follows: – Mean age of childbearing = 27.9 years– Variance of age of childbearing = 38.2
yearsIsland of Mauritius, 1985
Age Groupof Mother Women Births
15Ğ19 52,013 1,88420Ğ24 54,307 6,37125Ğ29 46,990 5,36230Ğ34 40,211 2,90135Ğ39 30,401 1,17040Ğ44 23,496 268
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33
Mean and Median Age of Mothers
Mean: Median x such that:
Ba = Number of births to women age a
∑∑ ∗+β
α=
a
aa
B
B)21a(
5.0B
B
44
15aa
x
15aa=
∑=
∑=
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34
Exercise Mean and Median Age of Mothers
Use the following data to calculate the mean and median age of mothers
Source: U.N. Demographic Yearbook, 1986
Island of Mauritius, 1985
Age Group of Mother Women Births
15–19 52,013 1,884 20–24 54,307 6,371 25–29 46,990 5,362 30–34 40,211 2,901 35–39 30,401 1,170 40–44 23,496 268
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35
Exercise Answer Mean and Median Age of Mothers
The correct answers are as follows:– Mean age of mothers = 26.9 years– Median age of mothers = 24.7 years
Island of Mauritius, 1985Age Groupof Mother Women Births
15Ğ19 52,013 1,88420Ğ24 54,307 6,37125Ğ29 46,990 5,36230Ğ34 40,211 2,90135Ğ39 30,401 1,17040Ğ44 23,496 268
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36
Parity
Mean Median x such that:
Mi = Proportion of women at or above parity imi = Proportion of women at parity i
∑=
=
)imax(I
1iiM 5.0m
x
1ii =∑
=
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37
Marital Fertility Rate (MFR)
Let Bm = Number of marital birthsBu = Number of non-marital birthsWm
15–44 = Number of married women of age 15–44
Wu15–44 = Number of unmarried
women of age 15–44
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38
General Marital Fertility Rate (GMFR)
General Marital Fertility Rate—Number of births per 1,000 married women of reproductive ages
1000W
B m44-15
∗=
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39
Marital Fertility Rate (MFR)
Marital Fertility Rate—Number of marital births per 1,000 married women of reproductive ages
WBm
44-15
m 1000∗=
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40
“Out-of-Wedlock” (Non-Marital) Fertility Rate
“Out-of-Wedlock” (Non-Marital) Fertility Rate—Number of non-marital births per 1,000 unmarried women of reproductive ages
W
B u
44-15
u 1000∗=
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41
Some Relationships
But
W
B
WB
WB
44-15u
44-15
u
m44-15
m≠+
W
B
WW
WB
WW
WB
44-1544-15
u44-15
u44-15
u
44-15
m44-15
m44-15
m=∗+∗
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42
Age-Specific Marital Fertility Rate (ASMFR)
Let Bma = Number of marital births to
women of age group “a”Wm
a = Number of married women in age group “a”
Bm(d) = Number of marital births to
women married for “d” yearsWm
(d) = Number of women married for “d” years
Continued
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43
Age-Specific Marital Fertility Rate (ASMFR)
Age-Specific Marital Fertility Rate—Number of marital births per 1,000 married women of age (group) “a”
maW
B
mla 1000∗=
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44
Duration (of Marriage)— Specific Fertility Rate (DSFR)DSFR—Number of marital births per 1,000 women who have been married for duration “d”
( )( )
1000dmW
dlB ∗=
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45
Order-Specific Fertility Rate (OSFR)
Let Bi = Number of births of order “i”, i>0
Bia = Number of order “i” births to
women in age group “a”Wa = Number of women in age
group “a”W15-44 = Number of women of age
15–44 (or 15–49)
Continued
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46
Order-Specific Fertility Rate (OSFR)
Order-Specific Fertility Rate—Number of order “i” births per 1,000 women of reproductive ages
Example: OSFR Poland 1984
100044-15W
iB ∗=
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47
Order-Specific Fertility RatesPoland, 1984
0
10
20
30
1st
2nd
3rd 4th 5th 6th 7th 8th 9th10
th+
Birth Order
Rat
e (p
er
thou
sand
)
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48
Exercise Order-Specific Fertility Rate (OSFR)
Use the following data to calculate the OSFR for birth orders 1 and 3
Source: U.N. Demographic Yearbook, 1986
Island of Mauritius, 1985Age Group Number of Birth Orderof Mother Women 1 3
15Ğ19 52,013 1,521 4020Ğ24 54,307 3,317 67825Ğ29 46,990 1,638 1,13230Ğ34 40,211 496 66535Ğ39 30,401 142 21540Ğ44 23,496 24 30
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49
Exercise Answer Order-Specific Fertility Rate (OSFR)
The correct answers are as follows:– OSFR(1) = 28.8 births of order 1 per
1,000 women 15–44– OSFR(3) = 11.2 births of order 3 per
1,000 women 15–44Island of Mauritius, 1985
Age Group Number of Birth Orderof Mother Women 1 3
15–19 52,013 1,521 40 20–24 54,307 3,317 678 25–29 46,990 1,638 1,132 30–34 40,211 496 665 35–39 30,401 142 215 40–44 23,496 24 30
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50
Age-Order Specific Fertility Rate (AOSFR [a,I])
AOSFR(a,i)—Number of order “i” births per 1,000 women of age (group) “a”
Example: AOSFR Poland 1984
1000aW
iaB
∗=
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51
Age-Order Specific Fertility Rates Poland 1984
0
20
40
60
80
100
120
-20 20-24 25-29 30-34 35-39 40-44 45+
Age
1st birth2nd3rd4th +
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52
Exercise Age-Order Specific Fertility Rate (AOSFR)
Use the following data to calculate the AOSFR for birth order 3 in age group 25–29
Source: U.N. Demographic Yearbook, 1986
Island of Mauritius, 1985Age Group Birth orderof Mother Women 1 3
15Ğ19 52,013 1,521 4020Ğ24 54,307 3,317 67825Ğ29 46,990 1,638 1,13230Ğ34 40,211 496 66535Ğ39 30,401 142 21540Ğ44 23,496 24 30
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53
Exercise Answer Age-Order Specific Fertility Rate (AOSFR)
The correct answer is as follows: – AOSFR = 24.1 births of order 3 per
1,000 women 25–29Island of Mauritius, 1985
Age Group Birth order of Mother Women 1 3
15–19 52,013 1,521 40 20–24 54,307 3,317 678 25–29 46,990 1,638 1,132 30–34 40,211 496 665 35–39 30,401 142 215 40–44 23,496 24 30
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54
Age-Order Specific Fertility Rate (AOSFR[a,i])
Note:
( ) SFR(i)O W
W i,a AOSFR 44-15
a44
15a=∗∑
=
( ) )a(ASFRi,a AOSFR1i
=∑∞
=
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55
Cumulative Order Specific Birth Rate (COSFR[i,a])
Cumulative up to age “a”COSFR(i,a)—Total number of order “i”births per 1,000 women of age (group) less than or equal to “a”
a
0xx)AOSFR(i,∑
==
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56
Birth Probability
Let Bi = Number of births of order “i”, i>0, in year “t”
Wi-1 = Number of women of parity “i-1” at beginning of year “t”
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57
Birth Probability, BP(i)
Birth Probability—Probability of having an “ith” order birth in a given year for women who already have “i-1” births
WB 1-i
i=
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58
Birth Probability
May be age-specific as wellBirth probabilities are the most sensitive indicators of temporal change in the pace of childbearing
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59
Paternal Fertility Rate
Let B = Number of birthsM15-54 = Number of men of age 15–54
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60
General Fertility Rate of Men (GFRm )
General Fertility Rate of Men—Number of births per 1,000 men age 15 to 54
100054-15M
B ∗=
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61
Summary
Fertility data are collected from vital statistics, censuses, or surveysVital statistics principally provide birth statisticsMany indicators have been developed to understand and explain the fertility patterns in populations based on vital statistics
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Section B
Indicators of Reproduction Based on Vital Statistics
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63
Gross Reproduction Rate (GRR)
Let Bf = Number of female birthsBm+f = Number of male and female
births, i.e., all births
Continued
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64
Gross Reproduction Rate (GRR)
Gross Reproduction Rate—Number of daughters expected to be born alive to a hypothetical cohort of women (usually 1,000) if no one dies during childbearing years and if the same schedule of age-specific rates is applied throughout the childbearing years
Continued
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65
If the sex ratio at birth is assumed constant across ages of women
births) female of n(Proportio TFRGRR ∗=
Gross Reproduction Rate (GRR)
(a)B(a)B
(a)ASFR GRR fm
f
+∗= ∑
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66
Exercise Gross Reproduction Rate (GRR)
Use the following data to calculate the GRR
You have 15 seconds to calculate the answer. You may pause the presentation if you need more time.
Sources: U.S. Census 1990 and Vital Statistics of the U.S. Vol. I
United States, 1990 Age
Group of Births Mother Women Total Males15-19 8 651 522 267 20-24 9 345 094 560 25-29 10 617 1277 653 30-34 10 986 886 454 35-39 10 061 318 163 40-44 8 924 49 25
Numbers are in 1,000s
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67
Exercise Answer Gross Reproduction Rate (GRR)
The correct answer for the gross reproduction rate is as follows:– 1.01 daughters per woman
United States, 1990 Age
Group of Births Mother Women Total Males15-19 8 651 522 267 20-24 9 345 094 560 25-29 10 617 1277 653 30-34 10 986 886 454 35-39 10 061 318 163 40-44 8 924 49 25
Numbers are in 1,000s
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68
Net Reproduction Rate (NRR)
Let Lfa = Life table person-years lived
by women in age group “a”l0 = Radix of life table
Bf = Number of female birthsBm+f = Number of male and female
births
Continued
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69
Net Reproduction Rate (NRR)
Net Reproduction Rate—Average number of daughters expected to be born alive to a hypothetical cohort of women if the same schedule of age-specific fertility and mortality rates applied throughout the childbearing years
Continued
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70
Net Reproduction Rate (NRR)
For single-year age groups
For five-year age groups
BB L ASFR NRR fm
f
f0
fa1
+∗∗=∑l
BB L ASFR NRR fm
f
f0
fa5
+∑ ∗∗=l
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71
Exercise Net Reproduction Rate (NRR)
Use the following data to calculate the NRR
Sources: U.S. Census 1990 and Vital Statistics of the U.S. Vol. I
United States, 1990 Age
Group of Births Mother Women Total Males15-19 8 651 522 267 20-24 9 345 094 560 25-29 10 617 1277 653 30-34 10 986 886 454 35-39 10 061 318 163 40-44 8 924 49 25
Numbers are in 1,000s
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72
Exercise Answer Net Reproduction Rate (NRR)
The correct answer for the NRR is as follows: – 1.00 daughter per woman
United States, 1990 Age Stationary
Group of Births PopulationMother Women Total Males 5Lx 15-19 8 651 522 267 493 629 20-24 9 345 094 560 492 399 25-29 10 617 1277 653 490 989 30-34 10 986 886 454 489 203 35-39 10 061 318 163 486 812 40-44 8 924 49 25 483 465
Numbers are in 1,000s
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73
Where l( ) = Life table probability of surviving beyond
= mean age of childbearing usually 20< < 30
Net Reproduction Rate (NRR)
GRR ) NRR ∗≈_
( al
a
aa
a
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74
Live Births and Fertility Rates: United States, 1920–1988
Source: U.S. Department of Health and Human Services, Monthly Vital Statistics Report, Vol. 39, No. 4, Supplement, August 15, 1990
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75Source: U.S. Bureau of the Census, Current Population Reports, Series P-25, No. 381, tables A-1 and A-2
Completed Fertility Rates for Birth Cohorts of Women
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76
Reproductivity
Reproductivity is usually studied in terms of mothers and daughters because of the following reasons:– The fecund period for females is shorter
than it is for males– Characteristics such as age are much
more likely to be known for the mothers of illegitimate babies than for their fathers
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77
Summary
Reproductivity data are collected from vital statisticsMany indicators have been developed to understand and explain reproductivity patterns in populations
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Section C
Indicators of Fertility Based on Censuses and Surveys
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79
Child-Woman Ratio (CWR)
Child-Woman Ratio—Number of children zero to four years old relative to number of women of reproductive ages
Continued
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80
Child-Woman Ratio (CWR)
Where P0-4 = Mid-year population ofpersons age 0-4 years
W15-44 = Number of women of reproductive ages
1000W
PCWR4415
40 ∗=−
−
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81
Exercise Child-Woman Ratio (CWR)
Use the following data to calculate the CWR
Source: Demographic and Health Survey, Kenya 1998
Age group Male Female Total0-4 268873 256705 525578…15-19 189272 192067 38134020-24 130899 158825 28972325-29 116747 142204 25895130-34 100827 99727 20055535-39 88445 103421 19186640-44 67218 68332 135550
Household population compositionby age and sex, Kenya 1998
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82
Exercise Answer Child-Woman Ratio (CWR)
The correct answer is as follows:– 687.4 children 0-4 per 1,000
women 15-44
Age group Male Female Total0-4 268873 256705 525578…15-19 189272 192067 38134020-24 130899 158825 28972325-29 116747 142204 25895130-34 100827 99727 20055535-39 88445 103421 19186640-44 67218 68332 135550
Household population compositionby age and sex, Kenya 1998
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83
Children Ever Born (CEB)
Children Ever Born—Total number of children a woman has ever given birth toThe survival status of the children is not considered hereAlmost all censuses tabulate mean CEB by marital status and by age of the mother
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84
Parity Progression Ratios (PPR[i])
Let N = Random variable for number of births
mi = Proportion of women of parity “i”Mi = Proportion of women at or
above parity “i”
Continued
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85
Parity Progression Ratios (PPR[i])
Parity Progression Ratios—Probability that a woman has an (i+1st) birth given that she already has had “i” births
i)N 1i(N Prob M
1iMa
i
i
≥+≥=
+=
=
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86
Exercise Parity Progression Ratios (PPR)
Given the following percentages of women at parity “i” for women 45-49 in 1995 in Colombia, calculate PPR(2)
Parity
Percentage0 9.21 7.52
13.9
3
18.64
15.6
5+
35.2Source: Demographic and Health Survey, Colombia 1995
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87
Exercise Answer Parity Progression Ratios (PPR)
The correct answer for the PPR(2) is as follows: – 0.83 (i.e., there is an 83% chance that a
woman 45–49 has a second birth given she already has had a first birth)
Parity Percentage0 9.21 7.52 13.93 18.64 15.65+ 35.2
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Parity Progression Ratios (PPR)
Note: a0 = Prob (ever give birth)1-a0 = Prob (never have a birth)M0 = 1
ai need not decrease with increasing IMi does decrease
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Proportion of Women of Parity i(mi)
Is an unconditional probability
)1( ia−∗∗∗∗=+≥≥=
= +
a ... a a 1)i (N Prob - i) (N Prob
M - M
1-i10
1ii
Continued
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Proportion of Women of Parity i(mi)
Given the following percentages of women at parity “i” for women 45–49 in 1995 in Colombia, verify the relationships indicated on the previous slide
Parity
Percentage0 9.21 7.52 13.93 18.64 15.65+
35.2
Source: Demographic and Health Survey, Colombia 1995
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Mean Parity
∑∑==
∗==max(i)
1ii
max(i)
1ii mi M
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Exercise Mean Parity
Given the following percentages of women at parity “i” for women 45–49 in 1995 in Colombia, calculate the mean parity using both formulas on the previous slide (assume that women at parity 10+ are on average at parity 11)
Parity Percentage Parity Percentage
0 9.2 6 8.01 7.5 7 5.92 13.9 8 3.23 18.6 9 3.24 15.6 10+ 4.85 10.1
Source: Demographic and Health Survey, Colombia 1995
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Exercise Answer Mean Parity
The correct answer is as follows:– Mean parity = 4.01
Parity Percentage Parity Percentage
0 9.2 6 8.01 7.5 7 5.92 13.9 8 3.23 18.6 9 3.24 15.6 10+ 4.85 10.1
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Estimation of GFR from Census Data on Ratio of Children to Women
Let P0-4 = Enumerated number of children under 5
W15-44 = Enumerated number of women of age 15–44
W20-49 = Enumerated number of women of age 20–49
Continued
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95
Estimation of GFR from Census Data on Ratio of Children to Women
Also let l0 = Radix of life table
n La = Life table person-yearslived between the ages “a”and “a+n” (female life table)
Continued
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96
2LL
L2
WWL
P GFR
15302030
153049204415
05
04-0
est
+∗
+
∗=
−−
l
Estimation of GFR from Census Data on Ratio of Children to Women
Continued
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97
Estimation of GFR from Census Data on Ratio of Children to Women
Note:– Assumes that a life table is available– Estimated GFR may be used in the
absence of birth statistics to compare fertility levels in various areas
Continued
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98
Estimation of GFR from Census Data on Ratio of Children to Women
The life table survivorship functions are inverted in order to estimate the number of persons at the mid-point of the preceding five-year periodA lexis diagram makes it easier to understand this calculation
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99
Summary
Fertility data are collected from vital statistics, censuses, or surveys
Continued
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Summary
Censuses provide the following:– Data on births and fertility– Statistics on children by family status of
the parents– Population data on fertility-related
variables– Population bases for calculating various
types of fertility measures
Continued
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101
Summary
Surveys provide the following:– Same type of data as censuses– Additional detailed data on special
aspects of fertility, including number and timing of births, marriages, pregnancies, birth intervals, and birth interval components
Continued
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102
Summary
Many indicators have been developed to understand and explain the fertility patterns in populations
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Section D
Relationship among Indicators, Indicators and Models of Birth Intervals, and Fertility Models
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104
Relations among Indicators
At age 50:
Completed cohortfertility rate
= Mean CEB
)COSFR(i,50max(i)
1i∑=
=
∑=
=max(i)
1iiM
Continued
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105
( )∑= −
∑=
=imax
1i 4415
imax(i)
1i WB )i(OSFR
4415WB−
=
GFR=
Relations among Indicators
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106
Pregnancy Histories and Birth Histories
Data needed– Age or birth date of woman– Dates of pregnancy terminations– Type of termination (live birth or not)
Continued
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107
Pregnancy Histories and Birth Histories
Two ways of collecting data– Forward, i.e., from first to last birth– Backward, i.e., from last to first birth
Continued
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108
Pregnancy Histories and Birth Histories
Problems– Dating of events– Forgetting events– Age misreporting
Continued
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109
Legend:
xx: Forward
xx: Backward
Cohort fertility (births per 1000 women) calculated from survey data for forward and backward questionnaires by five-year age groups and five-year periods before the surveyBangladesh, 1984
Years before the survey5 0101520
Age
20
15
25
30
35
112100
317311
269278
11089
241258
253277
5888
8477
274277
332313
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110
Birth Interval Measures and Models
Let NS = Time from previous pregnancy outcome to resumption of ovulation (postpartum non-susceptibility subinterval)
For first order births use dates of marriage or beginning of sexual relations
Continued
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111
Birth Interval Measures and Models
Also let C = Time from resumption of ovulation to next conception (conception-wait subinterval)
G = Time from conception to next pregnancy outcome (gestational subinterval)
W = Waiting time due to non-live births
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112
Pregnancy and Live Birth Intervals
Pregnancy interval– PI = Interval between two pregnancies
Live birth interval– LBI = Interval between two live births
GCNS ++=
WPI +=
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113
Observed Birth Intervals
Closed intervalsLeft censored intervalsRight censored intervalsLife table methods can be used to incorporate the different intervals and calculate median birth interval lengths
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114
Birth Interval
Note:– Mean birth interval for women is
different from mean birth interval for births in a given time period
– The latter is shorter
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115
Birth Interval Mathematical relationships
In populations with nothing changingLet p = Fecundability (assumed fixed)
e = Effectiveness of contraceptionu = Proportion using contraceptions = Non-susceptible period (constant)
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116
Mean Birth Interval
Mean birth interval
Fertility rate forfecund women
=IntervalirthB Mean
1
s) ue)-(1 p (
1 +=
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117
Mean Conception-Wait Subinterval (MC)
Mean Conception-Wait Subinterval—Mean time it takes to get pregnant under natural fertilityConstant fecundability
p = Monthly probability of conception (assumed fixed in time and for all women)
p1
...pp)-3(1p)p-2(1p1 MC 2
=
+++∗=
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118
Heterogeneous Fecundability
Probability of conception in month “k”“p” is assumed to vary between women with distribution “f(p)”
– Where q = 1-p
∫= 10
1-k dp f(p) q p
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119
Probability of Conceiving In Month “k” Given No Conception Before Then
Note– Here the probability of conception
decreases over time– This has important implications for the
study of infertility
∫
∫=
10
1-k
10
k
dq q)-f(1 q
dq q)-f(1 q - 1
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120
Fertility Models Coale and Trussell
Let r(a) = Observed fertility schedule at age “a”
n(a) = Natural fertility pattern at age “a”M = Level of fertility (estimated)m = Degree to which fertility control
is practiced (estimated)v(a) = Estimated from U.N.
Demographic Yearbook 1965; data for 43 fertility schedules
Continued
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121
Fertility Models Coale and Trussell
v(a)) (m e M)a(n)a(r ∗∗=
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122
Fertility Models Bongaarts
Bongaarts model of intermediate fertility variablesLet Cm = Index of marriage
Cc = Index of contraceptionCa = Index of induced abortionCi = Index of post-partum infecundabilityK = Estimated total natural fertility
rate (15.3 [Bongaarts 1982])Each “C” varies between 0.0 and 1.0
Continued
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123
Fertility Models Bongaarts
Methods of estimation of each “C” are provided by Bongaarts (1982)
KCCCC TFR iacm ∗∗∗∗=
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124
Summary
Information on women's fertility can be obtained by asking them to report their pregnancy and birth historiesIndicators and models have been developed to understand and explain the fertility patterns in populations