1. Demographic Analysis and Evaluation
Workshop on
Demographic Analysis and Evaluation 1

2. Mortality: Estimation from Child Survivorship Data

3. Child Mortality as an Index of Mortality Level
In this part of the workshop we will cover:
An indirect technique for estimating child mortality from child survivorship data
The derivation of a life table based on child mortality 3

4. Brass' Child Survivorship Technique
Brass’ childhood mortality technique estimates probabilities of dying between birth and certain ages based on numbers of children ever born and children surviving by age of mother.
Based on information on children ever born and children surviving, classified by age of their mothers or by marriage duration, proportion of dead children (in relation to those born) are converted into probabilities of surviving from birth to an exact age (1, 2, 3, 5, 10, 15, and 20 years). 4

5. Brass' Child Survivorship Technique
Brass noticed that the proportions dead of children ever born, classified by age of mother, were close to the probability of dying between birth and certain ages, and that the differences were primarily a function of the pattern of fertility.
He therefore developed a set of multipliers to convert the proportions dead to the life table xq0 values, the probability of dying between birth and age x… 5

6. Brass' Child Survivorship Technique
…Multipliers to convert the proportions dead to the life table xq0 values, the probability of dying between birth and age x:
xq0 = ki . Di
Where:
 xq0 is the probability of dying between birth and age x;
 ki is a multiplier;
 Di is the proportion of children dead; and
 i is the age group of the mother.
And the multiplier, denoted by k, was used in the following way… 6

7. Brass' Child Survivorship Technique
The ki multipliers vary as a function of the fertility pattern in the population being studied. The multipliers are usually estimated based on ratios of successive average parities, P(i)/P(i+1), where i is the index of the age group (i = 15-19, = 45-49). 7

8. Brass' Child Survivorship Technique
The data for mothers at selected age groups provide the following information:   
Index Age of
(i) mother Derived values _______________________________
q0 probability of dying between birth and age 1
q0 probability of dying between birth and age 2
q0 probability of dying between birth and age 3
q0 probability of dying between birth and age 5
q0 probability of dying between birth and age 10
q0 probability of dying between birth and age 15
q0 probability of dying between birth and age 20 8

9. Brass' Child Survivorship Technique
Brass' original calculations were based on a limited range of fertility and mortality patterns.
Refinements of the Brass method have used correlation coefficients obtained from information derived from a broader range of mortality and fertility patterns.
Trussel's equations were introduced in Manual X (1983), for use with Coale-Demeny model life table mortality. 9

10. Brass' Child Survivorship Technique
The most recent refinement is that by Palloni and Heligman, which requires calculation of mean age at maternity – an indicator of the average age difference between women and their children – and uses the UN's regional model mortality patterns.
Both the Trussel and Paloni-Heligman versions rely on the Coale and Trussel model fertility schedules (1974).
Both the Trussel and Paloni-Heligman estimates are calculated in the United Nations' QFIVE program. 10

11. Brass' Child Survivorship Technique
Data required:
Children ever born classified by 5-year age groups of mother, from a census or survey.
Children surviving up to the time of the same census or survey, again classified by age of mother.
Number of women by 5-year age groups, from the same census or survey. 11

12. Brass' Child Survivorship Technique
Assumptions:
The risk of a child dying is a function only of the age of the child.
Information on CEB and CS by age of mother are equally well reported.
Fertility levels and patterns have remained constant for at least 15 to 20 years before the census or survey. (United Nations (1990:23) says years.)
The age pattern of mortality is known. 12

13. Brass' Child Survivorship Technique
Assumptions:
There is no relationship between mortality of mothers and mortality of their children; between age of mother and parity; nor between age of mother and child mortality. That is, the risk of a child dying is a function only of the age of the child.
Age of mothers is reported correctly.
Emphasize MORTALITY of mothers… 13

14. Brass' Child Survivorship Technique
Assumptions:
Completeness of reporting is the same for children ever born as for children surviving.
As the authors mention, the mortality model used has been well identified. 14

15. Brass' Child Survivorship Technique
Procedure:
Though Brass’ original procedure used a set of multipliers to convert proportions of children dead to life table xq0 values …
… Trussell’s equations are used in the Palloni-Heligman variation (United Nations 1990: chV-VI).
The first step, in using equations based on United Nations models, is the calculation of mean age at maternity, or accepting the default value
So, Trussell’s equations are used in place of Brass’ multiplyer set?
We don’t need to get too hung up on the formula’s we can trust that our research assistant (the QFIVE program) will implement the right ones properly; however we do need to apply analytical thinking when reviewing results, and selecting from the options provided in them. 15

16. Calculation of Mean Age at Maternity with Mbar.xls
Mean age of maternity is very similar to mean age of childbearing. Difference is, whereas maternity relies on births (converted from ASFRs) for the calculation, childbearing relies on ASFRs.
Maternity could be advantageous if population data for women has problems and you have births data…
Mean of childbearing could be advantagous if you only have data on ASFRs (for example from a sample survey) available on hand to use.
(Doesn’t make a big diff in QFIVE anyway.)
Spreadsheet:
Mbar.xls 16

17. Brass' Child Survivorship Technique
Technique implemented in QFIVE (United Nations)
Appearance in DOS
Program:
QFIVE 17

18. Brass' Child Survivorship Technique
Technique implemented in QFIVE (United Nations), as accessed through PASEX interface:
Spreadsheet:
QFIVE.xls 18

19. Brass' Child Survivorship Technique
After entering required data and running the QFIVE program (which automatically applies the calculations described above), several sets of child mortality rates will be generated.
Each set includes the following measures:
1q0 infant mortality rates
4q1 probability of dying between ages 1 and 4
5q0 probability of dying between ages 0 and 5
After computing key calcs/running the software QFIVE to implement you will be provided with several choices. This can be daunting! How do you choose among the choices? …For now know… we will go into more details on how to do this later.
Spreadsheet:
QFIVE.xls 19

20. Brass' Child Survivorship Technique
Each set includes the following measures:
1q0 infant mortality rates
4q1 probability of dying between ages 1 and 4
5q0 probability of dying between ages 0 and 5
Each measure is generated for several reference dates (that correspond to the age-specific input from which they are derived).
And all measures (for all reference dates) are available for Coale Demeny and United Nations life table models.
After computing key calcs/running the software QFIVE to implement you will be provided with several choices. This can be daunting! How do you choose among the choices? …For now know… we will go into more details on how to do this later.
Spreadsheet:
QFIVE.xls 20

21. Brass' Child Survivorship Technique
Spreadsheet:
QFIVE.xls 21

22. Brass' Child Survivorship Technique
The analyst then has two tasks:
1. Identify the measures corresponding to the regional model life table that best represents the mortality in the country under study.
2. Within the results falling in the appropriate life table model, identify reference dates associated with most reliable age-specific input data.
After computing key calcs/running the software QFIVE to implement you will be provided with several choices. This can be daunting! How do you choose among the choices? …For now know… we will go into more details on how to do this later.
Spreadsheet:
QFIVE.xls 22

23. Brass' Child Survivorship Technique
Choice of regional model life table may be based on:
The results of a comparison of the consistency of estimates from another source survey (MORTPAK/COMPAR, COMPAR.xls, DHSQCOM.xls),
Knowledge of the pattern of child mortality for the population in question, or
A desire to be consistent with previous choice.
After computing key calcs/running the software QFIVE to implement you will be provided with several choices. This can be daunting! How do you choose among the choices? …For now know… we will go into more details on how to do this later. 23

24. Brass' Child Survivorship Technique
Choice of reference date should consider the following:
Measures for the most recent reference dates are based on information reported by females ages and 20-24
Measures for reference dates furthest in the past are based on information reported by females ages and 45-49
Data for these youngest and oldest reproductive age groups tend to be affected by quality issues
After computing key calcs/running the software QFIVE to implement you will be provided with several choices. This can be daunting! How do you choose among the choices? …For now know… we will go into more details on how to do this later. 24

25. Brass' Child Survivorship Technique
Advantages:
A small amount of data, often collected in a census or survey, is required.
Mortality trend covering more than 1 years generated.
Estimates based on data on births for several years may be less affected by sampling error than methods based on data for only one year. 25

26. Brass' Child Survivorship Technique
Limitations:
Estimates based on information from women ages , as well as ages 40 and above, should be interpreted with caution.
Results may be affected by changing fertility pattern.
Poor quality data will produce results of uncertain reliability.
Age misreporting affects the results since the children’s length of exposure to the risk of dying is inferred from their mothers’ ages. 26

27. Brass' Child Survivorship Technique and Development of Life Table
Once infant mortality or under-5 mortality is calculated, MATCH may be used to calculate the rest of the life table.
Spreadsheet:
MATCH.xls or MATCH_BS.xls 27