Survival of Births During Preceding Year Method (SBPY)

to Estimate q(1) By

Salih Hamza Abu-El-YamenCentral Bureau of Statistics - Sudan

Introduction:

* q(1) is defined as the probability of dying from birth before reaching the first birth date

* It is an important demographic indicator which reflects the health and socioeconomic conditions of the population

* It is directly and easily calculated from Birth and Deaths Registration Systems provided that these system are complete and accurate

* Where these systems are not complete or accurate demographers developed different indirect techniques to estimate child mortality indicators from different types of data collected through censuses or surveys

* One of the famous and often used indirect technique is Brass method to estimate child mortality from data on child survival

* Recently a direct method has been developed using data on child birth history. The DHS survey was the pioneer in this regard

* Since then the subject started to be controversial as which method is the best estimator of these indicators

* In this paper we introduce a new method to estimate q(1) from data on survival of births during the year preceding the census or survey which support the pro-Brass scholars

Objectives1. Development of new method to estimate q(1)2. Assessment of the differences of q(1) calculated by

SBPY and Brass methods 3. Assessment of the impact of data errors on the

differences of estimates from the two methods4. Initiation of a measure to assess the impact of

errors in data used by different methods to estimate indicators, on the value of estimates

5. Provision of q(1) estimates by different methods for the studied countries and their subdivisions

1. SBDPY method to estimate q(1)

Data:

1-Births during the year preceding the census or survey2-Number of them died

Questions (two alternatives):

A-Whether there is a live birth during the year preceding the census or survey and whether he/she is alive B-Date of birth and death of last live birth

Assumptions:

Births and deaths are evenly distributed through the 12 months preceding and following the census or survey

Rationality:

* The number of deaths from births in the first month of the 12 months preceding the census or survey is estimated by a factor based on the above assumption. Hence q(1) is the probability of death of births born alive in the first month before completing the 12th month

Dec

Nov

Oct

Sep

Aug

Jul

Jun

May

Apr

Mar

Feb

Jan

Dec

Nov

Oct

Sep

Aug

Jul

Jun

May

Apr

Mar

Feb

Jan

J F M A M J Jl A S O N D

Births

Units Of Deaths

ExpectedUnits of Deaths

Method:

B = Number of births during the preceding yearn = The average number of births = B/12D = Number of deaths during the preceding yearf = 12/(1+2+3+4+5+6+7+8+9+10+11+12) = 12/78 = 0.5138d= D*0.5138q(1) = d/n

Advantages:

1- Simple method that uses simple calculations2- Data used likely to be of good quality3- A direct method that uses direct information

Disadvantages:

1- As for many methods of calculation of demographic indicators it is based on assumptions that may not always be true

2 - Assessment of the differences of q(1) calculated by SBPY and Brass methods for 140 records

Unit of research:

* The research units are: a country, a country subdivision, resource of data in a country and population subgroup

* The countries are Brazil, Ethiopia, Egypt, India, Sudan and Turkey * The resources of data are the 1983 and 1993 population censuses in Sudan

* The population subgroups are urban/rural & male/female

* The above units account for 140 records

Sources of data:

1- DHS Surveys Archive2- Sudan 1983 population census3- Sudan 1993 population census

Data processing:

1- For DHS data the required information for the six countries and their subdivisions obtained by processing the row data from DHS Archive using SPSS

2- For the 1983 population census in Sudan the required information are obtained from the Tabulation reports

3- For the 1993 population census in Sudan the q(1) estimates by the two methods already calculated by the author in the 1993 Census Analytical Report

Methodology:

1- Calculation of q(1) by SBPY method and Brass Adjusted method for the 140 records

2- Testing the significance of the differences between the two sets of estimates

The variables:

1- Three variables of q(1) by the two methods and the difference between them

2- Four variables of four groups of differences:lower than 6 per 1000lower than 11 per 1000lower than 16 per 1000lower than 21 per 1000

3- Four variables of percent difference of the above four groups

Methods:

* Classification of records into a number of subgroups1- Census records2- Survey records

3- Total unit records 4- Individual countries and subdivision records

* Calculation of differences of q(1) for the subgroups of records

* Examining the percent number of records by the four groups of differences for the above subgroups of records

* Using paired t-test to examine the value and the significance of the mean difference

* Using one t-test to examine whether the mean difference differs from a specific value

Source Difference in q(1) per 1000 Total Number Records

< 6 < 11 < 16 < 21 All sources 26% 44% 51% 67% 140Censuses 30% 48% 56% 74% 80Surveys 22% 40% 45% 58% 60Total units 46% 77% 92% 100% 13

Results

All sources; censuses, surveys & total subgroups

Source Difference in q(1) per 1000 Total Number of

Records

< 6 < 11 < 16 < 21

Egypt 14% 14% 29% 57% 7

Brazil 50% 100% 100% 100% 4

Turkey 50% 67% 67% 67% 6

India 22% 41% 44% 67% 27

Ethiopia 11% 11% 22% 22% 9

Sudan 0% 43% 43% 43% 7

Sudan 1983 19% 28% 39% 64% 36

Sudan 1993 35% 65% 65% 65% 17

Sudan 1993 adv. 41% 63% 74% 93% 27

Countries

Variable Mean Paired Difference

Mean t Sig.

q(1)_BDPY 99.7 5.4 2.04 0.043

q(1)_Brass 94.3

Source Difference in q(1) per 1000 Total Number

of Records

0 1 2 3

All sources 6 4 5 8 140

Small differences

Paired t-test

Fixed Value t Sig.1 1.661 0.099

2 1.281 0.202

3 0.902 0.369

4 0.523 0.602

5 0.144 0.886

6 -0.236 0.814

7 -0.615 0.540

8 -0.994 0.322

9 -1.374 0.172

10 -1.753 0.082

11 -2.132 0.035

One t-test

Figure I: q(1) Estiamtes of Research Units by SBPY and Brass Methods

0

50

100

150

200

250

300

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101105109113117121125

129133137

Research Units

q(1)

per

10

00

Figure II: q(1) Percent Number of Research Units by Data Source and Level of Difference in q(1) Between SBPY

Method and Brass Adjusted Method

0%

20%

40%

60%

80%

100%

120%

<6 <11 <16 <21Level of difference in q(1)

All sourcesCensusesSurveystotals of all

Figure III: q(1) Percent Number of Research Units by Country and Level of Difference in q(1) Between

SBPY Method and Brass Adjusted Method

0% 20% 40% 60% 80% 100% 120%

<6

<11

<16

<21

Leve

l of d

iffer

ence

in q

( 1) Brazil

TurkeyIndiaEgyptSudanEthiopia

Figure IV: Percent Number of Sudan-Census Reseach Units by Source of Data and Level of Difference in q(1)

Between SBPY Method and Brass Method

0%20%40%60%80%

100%

<6 <11 <16 <21Level of Difference in q(1)

Sudan 83Sudan 93Sudan adv

Figure V: q(1) Estimates of DHS Research Units by DHS Method, Brass Adjusted Method and SBPY Method

0

50

100

150

200

250

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

q( 1

) per

1000

DHSSBYPBrass

Figure VI: q(1) Estimates of Sudan-Census Research Units by SBPY Method and Brass Adjusted Method

0

50

100

150

200

250

300

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79

q( 1

) per

1000

SBYPBrass

3 – Impact of data errors on the differences

The variables:

* Two groups of variables

A – First group - differences variables:1-differences lower than 21 and higher than 20 per 10002- differences by multiple options

B – Second group – data quality variables:1- sex ratios of children ever born2- no. of births during preceding year3- standard deviation of births

Methodology:

* Chi square test for the relationship between the difference variable and the sex ratio, the number of births and the standard deviation variables

* Linear regression between difference variable as a dependent variable and the sex ratio, the number of births as independent variables

* The correlation coefficients between the difference variables and the data quality variables

Difference in q(1) per 1000 Sex ratio of children ever born Total

102-107 <102 or >107

=<10 34 22 56

11-20 12 9 21

>20 12 24 36

Total 58 55 113

Pearson Chi Square = 6.925 (a) Sig. = 0.031

a. 0 cells (.0%) have expected count less than 5.

Difference in q(1) per 1000 Births Total

=<400 401-800 801-10000 >10000

=<10 13 5 8 34 60

11-20 3 3 5 19 30

>20 22 4 6 16 48

Total 38 12 19 69 138

Pearson Chi Square = 14.526 (a) Sig. = .024

a. 3 cells (25.0%) have expected count less than 5.

Chi Square Test: Difference and Sex ratio

Chi Square Test: Difference and No. of Births

Difference in q(1) per 1000 Standard deviation Total

0-5 5-10 > 10

=< 20 11 13 11 35

> 20 14 9 2 25

Total 25 22 13 60

Pearson Chi Square = 5.81 (a) Sig. = 0.055

0 cells (.0%) have expected count less than 5.

Model Coefficients t Sig.

B Standard Error

Constant 1.754 0.478 3.667 0.000

Sex Ratio 0.832 0.305 2.728 0.007

Adjusted R^2 = 0.054

Chi Square Test: Difference and Std Deviation

Linear Regression: Difference with Sex Ratio

Model Coefficients t Sig.

B Standard Error

Constant 3.924 0.337 11.639 0.000

Births -0.270 0.107 -2.511 0.013

Adjusted R^2 = 0.037

Model Coefficients t Sig.

B Standard Error

Constant 2.721 0.590 4.612 0.000

Sex Ratio 0.770 0.301 2.562 0.012

Births -0.314 0.111 -2.842 0.005

Adjusted R^2 = 0.122

Linear Regression: Difference with No. of Births

Linear Regression: Difference with Sex Ratio & Births

Difference in q(1) Sex Ratio of CEBN=113

BirthsN=138

Standard Deviation

N=60

Standard

Deviation

N=38

Difference =<5 _ > 50.062 -0.140 -0.032 *0.347

Difference =<10 _ > 10 0.045 -0.153 -0.168 0.116

Difference =<15 _ > 15 0.059 *-0.188 -0.235 -0.008

Difference =<20 _ > 20 0.172 **-0.285 *-0.307 -0.028

Difference_code_1 (a)**0.251 *-0.211 -0.183 0.120

Difference_code_2 (a)*0.235 **-0.233 -0.244 0.076

Correlation Coefficients

4 – Initiation of a measure to assess the impact of data errors on

the values estimated by different techniques

Introduction:

* Different demographic techniques of estimates come with different values for the same population

* Errors in data used by different techniques contribute to these differences

* To evaluate the relationship between errors in data and the technique estimate, the Specific Sensitivity of Technique (SST) is defined as the deflection of the estimated value as a result of a unit increase in the enumerator data used by the technique

Objectives:

* The objective of SST is to measure the risk of data errors on values estimated by different techniques

Method:

* Data: any hypothetical data as specified by the technique for a number of cases

* Steps:1- Calculation of the indicator values by the specific technique for all the cases2- Increasing the value of the enumerator by a unit for the different steps of calculation3- Recalculate the values of the indicator for all the cases4- Subtract the estimates in step 1 from that in step 35- Calculate the average differences in step 4 to be the SST measure

Applications:

A- The SST for SBPY method to estimate q(1) found to be = 1.85

B- The SST for Brass adjusted method to estimate q(1) found to be = 0.96

C- q(1) estimated by Brass adjusted method is less sensitive to data errors than the SBPY method by around 50%

Summary of findings and implications:

1- Generally speaking the differences between the two methods are somewhat small and they are not far from the limit of differences usually encountered between different methods

2 - The quality of data used by Brass adjusted method and the size of births used by SBPY method play important role in the difference of estimates by the two methods

3- For small sizes of births the validity of evenness assumption of SBPY method has a significant contribution to the differences in q(1) estimates

3- The SBPY method competes as a powerful estimate of q(1) for large sizes of births, and good quality of data which usually emerge from censuses and high quality surveys

4- The Brass adjusted method is supported as a powerful technique for estimation of q(1) in the case of good quality of data on children ever born and number of them surviving

5- For population surveys estimates of q(1) from Brass adjusted method are lower than those from SBPY method and higher than those from Births history data method

6- The above findings imply that q(1) values estimated by Births history data method are likely to be underestimated

Thanks