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Survival of Births During Preceding Year Method (SBPY) to Estimate q(1) By Salih Hamza Abu-El-Yamen Central Bureau of Statistics - Sudan

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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

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* 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

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Objectives 1.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 methods 4.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

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1.SBDPY method to estimate q(1)

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Data: 1-Births during the year preceding the census or survey 2-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

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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 12 th month

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Births Dec Nov Oct Sep Aug Jul Jun May Apr Mar Feb Jan Dec Nov Oct Sep Aug Jul Jun May Apr Mar Feb Jan De c NovOctSepAu g JulJunMayAp r MarFe b Jan DNOSAJlJMAMFJ Births Units Of Deaths Expected Units of Deaths

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

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Advantages: 1- Simple method that uses simple calculations 2- Data used likely to be of good quality 3- 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

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

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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

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Sources of data: 1- DHS Surveys Archive 2- Sudan 1983 population census 3- Sudan 1993 population census

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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

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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

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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 1000 lower than 11 per 1000 lower than 16 per 1000 lower than 21 per 1000 3- Four variables of percent difference of the above four groups

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Methods: * Classification of records into a number of subgroups 1- Census records 2- 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

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SourceDifference in q(1) per 1000Total Number Records < 6< 11< 16< 21 All sources 26%44%51%67%140 Censuses 30%48%56%74%80 Surveys 22%40%45%58%60 Total units 46%77%92%100%13 Results All sources; censuses, surveys & total subgroups

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SourceDifference in q(1) per 1000Total Number of Records < 6< 11< 16< 21 Egypt 14% 29%57%7 Brazil 50%100% 4 Turkey 50%67% 6 India 22%41%44%67%27 Ethiopia 11% 22% 9 Sudan 0%43% 7 Sudan 1983 19%28%39%64%36 Sudan 1993 35%65% 17 Sudan 1993 adv. 41%63%74%93%27 Countries

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VariableMeanPaired Difference MeantSig. q(1)_BDPY 99.7 5.42.040.043 q(1)_Brass 94.3 SourceDifference in q(1) per 1000Total Number of Records 0123 All sources6458140 Small differences Paired t-test

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Fixed ValuetSig. 1 1.6610.099 2 1.2810.202 3 0.9020.369 4 0.5230.602 5 0.1440.886 6 -0.2360.814 7 -0.6150.540 8 -0.9940.322 9 -1.3740.172 10 -1.7530.082 11 -2.1320.035 One t-test

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3 – Impact of data errors on the differences

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The variables: * Two groups of variables A – First group - differences variables: 1-differences lower than 21 and higher than 20 per 1000 2- differences by multiple options B – Second group – data quality variables: 1- sex ratios of children ever born 2- no. of births during preceding year 3- standard deviation of births

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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

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Difference in q(1) per 1000Sex ratio of children ever bornTotal 102-107 107 =<10 342256 11-20 12921 >20 122436 Total 5855113 Pearson Chi Square = 6.925 (a) Sig. = 0.031 a. 0 cells (.0%) have expected count less than 5. Difference in q(1) per 1000BirthsTotal =<400401-800801-10000>10000 =<10 13583460 11-20 3351930 >20 22461648 Total 38121969138 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

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Difference in q(1) per 1000Standard deviationTotal 0-55-10> 10 =< 20 11131135 > 20 149225 Total 25221360 Pearson Chi Square = 5.81 (a) Sig. = 0.055 0 cells (.0%) have expected count less than 5. ModelCoefficientstSig. BStandard Error Constant 1.7540.4783.6670.000 Sex Ratio 0.8320.3052.7280.007 Adjusted R^2 = 0.054 Chi Square Test: Difference and Std Deviation Linear Regression: Difference with Sex Ratio

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ModelCoefficientstSig. BStandard Error Constant 3.9240.33711.6390.000 Births -0.2700.107-2.5110.013 Adjusted R^2 = 0.037 ModelCoefficientstSig. BStandard Error Constant 2.7210.5904.6120.000 Sex Ratio 0.7700.3012.5620.012 Births -0.3140.111-2.8420.005 Adjusted R^2 = 0.122 Linear Regression: Difference with No. of Births Linear Regression: Difference with Sex Ratio & Births

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Difference in q(1)Sex Ratio of CEB N=113 Births N=138 Standard Deviation N=60 Standar d Deviatio n N=38 Difference = 5 0.062-0.140-0.032*0.347 Difference = 10 0.045-0.153-0.1680.116 Difference = 15 0.059*-0.188-0.235-0.008 Difference = 20 0.172**-0.285*-0.307-0.028 Difference_code_1 (a) **0.251*-0.211-0.1830.120 Difference_code_2 (a) *0.235**-0.233-0.2440.076 Correlation Coefficients

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4 – Initiation of a measure to assess the impact of data errors on the values estimated by different techniques

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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

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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 cases 2- Increasing the value of the enumerator by a unit for the different steps of calculation 3- Recalculate the values of the indicator for all the cases 4- Subtract the estimates in step 1 from that in step 3 5- Calculate the average differences in step 4 to be the SST measure

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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%

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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

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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

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