1. 1
Estimation and Analysis of Child
Mortality for Indian States
through a Bayesian Approach
Reetabrata Bhattacharyya
Indian Statistical Institute, Kolkata
Arni S.R. Srinivasa Rao
Indian Statistical Institute, Kolkata
Population Association of America, Annual Meeting, Dallas, 17th April 2010
3. CHILD MORTALITY
Child mortality rate is defined as the number of
children who die before age five per thousand live
births.
Proportion of Children death is one of the important
health indicators in terms of impacts of overall health
and nutritional programs by Indian government.
According to the World Health Organization, hunger
and malnutrition are the biggest causes of child
mortality in developing countries(WHO,2002-2008
estimates).
3
INTRODUCTION
Population Association of America, Annual Meeting , Dallas,17th April 2010
4. 4
BAYESIAN APPROACH
In Bayesian Inference we use current observed
data and past information which led to the observed
data and blend these above two to arrive an estimate
of the parameter which we call a Bayes estimate.
Sometimes,this approach helps us in updating the
prior information and continuously update prior
probability densities.
Population Association of America , Annual Meeting , Dallas, 17th April 2010
5. OBJECTIVE
5
Estimating the impact of Mother’s Education
on Child Mortality through a Bayesian
Approach.
Population Association of America, Annual Meeting, Dallas, 17th April 2010
6. ●During the last two decades, India has experienced
moderate reduction in child mortality.
●United Nations warns that Indian child deaths are
mostly due to malnutrition (Voanews,2007).
●Average education level of mother is strongly
related to child mortality in India(Kravdal,2004).
6
BACKGROUND
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Year National Family Health Survey Child Mortality(Per 1000)
1992-93 NFHS-1 109.3
1998-99 NFHS-2 94.9
2005-06 NFHS-3 74.3
7. 7
Figure:1 Association between mother’s education and
child mortality
Mother’s Individual Level
Attitude, economic resources
and women’s autonomy in
family of 0rigin
Education
Economic resources
Women’s autonomy
Knowledge, Attitudes
Type of Work
Living Standard
Birth Interval
Nutrition
Morbidity
Child Mortality
Population Association of America, Annual Meeting, Dallas, 17th April 2010
Source:(Kravdal,2004)
8. 8
●Vital registration is often incomplete or totally
absent so that mortality statistics must be
computed or estimated from survey or census data.
●Principal objective of National family Health
Survey (NFHS) was providing state level and
National level estimates of fertility ,infant and child
mortality, family planning and socio-economic
structure.
●National Family Health Survey(NFHS) used
uniform questionnaires, methods of sampling and
data collection.
Population Association of America , Annual Meeting , Dallas,17th April 2010
9. 9
Methodology
National Family Health survey
National Family
Health Survey-1
1992-93
April 1992-Sep 1993
National Family
Health Survey-2
1998-99
Nov 1998-June 1999
National Family
Health Survey-3
2005-06
Nov 2005-Aug 2006
Population Association of America , Annual Meeting , Dallas, 17th April 2010
●Formation of data sets from 1992-93,1998-99 and
2005-06.
●Eventually constructing Cohorts from 1958 to 2006.
10. 10
Prior Information
Observed Child
Mortality data
Posterior Distribution of Child Mortality
Estimated Child
Mortality data
Population Association of America, Annual Meeting, Dallas, 17th April 2010
Diagrammatic Representation
11. Mathematical Representation
● Let M denote the observed child mortality data, which
is being generated by random mechanism,(say, )
where .
● Let be the prior information on child mortality in
various states, be the information function (similar to
Shanon’s general information theory), then
11
Population Association of America, Annual Meeting , Dallas, 17th April 2010
)/(Mp
)(p
d
p
kp
kpEk
)(
)/(
log)/(/
=
dkd
pkp
kp
ppTI
T )()(
),(
log)(()}(,{
12. ●Here we assume, that is expected to be
obtained by complete data M.
●We use sharp prior knowledge as well as conventional
Bayesian approach. (See Lindley, (1957), Bernardo and
Smith (1994)).
●In the absence of sharp prior, we use intrinsic
approach. Suppose p1(y|α), p2(y|β) are two alternatives
for the data y ε M .
●In general, intrinsic discrepancy δ(p1,p2) is minimum
expected log likelihood ratio, in favor of the true
sampling distribution. We use conventional definition of
δ(p1,p2) as follows:
12
Population Association of America , Annual Meeting , Dallas, 17th April 2010
)}(,{ pTI
M M
dy
yp
yp
ypdy
yp
yp
yppp
)(
)(
log)(,
)(
)(
log)(min),(
1
2
2
2
1
121
13. 13
●let Cm be the event of child mortality in the
population, and E be the event that the mother of
the child is educated (primary, middle and high
school and above). We estimate posterior
probability We have considered
mechanisms of generating the data on child
mortality. Bayes theorem on inverse
probabilities, gives us
Population Association of America, Annual Meeting, Dallas,17th April 2010
).,/( ICEP m
E
m
m
m
dEIEPECP
IEPECP
ICEP
)/()/(
)/()/(
),/(
14. dataTable:1 State wise Childhood Mortality and Mothers Education Rate, India
State Child Mortality Rate(Per 1000) Mother's Education Rate (%)
1992-93 1998-99 2005-06 1992-93 1998-99 2005-06
Delhi 83.1 55.4 46.7 70.8 70.9 77.3
Haryana 98.7 76.8 52.3 45.9 44.8 60.4
Himachal
Pradesh
69.1 42.4 41.5 57.4 63.7 79.5
Jammu &
Kashmir
59.1 80.1 51.2 51.8 30.2 53.9
Punjab 68 72.1 52 52 61.2 68.7
Rajasthan 102.6 114.9 85.4 25.4 24.5 36.2
Uttaranchal
*
56.8
*
64.6
Chhattisgarh 90.3 44.9
Madhya
Pradesh
130.3 137.6 94.2 34.3 31.5 44.4
Note: Uttaranchal, Chhattisgarh was respective the part of Uttar
Pradesh, Madhya Pradesh when NFHS-1 & NFHS -2 are conducted. So, we
don’t get these data separately 14
15. State Child Mortality Rate(Per 1000) Mother's Education Rate (%)
1992-93 1998-99 2005-06 1992-93 1998-99 2005-06
Uttar
Pradesh
141.3 122.5 96.4 31.5 29.8 44.8
Bihar 127.5 105.1 84.8 28.6 23.4 37
Jharkhand * 93 * 37.1
Orissa 131 104.1 90.6 41.4 40.5 52.2
West Bengal 99.3 67.6 59.6 55.2 50 58.8
Arunachal
Pradesh
72 98.1 87.7 42.1 47.3 52.7
Assam 142.2 89.5 85 50.7 46.1 63
Manipur 61.7 56.1 41.9 63 57.1 72.6
Meghalaya 86.9 122 70.5 60.2 61.9 69.5
Mizoram 29.3 54.7 52.9 88.9 90 94
Note: Jharkhand was the part of Bihar when NFHS-1 & NFHS -2 are
conducted. So, we don’t get these data separately
15Population Association of America Annual Meeting , 17th April 2010
16. State Child Mortality Rate(Per 1000) Mother's Education Rate (%)
1992-93 1998-99 2005-06 1992-93 1998-99 2005-06
Nagaland 20.7 63.8 64.7 71.8 60.2 75.2
Sikkim ** 71 40.1 ** 50.6 72.3
Tripura 104.6 ** 59.2 64.4 ** 68.5
Goa 38.9 46.8 20.3 73.1 71.4 83.6
Gujarat 104 85.1 60.9 51.3 49.7 63.8
Maharashtra 70.3 58.1 46.7 55.9 55.4 70.3
Andhra
Pradesh
91.2 85.5 63.2 38.5 36.2 49.6
Karnataka 87.3 69.8 54.7 46.5 44.8 59.7
Kerala 32 18.8 16.3 82.4 87.4 93
Tamil Nadu 86.5 63.3 35.5 56.1 52.5 69.4
Note:** Data are not available in NFHS-1 and NFHS-2
16Population Association of America Annual Meeting , 17th April 2010
17. Comment: It gives all India trend estimated from a proper prior
probabilities.
17
results
Population Association of America, Annual Meeting, Dallas,17th April 2010
19. Figure:4 Bayesian Posterior Estimates for Indian States by NFHS -2
0
50
100
150
200
250
300
350
400
Delhi
Haryana
HimachalPradesh
Jammu&Kashmir
Punjab
Rajasthan
MadhyaPradesh
UttarPradesh
Bihar
Orissa
WestBengal
ArunachalPradesh
Assam
Manipur
Meghalaya
Mizoram
Nagaland
Sikkim
Goa
Gujarat
Maharashtra
AndhraPradesh
Karnataka
Kerala
TamilNadu
ChildMortalityRate(Per1000)
States
Child Mortality Rate(Per 1000) Bayes Estimates
19
Population Association of America, Annual Meeting,Dallas,17th April 2010
Comment: We observe that Bayes estimator of Mizoram and Jammu&
Kashmir are respectively higher and lower where as Madhya Pradesh
and Kerala are respectively higher and lower child mortality rates
among all Indian states in 1998-1999
21. Discussion
Bayesian type of estimation procedure adopted
here for the child mortality data worked well and
results are consistent with the National Family
Survey data.
The formula for consists of several
probabilities (also known as conditional measures of
uncertainty), which determine the posterior
probability.
The Bayes estimates indicate both the measures of
uncertainty and also an estimate of the proportion of
children in the population (74.3 per 1000 live births)
that would eventually die who were born to less
educated mothers.
21
Population Association of America, Annual Meeting ,Dallas, 17th April 2010
).,/( ICEP m
22. 22
We are trying to formulate Child Mortality
Rate(CMR) based on the child deaths for the
mothers who were captured during all three round
of NFHS.
We will adjust posterior probabilities based on
three rounds to the available computed Child
mortality Rate (CMR).
FURTHER WORKs
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23. References
Bernardo, J. M. and Smith, A. F. M. (1994). Bayesian
Theory, Chicester: Wiley.
Kravdal, O (2004). Child mortality in India: The
community-level effect of education, Population
Studies, Volume 58, Issue 2 July 2004 , pages 177 – 192.
Lindley, D.V. (1957). A statistical paradox.
Biometrika, 44, 187-192.
Mauskopf, J (1983). Reproductive response to child
mortality: a maximum likelihood estimation model,
Journal of the American Statistical Association,
78,382, 238-248.
Sullivan, J.M. (1972) Models for the estimation of the
probability of dying between birth and exact ages of early
childhood. Population Studies 26, 79–98.
23
Population Association of America, Annual Meeting , Dallas,17th April 2010
24. 24
Voanews.com. UN Says India Must Reduce Child
Mortality Rates.
NFHS-I. (1991-1992) National Family Health
Survey, International Institute for Population
Sciences, Bombay.
NFHS-II (1998-1999) National Family Health
Survey , International Institute for Population
Sciences, Bombay.
NFHS-III.(2005-2006) National Family Health
Survey, International Institute for Population
Sciences, Bombay.
SRS. Sample Registration System, Registrar General
of India, New Delhi, 2001.
Population Association of America, Annual Meeting, Dallas , 17th April 2010
