PAA Presentation 17-4-2010

1

Estimation and Analysis of Child Mortality for Indian States

through a Bayesian Approach

Reetabrata Bhattacharyya

Indian Statistical Institute, KolkataArni S.R. Srinivasa Rao

Indian Statistical Institute, Kolkata

Population Association of America, Annual Meeting, Dallas, 17th April 2010

http://www.isical.ac.in/

Introduction

Objective

Background

Methodology

DATA

Results and Discussion

Further work

References

2


OVERVIEW

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).

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INTRODUCTION

Population Association of America, Annual Meeting , Dallas,17th April 2010

http://en.wikipedia.org/wiki/World_Health_Organization





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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

OBJECTIVE

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Estimating the impact of Mother’s Education

on Child Mortality through a Bayesian

Approach.


●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

Population Association of America, Annual Meeting , Dallas, 17th April 2010

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

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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


Source:(Kravdal,2004)

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●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

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MethodologyNational 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


●Formation of data sets from 1992-93,1998-99 and

2005-06.

●Eventually constructing Cohorts from 1958 to 2006.

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Prior InformationObserved Child

Mortality data

Posterior Distribution of Child Mortality

Estimated Child

Mortality data


Diagrammatic Representation

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

11Population Association of America, Annual Meeting , Dallas, 17th April 2010

)/(Mp

)(p

dp

kpkpEk

)(

)/(log)/(/

=

dkdpkp

kpppTI

T )()(

),(log)(()}(,{

●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


)}(,{ pTI

M M

dyyp

ypypdy

yp

ypyppp

)(

)(log)(,

)(

)(log)(min),(

1

2

2

2

1

121

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

).,/( ICEPm

E

m

m

mdEIEPECP

IEPECPICEP

)/()/(

)/()/(),/(

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


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


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

Comment: It gives all India trend estimated from a proper prior

probabilities.

17

results

Population Association of America, Annual Meeting, Dallas,17th April 2010

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States

Child Mortality Rate(Per 1000) Bayes Estimates

Figure:3 Bayesian Posterior Estimates for Indian States

by NFHS-1

18Population Association of America, Annual Meeting, Dallas,17th April 2010

Comment: We observe that Bayes estimator of Delhi and Rajasthan are

respectively higher and lower where as Assam and Nagalan are respectively

higher and lower child mortality rates among all Indian states in 1992-1993

Figure:4 Bayesian Posterior Estimates for Indian States by NFHS -2

0

50

100

150

200

250

300

350

400

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19Population 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

0

50

100

150

200

250

300

350

400

450

500

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States


Figure :5 Bayesian Posterior Estimators for Indian States

by NFHS -3

20Population Association of America, Annual Meeting ,Dallas, 17th April 2010

Comment: We observe that Bayes estimator of Mizoram and Rajasthan

are respectively higher and lower where as Uttar Pradesh and Kerala

are respectively higher and lower child mortality rates among all Indian

states in 2005-2006.

DiscussionBayesian 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.

21Population Association of America, Annual Meeting ,Dallas, 17th April 2010

).,/( ICEPm

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

Population Association of America, Annual Meeting,Dallas,17th April2010

ReferencesBernardo, 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.

23Population Association of America, Annual Meeting , Dallas,17th April 2010

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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

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YOUR ATTENTION


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PAA Presentation 17-4-2010