Pattern and differentials of morbidity
among under-five children in Bangladesh
Md. Mortuza Ahmmed
Pattern and differentials of morbidity among under-five children in
Md. Mortuza Ahmmed
Department of Statistics, IUBAT (International University of Business, Agriculture
and Technology), Uttara, Dhaka, Bangladesh
The study of infant and child mortality in developing countries is an important issue
in public health programs. With the increasing emphasis on planning programs in
recent years, it becomes increasingly important to determine the general context of
infant and child morbidity and mortality levels and policy implications. This study
analyzes pattern and determinants of morbidity and mortality of under-five children in
Bangladesh. The data for the study comes from the 2007 Bangladesh Demographic
and Health Survey (BDHS).
Key words: Child morbidity, Child mortality, ARI (acute respiratory infection),
Under-five mortality rate
The growing population in the developing world is an increasing challenge for local
health authorities. Now a days infant and child morbidity and mortality have become
a burning issue of a day. Morbidity and Mortality studies have received increased
attention of recent years. Infant and child morbidity and mortality in Bangladesh have
long been a topic of interest to population researchers because of its direct
relationship with the acceptance of modern contraception. Mortality is one of the
three major factors that contribute to population growth (the other two being fertility
and migration). In addition to its direct and indirect effect on fertility and thus on
various aspects of social and economic planning of a nation, demographers are
concerned recently about morbidity and mortality trends. The examination and
identification of reliable estimates of levels and trends of morbidity and mortality are
gaining increased interest. As about 50 percent of the total number of death in many
countries experienced with mortality under five, so mortality studies focuses more on
infant and child mortality. There is no doubt that infant and child mortality have been
considered as important indicator for describing the mortality situation, health
formation and indeed, the overall socio-economic condition of a country. There ids
only 75 to 80 percent children in developing countries reach their fifty birthday while
over 97 percent of all in developed countries survive through age five. Since these
deaths are preventable with current medical technology, the united nation has set a
target of 70 deaths under age five per 1000 live births to be achieved by all nations by
the year 2000.
Infant and child morbidity and mortality has for a long time been regarded as a true
reflection of a country's socio-economic and health conditions. The rate of loss in the
first year of life attracted particular attention because:
a) Mortality is relatively high, the probability of dying in the first year of life
after exceeding the values observed in the following fifty to sixty years of life.
b) It has a considerable impact on the average expectation of life and the rate of
c) It has disproportionate share in total mortality.
d) It is sensitive to environmental and sanitary condition.
ARI (acute respiratory infection) and diarrhea are major morbidity among under-five
children in Bangladesh. For ARI morbidity; age of child ,sex of child, wealth index,
division, mothers education, religion, sources of drinking water, vitamin-A coverage
and fever may have significant effect. In case of diarrhea; age of child, birth interval,
sources of drinking water, household sanitation and fever may have significant effect.
Objectives of the study
To analyze the patterns and determinants of morbidity among under- five
To analyze treatment seeking practices among under- five children.
To analyze the levels, trends and determinants of mortality among under- five
Data and Methodology
The data come from the 2007 Bangladesh Demographic and Health Survey (BDHS).
The household questionnaire elicited information on the age, sex, marital status, and
education etc. of each member. The main purpose of the household questionnaire was
to identify women and men who were eligible for individual interview. In addition,
information was collected about the dwelling itself such as the source of drinking
water, type of toilet facilities etc.the women's questionnaire was used to collect
information from ever- married women age10-49. These women were asked questions
on the topics like:
Background characteristics (age, education, religion etc)
Breast feeding & weaning practices
Vaccinations and health of children under age five
Husband's background and respondents work status
Causes of death of children under-five years of age
In this study acute respiratory infection (ARI) and diarrhea are considered as
dependent variables. Acute respiratory infection was defined as one or more of the
following signs, symptoms, or self reported syndromes for upper respiratory infection
(cough, runny/stuffy nose, sore throat/throat infection) or for lower respiratory
infection (rapid / difficult breathing, chest indrawn, bronchitis or bronchopneumonia).
The common symptom of acute respiratory infection (ARI) include cough and cough
with difficult or rapid breathing. According to WHO guidelines, ARI shows the
symptoms of inability to suck or drink presence of first or difficult breathing or chest
in drawing with cough and cold. However, fast or difficult breathing isn't always to
observe. Febrile illness with troublesome cough arouses suspicion about ARI in a
child and the degree of severity can be discriminated through observation of few
cardinal signs; inability to drink indicates severe infection; respiratory rate over 50 per
minute indicate moderate disease.
The term diarrhea is used to denote a type of illness as well as a symptom of other
illness. In Bangladesh, ineffective diarrhea is a major cause of mortality and
morbidity among children and infants. In the world of cosmopolitan medicine, public
health and epidemiology typically defined diarrhea as an increase in the fluidity of
stool and/ or frequency beyond what is normal for an individual. With the increase in
the fluidity the stool of diarrhea patient may be loose, liquid or watery in consistency.
The stool also varies from as little as 2-3 per day to as many 4-5 or even more per
hour, in some cases. Diarrhea may be classified into acute and persistent as well as
into dysenteric and non-dysenteric categories. Diarrhea that contains for more than
two weeks is generally regarded as persistent diarrhea. It follows an attack of acute
episode diarrhea and continuous for more than two weeks. Some pathogens for acute
diarrhea may be found in their stool. Young children in developing countries suffer,
on average about diarrhoeal episode. Any diarrhoeal episode in which loose or watery
stools contain visible bloody diarrhoeal and is an invasive enteric infection that carries
a substantial risk of serious morbidity or death in young children in developing
According to the guidelines of the United Nations Children Emergency Fund
(UNICEF), "the under-five mortality rate is the probability of dying between birth and
exactly five years of age per 1000 live births". According to the definition of the
World Health Organization (WHO) report 2006, "the under-five mortality rate is the
probability of a child born in a specific year or period dying before reaching the age
of five, if subject to age- specific mortality rates of that period".
The study deals with a large number of independent variables and examines their
relationship with morbidity status of under- five children. The independent variables
are categorized as:
Age of child (months), Sex of child, Mother's age at first birth, Mother's parity,
Duration of breast feeding, Sex of household head, Birth interval etc.
Wealth index, Place of residence, Division, mother's education, Religion, Sources of
drinking water, Household Sanitation, Family size, Mother's work status, Father's
work status etc.
At first bivariate and multivariate analysis (logistic regression analysis & Cox
Proportional Hazard model) are performed to asses the net and interaction effects of
the independent variables.
Bivariate Analysis: To determine which factors influence the morbidity status of
under -five children of the study population, data is analyzed by the variables which
affect morbidity status of under- five children. In case of bivariate analysis, which
examines the independent variables individually, that gives only a preliminary notion
of how much important each variable is by itself. The examination of percentage in a
bivariate analysis is an advantageous first step for studying the relationship between
two variables, though these percentages do not allow for qualification testing of that
For this purpose, it is useful to consider various indexes that measure the extend of
association as well as statistical test of the hypothesis that there is no association , chi-
square test of independence is performed to the existence of interrelationship among
the categories of two in qualitative variables.
Logistic Regression: The method that does not require any distributional assumptions
concerning explanatory variables is Cox linear logistic regression model (1970). The
logistic regression model can be used not only to identify risk factors but also to
predict the probability of success. The model is now widely used in research to asses
the influence of various socioeconomic characteristics controlling for the effect of
other variables on the livelihood of occurrence of the event of interest. Logistic
regression model is useful for situations in which we want to be able to predict the
presence or absence of a characteristic or outcome based on values of a set of
The advantage of linear logistic regression model over other related models such as
multiple regression analysis and discriminate analysis is that these models pose
difficulties when the dependent variable can have only two values, an event occurring
and not occurring. When the dependent variable can have only values, the assumption
necessary for hypothesis testing in regression analysis are necessarily violated. For
example, it is unreasonable to assume that the distribution of error is normal. Analysis
with multiple regression analysis is that predicted values can not be interpreted as
probabilities. They are not considered to fall in the interval between 0 and 1. Linear
discriminate analysis does not allow direct prediction of group membership, as well as
equal variance- covariance matrices in two groups, is required for the prediction rule
to be optional. However, linear logistic regression analysis requires far fewer
assumption than discriminate analysis, even when the assumption required for
discriminate analysis are satisfied , linear regression still performs well.
The logistic regression model is a multivariate technique for estimating the
probability that an event occurs. Let Y be a dichotomous dependent variable coded as:
Y 1 , if the event occurs
Y 0 , if the event does not occur
Now we can define the dependence of probability of success on the independent
variable for single independent variable (X), the logistic regression is of the form:
e 0 1
Prob. (event) = Prob. ( Y 1) =
1 e 0 1
Or equivalently, Prob. (event) = Prob. (Y 0 ) =
Where and are the regression coefficients to be estimated from the data.
For more than one independent variable, the model assumes the form:
Prob. (event) =
Or equivalently Prob. (event) =
Where Z= X X .......... X .
However logarithm of the ratio of P and 1- P which is called logit of P that turns
out to be a simple linear function of X . We define,
logit ( P ) =ln
The logit is the logarithm of the odds of success, that is, the logarithm of the ratio of
the probability of success to the probability of failure.
The parameters of the model are estimated using the maximum likelihood. That is the
coefficients that make our observed results most `likely' are selected. To understand
the interpretation of the logistic coefficients consider a rearrangement of the equation
for the logistic model. From the logistic regression model we see that the logistic
coefficient can be interpreted as the change in the log odds associated with a one-unit
change in the explanatory variable. As it is easier to think of odds, rather than log
odds, the equation can be written in terms of odds as:
= exp ( x )
1 - p
The exponential raise to the power is the factor by which the odds change when
the independent variables increases by one unit.
If is positive, the factor will be greater than 1, means that the odds are increased.
If is negative, the factor will be less than 1, means that the odds are decreased.
If is 0, the factor equal 1, which leaves the odds unchanged.
Cox Proportional Hazard Model: A hazard function is defined as the failure rate
during a very short interval (t, t+t) conditional upon the individual surviving to the
beginning to the interval t. For interval (t, t+t), the hazard function can be
expressed as h (t) =
pr. (an individual fails to survive during the interval (t, t+t));
where t is an infinitesimal interval of length t.
The proportional hazard model is non-parametric in the sense that it involves an
unspecified arbitrary base-line hazard function. This model is comparatively more
flexible and appropriate for the analysis of survival data with or without censoring
and with or without tied failure time. This assumes that the hazard of the study is
proportional to that underlying survival distribution. The Cox's proportional hazard
model specify that
h(t, z) h t
where h (t) is an arbitrary unspecified base line
hazard function for continuous failure time T and ( , ,........, ) is a vector
of p regression parameters and Z is a vector of covariates.
In this model the covariates act multiplicatively on the hazard function. If h (t)=h
then Cox's proportional hazard model reduces to the exponential regression model,
h(t, z) he .The Weibull regression model is the special case of proportional
h (t)=hp(ht) p 1
. Then the conditional Hazard is
h(t, z) hp(ht)
e The conditional density function for T given Z corresponding to
the Cox's model will be f(t;z)= h (t)e z exp(e z h (u)du) the conditional survivor
function for T given z is s(t;z)= s t
, where s (t) exp h (u)du Thus the
survivor function of for a covariate value Z is obtains by raising the base-line survivor
function s (t) to a power. The set of models produced by this process is sometimes
referred to as the class of Lehman alternatives.
For arbitrary h (.) the Cox's model is sufficiently flexible for many applications.
There are, however, two important generalizations that do not substantially
complicate the estimation of . First, the nuisance function h (t) can be admitted to
vary in specific subsets of the data and the second important generalization allows
regression variable to depend on time itself. The Cox's model assumes continuous
failure time, which may not be practical since in practice it quite likely that the data
will be recorded in a form informing ties. To cover this probability, a discrete
proportional hazards model was proposed by Cox, 1972 and specified a linear log
odds model for the hazard probability at each potential failure time. Cox generalized
( ; z)dt
h (t; z)dt
formally to discrete time by
1 h t
( ; z)dt
1 h (t; z)dt
Methods of estimation and Tests
The mathematical form of proportional hazards model is
h (t,z) = h (t) z
is a row vector of p measured covariates, is a column vector of p regression
parameters, h (t) is an unspecified bade-line hazard function and T is the associated
failure time. The survivor function and density function of T are also given by,
S(t:z)=exp[- h (u)ez du] and f(t;z)=h(t;z).s(t;z)
There are several methods for estimating and testing the set of parameters in the
model. However the method of partial likelihood is the most commonly used method.
Method of partial likelihood: The general method of partial likelihood was proposed
by Cox, 1975. The partial likelihood technique makes useful inferences in the
presence of many nuisance parameters. Let us suppose that the data consist of a vector
of observations from the density f(y;, ), where is the vector of parameters of
interest and is a nuisance parameter and typically of very high or infinite
dimension. In some applications is in fact a nuisance as, for example, the hazard
function h (.) in the proportional hazard model. Let us suppose that the data y are
transformed into a set of variables A B , A B ,........ .
. , A B in a one to one manner
( A , A ,.....A ) and
(B , B ,.....B ) . Suppose that the joint density
can be written as
( j )
1 ; , )
f (a / b , a (
1 ; ) the
second term of this function is called the partial likelihood of B based on A in the
sequence ( A , B ), that is, the partial likelihood B based on A in the sequence
( A , B ) is
f (a / b
1 ; ) where the number of terms could be
random or fixed. In this case it is important to note that the partial likelihood is not
likelihood in the ordinary sense.
Now in order to apply the partial likelihood method to estimate the parameters of
proportional Hazard model let us consider the model
h(t, z) h t