1. TIME SERIES ANALYSIS OF UNDER-FIVE MORTALITY
IN MULAGO HOSPITAL (1990-2010)
BY
OKUDA BONIFACE
09/U/3224/PS
209004160
A DISSERTATION SUBMITTED TO THE SCHOOL OF STATISTICS AND
APLLIED ECONOMICS IN PARTIAL FULFILLMENTOF THE
REQUIREMENTS FOR THE AWARD OF BACHELOR OF STATISTICS
AT MAKERERE UNIVERSITY.
JUNE 2012

2. DECLARATION
I Okuda Boniface affirm that this proposal is entirely my original work and has not been
presented for any award of a degree in any institution of higher learning unless otherwise cited.
………………………………… ………………………………..,.
Signature Date
This proposal has been submitted with my approval as a University Supervisor.
………………………………………… ……………………………………….
Mr. Odur Benard Date
Lecturer
SSAE, Makerere University Kampala

3. DEDICATION
This work is dedicated to my father Mr. Ogira Simon Peter, my mother Mrs. Akongo Sidonia,
brothers Ochen Benjamin and Ogira Gabriel, my sisters Akello Brenda and Achieng Mercy and
my friends for the support.
ii

4. ACKNOWLEDGEMENT
Special thanks to the almighty God for the special help and guidance. I am deeply indebted to
some individuals whose contributions made it possible to reach a successful completion of this
dissertation.
My utmost gratitude goes to my supervisor, Mr. Odur Bernard for his tireless effort in reading
and providing relevant comments and corrections that have enabled me produce this research
project.
Finaly special thanks goes to my father, mother and friends for all invaluable contributions both
financially and morally especially during this time.
iii

5. TABLEOFCONTENTS
DECLARATION ............................................................................................................................ i
DEDICATION ............................................................................................................................... ii
ACKNOWLEDGEMENT ........................................................................................................... iii
LIST OF TABLES ....................................................................................................................... vii
LIST OF FIGURES ................................................................................................................... viii
ACCRONYMS ............................................................................................................................. ix
DEFINITIONS AND CONCEPTS .............................................................................................. x
ABSTRACT ................................................................................................................................. xii
CHAPTER ONE: BACKGROUND ............................................................................................ 1
1.1 Introduction ............................................................................................................................... 1
1.2 Previous trends of child mortality ............................................................................................. 2
1.3 Problem statement ..................................................................................................................... 3
1.4 Objectives ................................................................................................................................. 4
1.5 Hypotheses ................................................................................................................................ 4
1.6 Significance of the study ........................................................................................................... 5
1.7 Scope of the Study .................................................................................................................... 5
1.8 Limitation of the study .............................................................................................................. 5
CHAPTER TWO: LITERATURE REVIEWS .......................................................................... 6
2.1 Introduction ............................................................................................................................... 6
2.2 demographic factors .................................................................................................................. 6
2.2.1 Sex of the child ...................................................................................................................... 6
2.2.2 Season .................................................................................................................................... 7
2.3 Infectious diseases and under-five mortality ............................................................................ 7
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6. 2.3.1 Malaria and under-five mortality ........................................................................................... 7
2.3.2 Tuberculosis and under-five mortality ................................................................................... 8
2.3.3 Tetanus and under-five mortality ........................................................................................... 9
2.3.4 Measles and under-five mortality ........................................................................................ 10
2.3.5 Pneumonia and under-five mortality.................................................................................... 10
2.3.6 HIV/ AIDS and under-five mortality ....................................................................................11
2.4 Forecasting model ................................................................................................................... 12
CHAPTER THREE: METHODOLOGY ................................................................................. 14
3.1 Introduction ............................................................................................................................. 14
3.2 Sources and nature of data to be used ..................................................................................... 14
3.3 Techniques of data collection .................................................................................................. 14
3.4 Analysis software .................................................................................................................... 14
3.5 Data processing and analysis .................................................................................................. 14
3.5.1 Time series analysis ............................................................................................................. 14
3.5.2 Data exploration techniques................................................................................................. 15
3.5.3 Autoregressive Integrated Moving Average (ARIMA) ........................................................ 19
3.6 Ethical considerations ............................................................................................................. 20
CHAPTER FOUR: DATA PRESENTATION AND ANALYSIS OF RESULTS ................... 21
4.1 Introduction ............................................................................................................................. 21
4.2. Graphical presentation of findings ......................................................................................... 21
4.3 Testing for stationarity in the mortality series ........................................................................ 27
4.4 Estimation of the model .......................................................................................................... 29
4.5 Diagnostic test ......................................................................................................................... 29
4.6: Forecasts of under-five mortality (2011Q1-2015Q4) ............................................................ 31
v

7. 4.7 Test of hypotheses ................................................................................................................... 31
4.7.1 Testing for death differentials by gender ............................................................................. 31
4.7.2 Testing for death differentials by year ................................................................................. 32
4.7.3 Testing for death differentials by disease ............................................................................. 33
4.7.4 Trend analysis of mortality series ........................................................................................ 33
4.7.5 Trend analysis of mortality series by gender ....................................................................... 34
4.7.6 Test for seasonality............................................................................................................... 34
4.8 Discussion ............................................................................................................................... 35
4.8.1 Child sex and under-five mortality ...................................................................................... 35
4.8.2 Seasonality and Under-five mortality .................................................................................. 36
4.8.3 Trend in under-five mortality ............................................................................................... 36
4.8.4 Infectious Diseases and Under-five mortality...................................................................... 37
CHAPTER FIVE: SUMMARY OF FINDINGS, CONCLUSIONS AND
RECOMMENDATIONS ........................................................................... 38
5.1 Introduction ............................................................................................................................. 38
5.2 Summary of the findings ......................................................................................................... 38
5.3 Conclusions ............................................................................................................................. 39
5.4 Recommendations ................................................................................................................... 39
5.5 Areas for further studies .......................................................................................................... 40
REFFERENCES ......................................................................................................................... 41
APPENDICES ............................................................................................................................. 44
vi

8. LIST OF TABLES
Table 4. 1: Unit Root Test ............................................................................................................. 27
Table 4. 2: Correlogram of Mortality Series ................................................................................. 28
Table 4. 3: Autoregressive Moving Average Model (9, 0, 0) ........................................................ 29
Table 4. 4: Model Description ...................................................................................................... 31
Table 4. 5: Forecasted Mortality Values ........................................................................................ 31
Table 4. 6: Death Differential by Gender ...................................................................................... 32
Table 4. 7: Death Differential by Year (Period) ............................................................................ 32
Table 4. 8: Death Differential by Disease ..................................................................................... 33
Table 4. 9: Runs Test on Mortality Series ..................................................................................... 33
Table 4. 10: Runs Test on Mortality Series by Gender ................................................................. 34
Table 4. 11: Kruskal-Wallis Test for Seasonality .......................................................................... 35
vii

9. LIST OF FIGURES
Figure 4. 1: Trend in Under-Five Mortality by Gender from 1990-2010 ..................................... 21
Figure 4. 2: Percentage Distribution of Under-Five Mortality by Disease (1990-2010) .............. 22
Figure 4. 3: Percentage Distribution of Under-Five Mortality for Each Month 1990-2010 ........ 23
Figure 4. 4: General Trend in Mortality Series ............................................................................. 24
Figure 4. 5: Variations in Mortality Series 2005-2010 by Quarters .............................................. 25
Figure 4. 6: Causes of Under-Five Mortality for the Period 1990-2010 ...................................... 26
Figure 4. 7: Bartlett‟s Test for White Noise for Under-five mortality .......................................... 30
viii

10. ACCRONYMS
UDHS Uganda Demographic Health Survey
WHO World Health Organisation
UNICEF United Nations International Children‟s Emergency Fund
UN United Nations
CHERG Child Health Epidemiology Reference Group
MDGs Millenium Development Goals
PEAP Poverty Eradication Action Plan
HIV Human Immune Virus
AIDS Acquired Immune Deficiency Syndrome
NGOs Non Government Organisations
MOH Ministry Of Health
ix

11. DEFINITIONS AND CONCEPTS
Adequate compilation and measurement of vital events requires that the concepts used be given
formal definitions even though the meaning of these concepts may appear as obvious to most
people.
Hospital: This is a residential establishment which provides short and long term medical care
consisting of observational and rehabilitative service to persons suffering from diseases or
suspected to be suffering from an injury.
Health: The World Health Organisation (WHO) defined health in 1948 as a „state of complete
physical, mental and social wellbeing not merely the absence of disease or infirmity‟.
Live birth: This is the complete expulsion from the womb of its mother, the product of
conception irrespective of the duration of the pregnancy, after which it shows evidence of life
such as breathing, crying, etc.
Premature baby: Babies born before 37 completed weeks of pregnancy are called premature.
Injury: This is usually defined as physical harm to a person‟s body.
Disease: This is any disturbance or anomaly in the normal functioning of the body that probably
has a specific cause and identifiable symptoms.
Types of diseases
Diseases are classified according to the following, though a great deal of overlapping may be
found in the different classes:
1. Infectious diseases. These are communicable and capable of infecting a large number of
persons within relatively short time intervals. This kind of disease has the following
different causes;
a. Parasitic
x

12. b. Bacterial
c. Viral
d. Fungal
2. Environmental diseases. in epidemiology, environmental disease is disease caused by
environmental factors that are not transmitted genetically or by infection. It can be
classified as follows;
a. Nutritional
b. Diseases due to unfavorable environmental factors
3. Other diseases
a. Diseases connected with eggs and fry
b. Tumors, genetic disorders
Mortality: This is the risk of dying in a given year, measured by the death rate which is the
number of deaths occurring per 100,000 people in a population.
Neonatal mortality: the probability of dying within the first month of life
Infant mortality: the probability of dying between birth and the first birthday
Post neonatal mortality: the arithmetic difference between infant and neonatal mortality
Child mortality: the probability of dying between exact age one and the fifth birth
Under-five mortality: the probability of dying between birth and the fifth birthday.
Cause specific mortality: mortality classified by cause.
Death: This is the permanent disappearance of all evidence of life after a life birth has occurred.
xi

13. ABSTRACT
The purpose of the current study was to carry out a time series analysis of under-five mortality in
Mulago hospital for the period of 1990-2010 with specific objectives of; establishing whether
there is trend in the mortality series over the time period, investigating the occurrence of
seasonality in the mortality series, to analyse mortality differences in terms of sex, cause and
period and lastly to make predictions of under-five mortality for the period of 2011-2015.
Secondary data obtained from the records department of Mulago hospital was used for this study.
Descriptive statistics showed that malaria accounted for most of the deaths (19.41%) followed by
Pneumonia and Diarrhoea with 12.68% and 10.80% respectively. Genital infection and oral
disease accounted for the least number of deaths recorded with 0.68% and 0.77% respectively.
Augmented Dickey-Fuller Test also revealed that the mortality series was stationary for the
recorded period of 1990-2010. Under-five mortality was also found to vary by gender, period and
sex, where the male deaths were higher than the female deaths. Run‟s test also revealed that the
mortality series did not exhibit any trend over the period of study. Whereas the mortality series of
the male did not exhibit trend, that of the female exhibited trend over the period of study.
Seasonality was also found to exist in the mortality series where most of the deaths were
recorded in the month of June, February, December, July and August and the least in January and
October. There was also a general reduction in mortality causes where causes due to measles and
tetanus had the least deaths in 2010.
The study therefore recommended political awareness, commitment and leadership that are
needed to ensure that child health receives the attention and resources needed to accelerate
progress towards MDG4, consistent use of treated mosquito nets for malaria prevention and
enhancing workers‟ skills through workshops. This would increase survival rates of children who
visit health units.
xii

14. CHAPTER ONE
BACKGROUND
1.1 Introduction
Infant and child mortality levels in Sub-Saharan Africa are the highest in the world. In the
median African country, more than 15 of 100 children die before their fifth birthday (Jameson et
al., 2006). This compares to less than 25 out of 1,000 in the richer parts of the world. Not only
are under-five mortality levels very high; in addition, progress in reducing child mortality is very
slow. Hence, Sub-Saharan Africa as a whole is seriously off track in terms of reaching MDG4.
In 2010, the world average under-five mortality was 57 (5.7%), down from 88 (8.8%) in 1990
and in 2006, the average in developing countries was 79 (down from 103 in 1990), whereas the
average in industrialized countries was 6 (down from 10 in 1990) (UNICEF press release, 2011).
A child in Sierra Leone, which has the world's highest child mortality rate 262 in 2007 (UNICEF
press release September, 12, 2010) is about 87 times more likely to die than one born in Sweden
with a rate of 3 (UNICEF Sweden statistics, 2010).
According to the World Health Organization, 2008 questions and answer archives, the main
causes of child death are pneumonia, diarrhea, malaria, measles, and HIV. Malnutrition is
estimated to contribute to more than one third of all child deaths in that 1 child dies every 5
seconds as a result of hunger ,700 every hour, 16 000 each day, 6 million each year (2002-2008
estimates Jacques Diouf). One in eight children in Sub-Saharan Africa dies before their fifth
birthday (UNICEF 2010). The biggest improvement between 1990 and 2006 was in Latin
America and the Caribbean, which cut their child mortality rates by 50% (UNICEF state of the
world‟s children report, 2008).
Child mortality was an important indicator of the successful implementation of the Poverty
Eradication Action Plan (PEAP) in Uganda, and for good reasons, the level of child mortality is a
consequence of a broad range of Government intervention areas in terms of access to education,
safe water, basic health care and provision of security and stability. Other determinants of child
mortality include household incomes, HIV/AIDS, gender disparities, cultural practices and
nutrition, all of which can be influenced by Government. Child mortality is therefore an
1

15. important health issue, but it must be stressed from the beginning that the health sector is not the
only sector responsible for the child mortality outcome.
Statistics from the Uganda Demographic and Health Survey (UDHS, 2006) reveal declining
trends in the levels of infant, under-five and maternal mortality. Between 2000 and 2005 infant
mortality decreased from 98 to 76 deaths per 1,000 births. This means that one in every 13
newborn Ugandan die within the first year of life. During the same period, under-five mortality
increased from 162 to 137 deaths per 1,000 births.
According to the world population data sheet of population reference bureau Washington (2009),
the average infant mortality rate was 46 deaths per 1000 live births in the world, 6 deaths per
1000 in the more developed world, 50 deaths per 1000 in the developing world and 76 deaths per
1000 in Uganda.
The World Bank policy study 2010 indicates that the highest rates of child mortality continue to
be in the Sub-Saharan Africa, where 1 child in 8 dies before age five that is nearly 20 times the
average of 1 in 167 for developed regions. Southern Asia has the second highest rates, with about
1 child in 14 children dying before age five.
1.2 Previous trends of child mortality
The global under-five mortality rate has declined by a third, from 89 deaths per 1,000 live births
in 1990 to 60 in 2009 (World Bank policy statement report, 2010). This report also highlights
that all regions except Asia and Oceania have seen reductions of at least 50 percent.
At regional levels, in 2009, the highest rates of under-five mortality continue to be in Sub-
Saharan Africa, where 1 child in 8 died before age of five (129 deaths per 1,000 live births) that
is nearly double the average in developing regions (66 deaths per 1,000 live births) and nearly 20
times the average in developed regions (6 deaths per 1,000 live births). For sub-Saharan Africa
as a whole there has been a decline in U5MR concentrated largely in the period between 1965
and 1990, during which the median U5MR dropped from 232 t o 170 per 1000. Since 1990, the
trend seems to have stalled. The pattern of this overall trend also characterizes each region,
2

16. though at different levels and speeds. The countries of the West region had the highest U5MR in
1960, with a median value around 290 per 1000 live births. This level fell Below 200 per 1000
by 1985, a level similar to that of the Middle region, which had a median around 260 per 1000 in
1960. The East region median oscillated around 200 per 1,000 prior to 1975 before declining to
170 per 1000 in 1990. The Southern Region had the lowest median U5MR in 1960 (around 200
per 1000) and experienced the sharpest decline to about 60 per 1000 by 1990. Declines appear to
have stalled in all regions in the 1990s. The West and Southern regions thus experienced the
fastest declines from 1960 t o 1990, with the countries of t he Middle and East regions showing
the slowest improvement.
In Uganda, Child mortality fell significantly between 1948 and 1970 as a result of political
stability, high economic growth, and increased access to health care and scientific progress
which, amongst others, increased access to vaccines against immunizable diseases. Uganda‟s
health sector was considered to be one of the best in Africa during this period (Hutchinson,
2001). The period from the early 1970s and mid-1980s was characterized by political turmoil and
conflict, severely limited access to health services, and a consequent stagnation in infant
mortality was observed. The recovery period of 1986-1995 with high economic growth, political
stability and poverty reduction under the NRM Government, produced a reduction in child
mortality (MFPED, 2002).
1.3 Problem statement
7.6 million Children under age five died in 2010, representing an under-five mortality rate of
57/1000 live births (WHO, 2011). Unlike in the developed countries where death rarely occurs
among infants and children, in developing countries like Uganda, it is estimated that on average
50% of the deaths occur to children aged 15 and below (UN, 2008).
According to various studies carried out, a small number of diseases and conditions are the
biggest killers of young children today. Pneumonia, measles, diarrhea, malaria, HIV and AIDS
and complications during pregnancy and after birth to mention but a few cause more than 90% of
deaths in children under five (WHO, 2010). Children who are malnourished are at far greater risk
of dying from these causes because they have low immunity.
3

17. The increasing focus on the reduction of child mortality arising from the Millennium Declaration
and from the Millennium Development Goal (MDG) 4 of “reducing by two-thirds, between 1990
and 2015, the under-five mortality rate”, has generated renewed interest in the development of
more accurate assessments of the number of deaths in children aged less than 5 years by cause.
Moreover, the monitoring of the coverage of interventions to control these deaths has become
crucial if MDG 4 is to be achieved; thus a more accurate establishment of the causes of deaths in
children aged less than 5 years becomes crucial.
Although various studies have been conducted about under-five mortality in the country, not
much has been done in Mulago concerning the documentation of trends, seasonality and
mortality by sex and cause of death hence the research would like to find out the behavior of
mortality rates over time and the specific causes of these deaths.
1.4 Objectives
The chief purpose of this study is to carry out a time series analysis of under-five mortality in
Mulago Hospital for the period 1990-2010.
Other objectives may include the following;
1. To establish if there is trend in under five mortality from 1990-2010
2. To investigate whether there is seasonality in the recorded figures from 1990-2010
3. To analyze death differentials by sex, year & diagnosis
4. To make predictions for under five mortality
5. To assess Cause reductions of under-five mortality overtime
1.5 Hypotheses
 there is no trend in child mortality
 there is no seasonality in child deaths
 more male children die than female children
 death differentials by sex, year & diagnosis is the same
4

18. 1.6 Significance of the study
 This study is an important addition to the mortality research already done by scholars in
Uganda
 The study will also be helpful to facilitate the improvement of the understanding of the
specific causes of death in infants on the basis of which proper policy measures for
prevention of diseases and reducing mortality can be developed.
 The analysis of child mortality data will present the demographic status of the population
as well as its potential growth, which will be of great importance to policy makers and
planners.
1.7 Scope of the Study
Under-five mortality data from the records department of Mulago hospital for the period 1990-
2010 will be used for the study. The data set will consider children less than 5 years of age.
The variables that will be used include gender, period of occurrence and the cause of death.
1.8 Limitation of the study
There was a problem of extracting huge amount of data from the record files since Mulago
hospital does not have a Hospital information management system. This took a lot of time for the
researcher.
5

19. CHAPTER TWO
LITERATURE REVIEWS
2.1 Introduction
In Uganda, according to UNICEF (2009), the causes of childhood morbidity and mortality like
elsewhere in Sub-Saharan Africa were malaria, diarrhoea, measles and acute respiratory
infections. In most recent years Acquired Immune Deficiency Syndrome (AIDS) has also joined
in as a major risk to women and children.
Despite droughts, natural disasters and famine, mortality appears to have fallen in all parts of
Africa though the rates of decline have shown substantial variation from one region to another.
The percentage of children dying before celebrating their fifth birth day almost halved in Ghana
over 30 years in the late 1930s and 1960s (from 37%-20%); in Congo over 20 years between the
1940s and the 1960s(from 29%-15%) and in Kenya over the 25 years between late 1940s and
early 1970s from 26-15% (UNICEF statistics-Ghana, 2010).
According to several studies conducted, age, sex and infectious disease have been found to be
major factors affecting mortality. But also season of the year play a role in determining mortality
levels (Kenneth Hill, 1988) hence mortality factors can be broken down into demographic factors
and infectious disease factors.
2.2 demographic factors
2.2.1 Sex of the child
In the reviewed micro-econometric studies, child characteristics typically show the expected
influence on mortality. Boys are often found to be significantly more likely to die than girls and
the same holds for first born children ( Lavy et al, 2000; Ssewanyana and Younger, 2007).
In terms of maternal proximate determinants, the studies in general confirm the important
influence in particular of mother‟s age and birth intervals (for example Mturi and Curtis, 1995;
Brockerhoff and Derose, 2000; Lavy et al, 2002; Lalou and Le Grand, 2000).
6

20. Overall, for the world as a whole, under-five mortality rates are the same for boys and girls.
However, the rate varies by income group and region. In general, under-five mortality is higher
for boys than it is for girls among low income countries and upper middle and high income
countries. The pattern seems reversed for lower middle income countries. Similarly, under-five
mortality is higher among boys for most regions of the world except the South East Asia region
where it is reversed, and there is little difference among boys and girls in the Eastern
Mediterranean region (WHO, 2010).
2.2.2 Season
According to the study by Nyombi in 2000, child deaths have a seasonal pattern occurring more
frequently during certain months of the year. There may exist seasonality in death level among
children, that is there are more deaths occurring in a particular time of the year or day due to
specific diseases being rampant in certain months of the year e.g. cases of death due to anemia,
are predominant in dry seasons when there is little vegetables, and also when malaria cases are
rampant causing break down of red blood cells. Cases due to malaria are most predominant in
months of April, June, July, September, and December, when there is stagnant water, which are
used by mosquitoes as breeding places.
2.3 Infectious diseases and under-five mortality
Preventable infectious diseases cause two-thirds of child deaths, according to a study published
by The Lancet in 2011. Experts from the World Health Organization (WHO) and UNICEF‟s
Child Health Epidemiology Reference Group (CHERG) assessed data from 193 countries to
produce estimates by country, region and the world. While the number of deaths has declined
globally over the last decade, the analysis reveals how millions of children under five die every
year from preventable causes. These causes include;
2.3.1 Malaria and under-five mortality
Malaria is a life-threatening disease caused by parasites that are transmitted to people through the
bites of infected mosquitoes. In 2010, malaria caused an estimated 655,000 deaths, mostly
among African children (WHO, 2011). According to the World Health Organization (WHO
2011) Malaria is responsible for 10 per cent of all under-five deaths in developing countries.
7

21. According to the world health report (2002), in 1970, there were 3.7 million deaths annually and
170 million cases, 88 percent of them in tropical Africa and the disease is endemic in 100
countries. The aim of the current global malaria strategy was to reduce mortality at least by 20
percent compared to 1995 in at least 75 percent of the countries that would have been affected by
the year 2000 in WHO accelerated malaria control activities in 24 endemic countries in Africa.
Africa still remains the region that has the greatest burden of malaria cases and deaths in the
world. In 2000, malaria was the principal cause of around 18% that is 803 000 (uncertainty range
710,000 - 896,000) of deaths of children under 5 years of age in Africa south of the Sahara as by
Rowe AK et al (2005).
During the 1980s and the early 1990s, malaria mortality in rural Africa increased considerably,
probably as a result of increasing resistance to chloroquine as by Korenromp EL et al (2003).
According to Ter Kuile FO et al (2004) Malaria is also a significant indirect cause of death:
malaria-related maternal anemia in pregnancy, low birth weight and premature delivery are
estimated to cause 75 000–200 000 infant deaths per year in Africa south of the Sahara.
2.3.2 Tuberculosis and under-five mortality
There has been a perception, particularly in the industrialized world, that TB is a disease of the
old. Fifty years ago, however, hospital services for children today dedicate entire wards for
infants and children with TB. In developing countries where a large proportion of the
population is under the age of 15 years, as many as 40 per cent of tuberculosis notifications
may be children; tuberculosis may be responsible for 10 per cent or more of childhood hospital
admissions, and 10 per cent or more of hospital deaths.
According to the WHO (2008), complacency towards tuberculosis in the three decades led
control programs to be run down in many countries. The result has been a powerful resurgence of
the disease, now estimated to kill three million people a year, with 7.3 million new cases
annually. The WHO declared tuberculosis a global emergency in 1993. About 3 million cases a
year occur in south East Asia and nearly two million in sub Saharan Africa, with 340000 in
Europe. One third of the incidence in the last five years can be attributed to HIV infection which
8

22. weakens the immune system and makes the person infected with tubercle bacillus 30 times more
likely to become ill with tuberculosis strains of bacillus resistant to one or more drugs may have
infected up to 50 million people.
Tuberculosis may be responsible for more death worldwide than any other disease caused by any
pathogen, Sundre et al, 2000. The incidence of Tuberculosis among children will therefore
increase in the areas where HIV prevalence is high because HIV negative individuals could
increase in the areas where HIV prevalence is high because HIV negative individuals could
increase by 13-14 percent in African countries, depending on the prevalence of tuberculosis and
AIDS.
2.3.3 Tetanus and under-five mortality
Tetanus is a potentially deadly infection that can occur if a baby‟s umbilical cord is cut with an
unclean tool or if a harmful substance such as ash or cow dung is applied to the cord, as is
traditional practice in some African countries. When tetanus develops, child death rates are
extremely high, especially in countries where health systems are not strong and access to more
advanced medical treatment can be difficult.
Tetanus is a major cause of neo- natal death in African as well as among other age groups.
Tetanus mortality rates in Africa are probably among the highest in the world. The few available
studies in Uganda suggest that the rates of 10 to 20 neo-natal tetanus deaths per 1000 live birth
are not usual (Kawuma et al., MOH 2000). According to the world health report (2008), tetanus
of the newborn is the third killer of children after measles and pertusis among the six EPI
vaccine preventable disease and is concern in all WHO regions except Europe. Between 800,000
and 1 million newborn a year died from tetanus in the early 1980s. An estimated 730,000 such
deaths are now preventable every year, particularly by targeting the elimination efforts to high
risk areas. In 1997, there was an estimated 275000 deaths WHO Estimated than 1995, about 90
percent of neonatal tetanus cases occurred in only 25 countries of which Uganda was not part.
9

23. 2.3.4 Measles and under-five mortality
Measles, an acute viral respiratory illness associated with high fever, rashes and vomiting, is
considered one of the most deadly vaccine-preventable diseases, accounting for an estimated
777,000 childhood deaths per year worldwide, with more than half occurring in Africa, according
to the United Nations Children's Fund (UNICEF, 2011).
Measles is caused by paramyxovirus called morbili. It is highly infectious and transmitted from
person to person via droplets spread (sneezes, coughs). Cough nasal congestion and
conjunctivitis follow the incubation period of approximately 10 to 12 hours. The characteristic
rash appears about 2 to 4 days after the onset of other symptoms. Measles is one of the major
causes of death among children in Africa. Its contributing factor is about 8 to 10% of deaths
among African children. (Ofosu- Amaah, 2003; Rodriguez).
Apart from death, children who are affected by measles may suffer from life-long disability
including brain damage, blindness and deafness. In Uganda, Measles deaths reduced from 6,000
to 300 between 1996 and 2006 and to none according to the New Vision Uganda (Oct 19, 2011).
Sabiiti and WHO officials attributed the achievement to aggressive immunisation of children
against killer diseases, measles inclusive. Babies are vaccinated against Measles at the age of
nine months.
2.3.5 Pneumonia and under-five mortality
Pneumonia is a form of acute respiratory infection that affects the lungs. The lungs are made up
of small sacs called alveoli, which fill with air when a healthy person breathes. When an
individual has pneumonia, the alveoli are filled with pus and fluid, which makes breathing
painful and limits oxygen intake.
Pneumonia is the single largest cause of death in children worldwide. Every year, it kills an
estimated 1.4 million children under the age of five years, accounting for 18% of all deaths of
children under five years old worldwide. Pneumonia affects children and families everywhere,
but is most prevalent in South Asia and sub-Saharan Africa (WHO, 2011).
10

24. In the early 1970s Cockburn & Assaad generated one of the earliest estimates of the worldwide
burden of communicable diseases. In a subsequent review, Bulla & Hitze described the
substantial burden of acute respiratory infections and, in the following decade, with data from 39
countries, Leowski estimated that acute respiratory infections caused 4 million child deaths each
year – 2.6 million in infants (0–1 years) and 1.4 million in children aged 1–4 years. In the 1990s,
also making use of available international data, Garenne et al. further refined these estimates by
modeling the association between all-cause mortality in children aged less than 5 years and the
proportion of deaths attributable to acute respiratory infection. Results revealed that between
one-fifth and one-third of deaths in preschool children was due to or associated with acute
respiratory infection. The 1993 World Development Report produced figures showing that acute
respiratory infection caused 30% of all childhood deaths.
2.3.6 HIV/ AIDS and under-five mortality
More than 1,000 children are newly infected with HIV every day, and of these more than half
will die as a result of AIDS because of a lack of access to HIV treatment (UNICEF, 2011). In
addition, over 7.4 million children every year are indirectly affected by the epidemic as a result
of the death and suffering caused in their families and communities.
Nine out of ten children infected with HIV were infected through their mother either during
pregnancy, labor and delivery or breastfeeding (UNAIDS, 2010). Without treatment, around 15-
30 percent of babies born to HIV positive women will become infected with HIV during
pregnancy and delivery and a further 5-20 percent will become infected through breastfeeding
(WHO, 2006). In high-income countries, preventive measures ensure that the transmission of
HIV from mother-to-child is relatively rare, and in those cases where it does occur a range of
treatment options mean that the child can survive - often into adulthood. This shows that with
funding, trained staff and resources, the infections and deaths of many thousands of children
could be avoided.
HIV has caused adult mortality rates to increase in many countries of sub-Saharan Africa
(Timaeus IM, 2000/2002), and there is some indication that child mortality rates are also rising
due to vertical transmission. Since HIV prevalence levels are high and still increasing in many
11

25. countries, the effect of AIDS on child mortality is likely to persist for several decades. However,
for a variety of reasons, direct evidence for the impact of HIV on child mortality is relatively
weak.
2.4 Forecasting model
a) The ARIMA procedure
The ARIMA procedure analyzes and forecasts equally spaced univariate time series data, transfer
function data, and intervention data using the autoregressive Integrated Moving Average
(ARIMA) or autoregressive moving-average (ARMA) model. An ARIMA model predicts a value
in a response time series as a linear combination of its own past values, past errors (also called
shocks or innovations), and current and past values of other time series. The ARIMA approach
was first popularized by Box and Jenkins, and ARIMA models are often referred to as Box-
Jenkins models. The general transfer function model employed by the ARIMA procedure was
discussed by Box and Tiao (1975). When an ARIMA model includes other time series as input
variables, the model is sometimes referred to as an ARIMAX model. Pankratz (2001) refers to
the ARIMAX model as dynamic regression. The ARIMA procedure provides a comprehensive
set of tools for univariate time series model identification, parameter estimation, and forecasting,
and it offers great flexibility in the kinds of ARIMA or ARIMAX models that can be analyzed.
The ARIMA procedure supports seasonal, subset, and factored ARIMA models; intervention or
interrupted time series models; multiple regression analysis with ARMA errors; and rational
transfer function models of any complexity.
Meyler (1998) states that the main advantage of ARIMA forecasting is that it require data on the
time series in question only. This feature is advantageous if one is forecasting a large set of time
series data. This also avoids a problem that occurs in multivariate models since timeliness can be
a problem. ARIMA models are unable to capture non linear relationships in time series and this
makes the process of forecasting limited.
b) Lee-carter forecasting model
The method proposed in Lee and Carter (1992) has become the “leading statistical model of
mortality forecasting in the demographic literature” (Deaton and Paxson, 2004). It was used as a
12

26. benchmark for recent Census Bureau population forecasts (Hollmann, Mulder and Kallan, 2000),
and two U.S. Social Security Technical Advisory Panels recommended its use, or the use of a
method consistent with it (Lee and Miller, 2001). Lee-Carter approach makes strong assumptions
about the functional form of the mortality surface. In the last decade, scholars have “rallied”
(White, 2002) to this and closely related approaches, and policy analysts forecasting all-cause
and cause-specific mortality in countries around the world have followed suit (Booth,
Maindonald and Smith, 2002; Deaton and Paxson, 2004; Haberland and Bergmann, 1995; Lee,
Carter and Tuljapurkar, 1995; Lee and Rofman, 2000; Lee and Skinner, 2002; Miller, 2001;
NIPSSR, 2002; Perls et al., 2002; Preston, 2004; Tuljapurkar and Boe, 2003; Tuljapurkar, Li and
Boe, 2000; Wilmoth, 1996, 2000). Lee-carter was able to capture non linear relationships in the
time series data whereas ARIMA models were not able to capture non linear relationships.
13

27. CHAPTER THREE
METHODOLOGY
3.1 Introduction
This chapter presents the data collection methods, sources of data, and methods of data analysis.
The selected variables used in this study are sex of the deceased, cause of death, and the period
of the occurrence of the death.
3.2 Sources and nature of data to be used
The data used is secondary data that was obtained from Mulago referral hospital‟s records
department office. The data was extracted from the mortuary register.
3.3 Techniques of data collection
The technique used was mainly by observation of the summaries made in the mortuary register
kept in the records department of the hospital.
3.4 Analysis software
Data entry was by use of the computer package, Microsoft Excel, and then exported to statistical
packages like SPSS, STATA, and E-Views for analysis.
3.5 Data processing and analysis
3.5.1 Time series analysis
A time series is a collection of observations of well-defined data items obtained through repeated
measurements over time. A basic assumption in any time series analysis is that some aspects of
the past pattern will continue to remain in the future.
Chatfield (1989) observed that time series methods are based on studying past behavior of the
series to make forecasts.
14

28. As an important step in analyzing time series data, the types of data patterns were considered so
that the models most appropriate to the patterns can be utilized. Four components of time series
can hence be distinguished.
i. Trend: This refers to the general direction, either upward or downward in which a series have
been moving.
ii. Cycle: This where the data exhibits a wave like pattern (rises and falls) that are not of fixed
periods.
iii. Seasonality: This is concerned with periodic fluctuations that recur on a regular periodic
basis.
iv. Irregular term: This is the movement left when Trend, Seasonality and Cyclic components
have been accounted for.
The analysis however concentrated on Trend and Seasonality.
Assuming a multiplicative model, then 𝑌𝑡=𝑇 𝑡 ∗𝑆 𝑡
Where 𝑌𝑡 is the mortality series, 𝑇 𝑡 is Trend and 𝑆 𝑡 is the seasons.
3.5.2 Data exploration techniques
a. Graphical presentation
This involved plotting the series 𝑌𝑡 against time t.
b. Statistical tests
Unit root test
The unit root test was used to establish if the mortality series is stationary. Stationarity
has to be established because;
15

29.  The stationarity or otherwise of a series can strongly influence its behavior and
properties -e .g. persistence of shocks will be infinite for non stationary series
 Spurious regressions. If two variables are trending over time, a regression of one
on the other could have a high R2 even if the two are totally unrelated.
 If the variables in the regression model are not stationary, then it can be proved
that the standard assumptions for asymptotic analysis will not be valid. In other
words, the usual “t -ratios” will not follow a t-distribution, so we cannot validly
undertake hypothesis tests about the regression parameters.
The early and pioneering work on testing for a unit root in time series was done by
Dickey and Fuller (Dickey and Fuller 1979, Fuller 1976). The basic objective of the test
is to test the null hypothesis that φ =1 in:
Yt = φyt-1+ ut
Against the one-sided alternative φ <1. So in general we have;
Ho: the series is stationary
Ha: the series is trended or has seasonality
We usually use the regression:
∆ yt = ψyt-1+ ut
So that a test of φ=1 is equivalent to a test of ψ=0 (since φ-1= ψ).
Conclusions
Reject Ho: this means there is sufficient evidence at a given level of confidence that the
series is trended or has seasonality.
Fail to reject Ho: this means that there is no sufficient evidence at a given level of
significance that the series is trended or has seasonality.
c. Non parametric tests for trend
Run’s test: The runs test (Bradley, 1968) can be used to decide if a data set is from a
random process.
16

30. A run is defined as a series of increasing values or a series of decreasing values. The
number of increasing, or decreasing, values is the length of the run. In a random data set,
the probability that the (i+1)th value is larger or smaller than the i th value follows a
binomial distribution, which forms the basis of the runs test.
Testing procedure
Ho: the mortality series is stationary
Ha: the mortality series is non-stationary
Test statistic
𝑚 (𝑚 −1)
𝑆 𝑅= 2𝑚 −1
𝑅−µ 𝑅
Z= 𝑆𝑅
Where m=number of pluses
Decision rule is at α=0.05
The researcher would reject Ho if Z>𝑍∝ 2 i.e. if the computed Z statistic is greater than
the notable value and then conclude with (1-α)*100% confidence, the series has trend.
d. Test for seasonality
Several scholars have come up with different ways of assessing seasonality in a series
such as graphical methods, non parametric methods, correlation analysis, analysis of
variance method, etc.
Despite the knowledge of seasonal effects on diseases for two millennia, the definition
and the measurement of seasonality has not been the center of attention until Edwards
(1961) developed a test based on a geometrical framework which was specially designed
for seasonality. It turned out to become the most cited and the benchmark against which
other tests are evaluated (Wallenstein et al, 2000, p. 817). In his article, Edwards
explicitly also mentions the possibility to estimate cyclic trends by considering the
ranking order of the events which are above or below the median number. This idea has
17

31. been taken up by Hewitt et al (2002). They did not use a binary indicator as suggested by
Edwards but all the ranking information. Rogerson (2000) made a first step to generalize
this test, relaxing the relatively strict assumption of Hewitt et al.(2000) that seasonality is
only present if a six-month peak period is followed by a six-month trough period.
Rogerson allowed that the peak period can also last three, four, or five months.
In this research, the researcher will use the Kruskal-Wallis test which is an alternative for
the parametric one-way analysis of variance test, if there are two or more independent
groups to compare (Siegel & Castellan 1988). Barker et al. (2006), for example, found
with the Kruskal-Wallis test that significant seasonal and monthly variations in mean
daily frequency of suicide attempts were observed in women, but not in men. In addition,
significant relationships (as assessed with the Mann-Whitney U-test) were found between
female parasuicides and „hot‟, „still‟, „still/hot‟ days as well as between male parasuicides
and „windy‟ days.
The test is described as below;
Ho: the series has no seasonality
Ha: the series has seasonality
2
Test statistics, H to compare with 𝑋∝ (Chi square)
12 𝑘 𝑅2𝑖
H= 𝑁(𝑁+1) 𝑖=1 𝑛 − 3(𝑁 + 1)
𝑖
ni is the number of observations in the ith season
N is the total number of specific seasons
Ri= 𝑟𝑎𝑛𝑘 (𝑦 𝑖 )
Yi is the specific season for time t.
Critical region
2
Reject Ho if H>𝑋∝(𝑖−1)
18

32. 3.5.3 Autoregressive Integrated Moving Average (ARIMA)
This is also known as the Box-Jenkins model. This methodology will be used to forecast the
under-five mortality rates. The model is based on the assumption that the time series involved are
stationary. Stationarity will first be checked and if not found, the series will be differenced d
times to make it stationary and then the Autoregressive Moving Average (ARMA) (p, q) will be
applied.
The ARIMA procedure provides a comprehensive set of tools for univariate time series model
identification, parameter estimation, and forecasting, and it offers great flexibility in the kinds of
ARIMA models that can be analyzed. The ARIMA procedure supports seasonal, subset, and
factored ARIMA models; intervention or interrupted time series models; multiple regression
analysis with ARMA errors; and rational transfer function models of any complexity.
The Box-Jenkins methodology has four steps that will be followed when forecasting the
mortality rates as stipulated below;
i. Identification. This involves finding out the values of p, d, and q where;
p is the number of autoregressive terms
d is the number of times the series is differenced
q is the number of moving average terms
The identification here will be done basing on the correlogram plot obtained. Where both
autocorrelation and partial correlation cuts of at a certain point, we conclude that the data follows
an autoregressive model. The order p, of the ARIMA model is obtained by identifying the
number of lags moving in the same direction. In case the series was non stationary, the number
of times we difference the series to obtain stationarity is the value of d.
ii. Estimation. This involves estimation of the parameters of the Autoregressive and Moving
average terms in the model. The non linear estimation will be used.
iii. Diagnostic checking. Having chosen a particular ARIMA model, and having estimated its
parameters, we now examine whether the chosen model fits the data reasonably well. The simple
19

33. test of the chosen model will be done to see if the residuals estimated from this model are white
noise. If they are, we can accept the particular fit and if not, the model will have to be started
over.
iv. Forecasting.
Exponential smoothing methods will be used for making forecasts. While exponential smoothing
methods do not make any assumptions about correlations between successive values of the time
series, in some cases you can make a better predictive model by taking correlations in the data
into account. Autoregressive Integrated Moving Average (ARIMA) models include an explicit
statistical model for the irregular component of a time series that allows for non-zero
autocorrelations in the irregular component.
3.6 Ethical considerations
Ethics in research refer to considerations taken to protect and respect the rights and well fare of
participants and other parties associated with the activity (Reynolds 2001). The rights of parties
involved at every stage of this study were treated with utmost care. The following considerations
were made to promote and protect the rights and interests of participants at the different stages of
the study.
During Data collection: steps taken to protect the rights of participants during actual data
collection included securing informed written consent by the head of department notifying the
management of Mulago hospital about my study and to grant me permission to collect data from
the hospital.
During analysis and reporting of findings: the investigation made sure to report modestly and
exactly what the findings were, without exaggerations that would create false impressions. In the
same respect, the database was created honestly using SPSS programme without any distortions.
20

34. CHAPTER FOUR
DATA PRESENTATION AND ANALYSIS OF RESULTS
4.1 Introduction
This chapter presents key findings on the trend of under-five mortality. It presents both
descriptive and inferential analysis of the relationship between variables. The choice of the
different test statistic used depended on the hypothesis to be tested. The data was obtained from
the records department of Mulago hospital and directly entered into Microsoft Excel from which
it was exported to SPSS, STATA and E-VIEWS for analysis
4.2. Graphical presentation of findings
Figure 4. 1: A Line Graph Showing the Trend of Under-Five Mortality by Gender from
1990-2010
1200
1000
total number of deaths
800
600
male
400
female
200
0
1991
1999
1990
1992
1993
1994
1995
1996
1997
1998
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
year
From the Figure 4.1 above, the mortality series of both male and female showed a downward
trend between 1990 and 1995. However, the rate of decline for the female is greater than that of
the male. For the male under-five the rate of decline is about 30.6% whereas for the female
under-five, the rate is 38.1%. However between 1995 and 2010, the series exhibited stationarity
with a rate of decline of only 6.7% and 8.8% for the female and male under-five respectively.
21

35. Variations in deaths by gender can also be observed in that the number of male deaths recorded
remained higher than that of female children except in 2003 where a total of 701 female deaths
were recorded against 633male deaths.
Figure 4. 2: A Bar Graph Showing Percentage Distribution of Under-Five Mortality by
Disease (1990-2010)
25.00
percenatage of deaths
19.41%
20.00
15.00 12.68%
10.80%
10.00
5.48%
4.81% 4.73%4.19%
3.85% 4.17%
5.00 2.88% 2.78% 3.32%
2.32%
3.68% 3.37%
2.98%
2.06%
1.10% 1.25% 1.28% 1.41%
0.68% 0.77%
0.00
Nervous system disorder
Cardiovascular disease
Resoiratory infection
Genital infection
Diabetes Mellitus
Oral Disease
Tuberculosis
Dehydration
Kwashiorkor
Septicaemia
Meningitis
Pneumonia
Diarrhoea
Dysentry
Marasmus
Injuries
Measles
Tetanus
Malaria
Anaemia
Asthma
Aids
DISEASES
From Figure 4.2 above, Malaria accounted for most of the deaths (19.41%) for the period 1990
to 2010 followed by Pneumonia and Diarrhoea with 12.68% and 10.80% respectively. Genital
infection and oral disease accounted for the least number of deaths recorded with 0.68% and
0.77% respectively. The high number of deaths due to malaria can be attributed to the rainy
season that cause a lot of stagnant water which acts as breeding places for mosquitoes since most
deaths were recorded in June, February, December, July and august of which these months are
faced with heavy rains at times.
22

36. Figure 4. 3: A Bar Graph Showing Percentage of Under-Five Mortality Recorded for Each
Month for the Period 1990-2010
12.00
10.71% 10.73%
10.00
9.36%
9.13% 9.03%
8.85%
8.00 7.70% 7.76%
7.50% 7.48%
percentage deaths
6.34%
6.00
5.36%
4.00
2.00
0.00
Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec
months
Figure 4.3 above shows that most deaths were recorded in June, February, December, July and
August of which each accounted for 10.73%, 10.71%, 9.36%, 9.13% and 9.03% of the total
deaths respectively. The least number of deaths were recorded in the months of January and
October accounting for only 5.36% and 6.34% of the total number of deaths recorded for the
period 1990 to 2010.
23

37. Figure 4. 4: General Trend in Under-five Mortality (1990-2010)
2500
2000
deaths
1500
1000
total number of
500
0
1996
1990
1991
1992
1993
1994
1995
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
year
From Figure 4.4 above, Mulago Hospital recorded the highest number of child deaths in 1990
with 2062 deaths and the lowest in 2009 with 1172 deaths. The mortality series exhibited a
downward trend between 1990 and 1995 but after wards the series remained almost constant
over the remaining years. The down ward trend between 1990 and 1995 can be attributed to the
government constant effort to improve child health care over the years through provision of
better health facilities and increased number of health workers. The period of 1990-1995
according to (MFPED, 2002) was characterized with high economic growth, political stability
and poverty reduction under the NRM Government. Between 1996 and 2007, the series was
stationary and this can be attributed to the non improving health facility standards and inadequate
budget provisions for the health sector.
24

38. Figure 4. 5: Line Graph showing Variations in Mortality Series 2005-2010 by Quarters
500
450
400
350
300
250
total number of deaths
200
150
deaths
100
50
0
Q1 2006
Q3 2007
Q1 2009
Q1 2005
Q2 2005
Q3 2005
Q4 2005
Q2 2006
Q3 2006
Q4 2006
Q1 2007
Q2 2007
Q4 2007
Q1 2008
Q2 2008
Q3 2008
Q4 2008
Q2 2009
Q3 2009
Q4 2009
Q1 2010
Q2 2010
Q3 2010
Q4 2010
year
From figure 4.5 above, the mortality series varied between different months of the year. The
series indicated consistently high number of deaths for the second quarter and first quarter of the
year as seen above. This can be attributed to the rainy season in the first and second quarter of
the year that cause a lot of stagnant water which acts as breeding places for mosquitoes which
cause malaria and lead to death of children with weak immune systems.
25

39. Figure 4. 6: A Line Graph Showing Various Causes of Under-Five Mortality for the Period
1990-2010
450
400
350
300
250 MEASLES
deaths
TETANUS
200 AIDS
MALARIA
150 PNEUMONIA
ANAEMIA
100
50
0
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
year
From Figure 4.6 above, there has been a down ward trend in mortality by the selected causes;
malaria, tetanus, Aids, measles, pneumonia and anaemia for the period of 1990-2010. Tetanus
and measles according to WHO report 2011 was declared nonexistent in Uganda although
malaria still remains a big challenge. The general downward trend for the period of 1990-2010
can be attributed to improved health facilities and the government effort to achieve the MDG 4.
26

40. 4.3 Testing for stationarity in the mortality series
Before fitting a particular model to time series data, the series must be made stationary.
Stationary occurs in a series when statistical properties in the series tend to remain the same over
a given period of time. The test hypotheses are stated below;
Ho: mortality series is stationary
Ha: mortality series is not stationary
Table 4. 1: Unit Root Test for Under-five mortality
Null Hypothesis: TOTAL has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic based on SIC, MAXLAG=4)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -5.287243 0.0004
Test critical values: 1% level -3.808546
5% level -3.020686
10% level -2.650413
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(TOTAL)
Method: Least Squares
Date: 04/27/12 Time: 08:49
Sample (adjusted): 1991 2010
Included observations: 20 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
TOTAL(-1) -0.323773 0.061237 -5.287243 0.0001
C 412.2893 87.07992 4.734608 0.0002
R-squared 0.608312 Mean dependent var -43.00000
Adjusted R-squared 0.586551 S.D. dependent var 90.10111
S.E. of regression 57.93498 Akaike info criterion 11.05116
Sum squared resid 60416.32 Schwarz criterion 11.15073
Log likelihood -108.5116 Hannan-Quinn criter. 11.07060
F-statistic 27.95493 Durbin-Watson stat 2.407887
Prob (F-statistic) 0.000050
According to Table 4.1 above, the Dickey-Fuller Unit root test on the original series shows that
the series is stationary since the absolute value for the combined test statistics (5.287243) is
greater than the three test statistics at 1%, 5%, and 10% critical values 3.808546, 3.020686,
27

41. 2.650413 respectively. Since the series is stationary, we now obtain the Autoregressive Moving
Average (p, q). Here the chief tools of model identification are the autocorrelation function
(ACF) and the Partial Autocorrelation Function (PAF) and there corresponding correlogram
plots.
Table 4. 2: Correlogram Plot for Mortality (1990-2010)
From the above captured correlogram in Table 4.2, we observe that Both AC and PAC cuts off
after a certain point hence we can say that the data follows an autoregressive model. The order of
the ARIMA model is now obtained by identifying the number of lags moving in the same
direction. By counting the lags moving in the same direction, we obtain 9 lags. Hence it‟s AR
(9).
28

42. 4.4 Estimation of the model
Table 4. 3: Autoregressive Moving Average Model (9, 0, 0)
According to Table 4.3 above, the probability value of (0.000) is less than 0.05. This means that
the deaths in the previous quarter can significantly determine the deaths in the current quarter.
4.5 Diagnostic test
In order to check whether the model was good for the data, Bartlett‟s white noise test was carried
out. The residuals generated were plotted using a cumulative periodogram white Noise test.
29

43. Figure 4. 7: Bartlett’s Test for White Noise
As presented in Figure 4.7, using the periodogram white noise test for goodness of fit of the
model to the data, the researcher found that the model best fits the data since almost all values
appeared within the confidence bands thus the model is good for this data.
After carrying out the white noise test, the mortality series were predicted within the range of the
original series. This is done in order to find out whether the model is good for the data.
30

44. 4.6: Forecasts of under-five mortality (2011Q1-2015Q4)
Table 4. 4: Model Description
Model Type
Model ID Mortality Model_1
forecast ARIMA(9,0,0)
Table 4. 5: Forecasted Mortality Values
year quarter Forecast values
2011 Q1 303
2011 Q2 327
2011 Q3 281
2011 Q4 225
2012 Q1 294
2012 Q2 317
2012 Q3 272
2012 Q4 218
2013 Q1 284
2013 Q2 306
2013 Q3 263
2013 Q4 211
2014 Q1 274
2014 Q2 296
2014 Q3 254
2014 Q4 203
2015 Q1 265
2015 Q2 285
2015 Q3 245
2015 Q4 196
4.7 Test of hypotheses
4.7.1 Testing for death differentials by gender
A paired sample t-test was conducted to find out whether on average the male deaths and female
deaths are significantly different and the output is displayed below.
Ho: more male children die than female children
Ha: the number of deaths is the same between the sexes
31

45. Table 4. 6: Death Differential by Gender
Paired Differences
95% Confidence Interval of
the Difference
Std. Std. Error
Mean Deviation Mean Lower Upper t df Sig.
Pair 1 male -
female 58.000 50.444 11.008 35.038 80.962 5.269 20 0.000
From Table 4.6 above, it is revealed that the means of the male and female death figures have a
probability value of 0.000 which is less than 0.05. This implies that if 100 similar studies were
carried out under the same conditions, all of them would show that there is a significant
difference between the male mortality and female mortality. The null hypothesis is therefore
rejected and it‟s concluded that on average, more male children died than female children.
4.7.2 Testing for death differentials by year
Ho: mortality in the different years studied differ
Ha: mortality in the different years studied is the same
Table 4. 7: Death Differential by Year (Period)
Test Value = 0 (one sample t-test)
95% Confidence Interval of the
Difference
t df Sig. Mean Difference Lower Upper
total 29.601 20 0.000 1396.476 1298.07 1494.89
It is revealed from Table 4.7 above that the mean deaths of the years 1990-2010 are significantly
different with a probability value of 0.000 which is less than 0.05. This implies that if 100 similar
studies were carried out under the same conditions, all of them would show that there is a
significant difference in the deaths over the period of 1990-2010. This leads to the rejection of
the null hypothesis and a conclusion is made that on average the mean deaths in the years
considered are significantly different.
32

46. 4.7.3 Testing for death differentials by disease
Ho: under-five deaths due to the different diseases differ
Ha: under-five deaths due to the different diseases is the same
Table 4. 8: Death Differential by Disease
One sample test
95% Confidence Interval of the
Mean Difference
t df Sig. Difference Lower Upper
deaths 4.758 22 0.000 1271.304 717.16 1825.45
From Table 4.8 above, it is established that means between figures of disease give a combined
significance value of 0.000 which is less than 0.05. This implies that if 100 similar studies were
carried out under the same conditions, all of them would show that there is a significant
difference in the number of deaths due to the different diseases. The null hypothesis is thus
rejected and a conclusion is made with 95% confidence that on average, deaths due to the
different diseases vary.
4.7.4 Trend analysis of mortality series
Run‟s test was used to establish whether there was a trend in the series of observations recorded.
Summary statistics generated are presented in the table below.
Ho: the mortality series is not trended
Ha: the mortality series is trended
Table 4. 9: Runs Test forUnder-five Mortality ( 1990-2010)
DEATHS
a
Test Value 334
Cases < Test Value 42
Cases >= Test Value 42
Total Cases 84
Number of Runs 34
Z -1.976
Asymp. Sig. 0.055
a. Median
33

47. From Table 4.9 above, the probability value (0.055) is greater than 0.05. This implies that if 100
similar studies were carried out under the same conditions, about 95 of them would show that the
series exhibited trend. Thus the null hypothesis is not rejected and it is concluded at 95% level of
confidence that the series did not significantly exhibited trend for the years observed (1990-
2010).
4.7.5 Trend analysis of mortality series by gender
Ho: the mortality series of male children is not trended
Ha: the mortality series of male children is trended
Ho: the mortality series of female children is not trended
Ha: the mortality series of female children is trended
Table 4. 10: Runs Test for Under-five Mortality by Gender
male female
Test Valuea 693 644
Cases < Test Value 10 10
Cases >= Test Value 11 11
Total Cases 21 21
Number of Runs 8 6
Z -1.336 -2.234
Asymp. Sig. (2-tailed) 0.82 0.026
a. Median
According to Table 4.10 above, the probability value of the male mortality series is 0.82 which is
greater than 0.05 and that of female is 0.026 which is less than 0.05. This implies that if 100
similar studies were carried out under the same conditions, only 18 of them would show that
trend significantly exists in the male mortality series and 97 of them would show that trend
significantly exists in the female mortality series.
4.7.6 Test for seasonality
The Kruskal-Wallis test also known as the H-test was used to investigate whether there was
seasonality in the recorded figures from 1990-2010.
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48. Table 4. 11: Kruskal-Wallis Test for Seasonality
quarter Number of Rank sum
observations
1 20 606.50
2 20 1182.50
3 21 1030.00
4 20 502.00
chi-squared = 27.580 with 3 d.f.
probability = 0.0001
It is established that the probability value =0.0001 which is less than 0.05 (5% level of
significance). The null hypothesis is thus rejected and it is concluded that the series exhibited
seasonality for the periods recorded. This also implies that if 100 similar studies were carried out
under the same conditions, all of them would show that seasonality significantly exists in the
mortality series. As observed in figure 4.3, most deaths were recorded in June, February,
December, July and August of which each accounted for 10.73%, 10.71%, 9.36%, 9.13% and
9.03% of the total deaths respectively. The least number of deaths were recorded in the months
of January and October accounting for only 5.36% and 6.34% of the total number of deaths
recorded for the period 1990 to 2010.
4.8 Discussion
The discussion of the key findings has been arranged in relation to the research hypotheses that
were investigated. The findings are also discussed in reference to the findings from some
relevant previous studies that were either similar or contrary to the findings in the present study.
4.8.1 Child sex and under-five mortality
The study findings revealed that mortality of under-five male children remained higher than
those of the female children. This study is in line with a study carried out by Lavy, 2000;
Ssewanyana and Younger, 2007 who also found out that boys are often found to be significantly
more likely to die than girls. Also according to (WHO, 2010), for the world as a whole, under-
five mortality rates are the same for boys and girls. However, the rate varies by income group
35

49. and region. In general, under-five mortality is higher for boys than it is for girls among low
income countries and upper middle and high income countries. The pattern seems reversed for
lower middle income countries. Similarly, under-five mortality is higher among boys for most
regions of the world except the South East Asia region where it is reversed, and there is little
difference among boys and girls in the Eastern Mediterranean region.
4.8.2 Seasonality and Under-five mortality
According to this study, the mortality series in Mulago varied between different months of the
year. The series indicated consistently high number of deaths for the second quarter and first
quarter of the year. According to the study by Nyombi in 2000, child deaths have a seasonal
pattern occurring more frequently during certain months of the year. There may exist seasonality
in death level among children, that is there are more deaths occurring in a particular time of the
year or day due to specific diseases being rampant in certain months of the year e.g. cases of
death due to anemia, are predominant in dry seasons when there is little vegetables, and also
when malaria cases are rampant causing break down of red blood cells.
4.8.3 Trend in under-five mortality
The study findings revealed that there is no trend in under-five mortality (0.055> 0.05). The
mortality series exhibited a downward trend between 1990 and 1995 but after wards the series
remained almost constant over the remaining years. The down ward trend between 1990 and
1995 can be attributed to the government constant effort to improve child health care over the
years through provision of better health facilities and increased number of health workers. Child
mortality fell significantly between 1948 and 1970 as a result of political stability, high economic
growth, and increased access to health care and scientific progress which, amongst others,
increased access to vaccines against immunizable diseases. Uganda‟s health sector was
considered to be one of the best in Africa during this period (Hutchinson, 2001). The recovery
period of 1986-1995 with high economic growth, political stability and poverty reduction under
the NRM Government, produced a reduction in child mortality (MFPED, 2002).
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50. 4.8.4 Infectious Diseases and Under-five mortality
According to this study,Malaria accounted for most of the deaths (19.41% ) for the period 1990
to 2010 followed by Pneumonia and Diarrhoea with 12.68% and 10.80% respectively. Genital
infection and oral disease accounted for the least number of deaths recorded with 0.68% and
0.77% respectively. The high number of deaths due to malaria can be attributed to the rainy
season that cause a lot of stagnant water which acts as breeding places for mosquitoes since most
deaths were recorded in June, February, December, July and august of which these months are
faced with heavy rains at times. This is in line with the study of (Nyombi 2000) who also found
out that cases due to malaria is predominant in the months of April, June, July, September and
December. According to the World Health Organization (WHO 2011) Malaria is responsible for
10 per cent of all under-five deaths in developing countries.
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51. CHAPTER FIVE
SUMMARY OF FINDINGS, CONCLUSIONS AND RECOMMENDATIONS
5.1 Introduction
This chapter summarizes the findings, conclusions and recommendations in line with the
objectives of the study. The major objective of the study was to carry out a time series analysis of
under-five mortality in Mulago Hospital for the period 1990-2010.
5.2 Summary of the findings
This study focused on the behavior of the mortality series for under-five children obtained from
the records department of Mulago hospital. The study found out that mortality series in Mulago
hospital recorded the highest number of child deaths in 1990 and the lowest in 2009. The
mortality series exhibited a downward trend between 1990 and 1995 but after wards the series
remained almost constant over the remaining years. Malaria accounted for most of the deaths for
the period 1990 to 2010 followed by Pneumonia and Diarrhoea. Genital infection and oral
disease accounted for the least number of deaths recorded.
The study also revealed seasonality in Under-five mortality (0.0001<0.05). Most deaths were
recorded in June, February, December, July and August. The least number of deaths were
recorded in the months of January and October for the period 1990 to 2010. . It was also revealed
that under-five deaths varied by gender, year and disease (0.000<0.05) respectively.
The forecasted under-five mortality shows a decline in under-five mortality for the periods of
2011, 2012, 2013, 2014 and 2015. The study also revealed a general downward trend in under-
five mortality causes. Tetanus and measles accounted for the least deaths by 2010 and in 2011
Uganda was declared free of measles according to the ministry of health report 2011 and WHO
report 2011.
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52. 5.3 Conclusions
Basing on the findings of this study, it was possible to draw a number of conclusions. It was
inferred from the findings that the mortality series observed over the period 1990-2010 is
stationary since the Augmented Dickey-Fuller Test (Unit root) revealed that the series had a unit
root.
Run‟s test also revealed that the mortality series did not exhibit trend for the period studied.
However, the mortality series for the female exhibited trend whereas that of the male did not
exhibit any trend for the period 1990-2010.
It was also found out that under-five mortality significantly differ by gender. It was found out
that more male children die than the female children. Under-five mortality was also found to
vary significantly over the period of study.
The study also found out that under-five mortality varies significantly for the different causes
observed over the period 1990-2010. Malaria accounted for most of the deaths observed
followed by pneumonia and diarrhoea.
The study also established that the mortality series exhibited seasonality for the periods recorded.
As observed in figure 4.3, most deaths were recorded in June, February, December, July and
August. The least number of deaths were recorded in the months of January and October.
5.4 Recommendations
The study revealed that most under-five deaths are due to infectious diseases. By scaling up
effective health services, the government will be able to ensure that most of the under-five
mortality can be avoided with proven, low-cost preventive care and treatment. Preventive care
includes: continuous breast-feeding, vaccination, adequate nutrition and, the use of insecticide
treated bed nets. The major causes of under-five deaths need to be treated rapidly, for example,
with salt solutions for diarrhoea or simple antibiotics for pneumonia and other infections. To
reach the majority of children who today do not have access to this care, we need more and
39