UNIVERSITY OF GONDAR

COLLEGE OF NATURAL AND COMPUTATIONAL SCIENCES

DEPARTMENT OF STATISTICS

BY

DESSALEW SHEFERAW

THESIS SUBMITTED TO

SURVIVAL ANALYSIS ON THE RISK FACTORS OF WOMEN’S WITH

CERVICAL CANCER: A CASE STUDY AT BLACK LION HOSPITAL,
ADDIS ABABA, ETHIOPIA.

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE IN BIOSTATITICS

UNIVERSITY OF GONDAR, GONDAR, ETHIOPIA

April, 20

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SURVIVAL ANALYSIS ON THE RISK FACTORS OF WOMEN’S WITH
CERVICAL CANCER: A CASE STUDY AT BLACK LION HOSPITAL,
ADDIS ABABA, ETHIOPIA.

BY

DESSALEW SHEFERAW

ADVISOR

KASSIM MOHAMMED (Ass. professor)

Co-ADVISOR
TIGEST JEGNAW (MSc)

UNIVERSITY OF GONDAR, GONDAR, ETHIOPIA

April, 20

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APPROVAL SHEET-1
This is to certify that the thesis entitled “SURVIVAL ANALYSIS ON THE RISK FACTORS
OF WOMEN’S WITH CERVICAL CANCER: A CASE STUDY AT BLACK LION
HOSPITAL, ADDIS ABABA, ETHIOPIA.”, submitted in partial fulfillment of the
requirements for the degree of Master of Science in Bio-statistics with the graduate program of
the department of Statistics, University of Gondar and is a record of original research carried out
by DESSALEW SHEFERAW. No. GUN/8972/08 under my supervision and no part of the
thesis has been submitted for any other degree or diploma.

The assistance and the help received during the course of this investigation have been duly
acknowledged. Therefore, I recommend that the thesis would be accepted as partial fulfillment of
the requirement for Master of Science.

___________________________ __________ ______________

Advisor Signature Date

__________________________ ___________ _____________

Co-advisor Signature Date

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APPROVAL SHEET-2

We, the undersigned, members of the board of examiners of the final open defense by
DESSALEW SHIFERAW have read and evaluated his thesis entitled “SURVIVAL
ANALYSIS ON THE RISK FACTORS OF WOMEN’S WITH CERVICAL CANCER: A
CASE STUDY AT BLACK LION HOSPITAL, ADDIS ABABA, ETHIOPIA.” and
examined the candidate. This is therefore to certify that the thesis has been accepted in partial
fulfillment of the requirements for the degree of Master of Science in statistics with
specialization of Biostatistics.

______________________________________ _______________ ________________

Name of Chairperson Signature Date

______________________________________ _______________ ________________

Name of Advisor Signature Date

______________________________________ _______________ ________________

Name of Co-advisor Signature Date

______________________________________ _______________ ________________

Name of External Examiner Signature Date

______________________________________ _______________ ________________

Name of Internal Examiner Signature Date

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 Acknowledgment
For the successful completion of this work, I am thankful to Allah. First and for most, I thank my
brother Mekash Sheferaw for giving me the opportunity to pursue my graduate study at the
department of statistics, university of Gondar.

I would like to gratefully and sincerely thank my thesis advisor Kassim Mohammed and Tigest
Jegnaw by giving the patience in repeatedly reading the draft manuscript of this study and for
making constructive comments. By the suggestion of them I have benefited a lot. It is palpable
fact that, without these closer follow-up and continuous encouragements with valuable
comments this thesis would not have been finalized in its present structure.

I am also indebted to take this opportunity to appreciate my family specially my father Mr.
Sheferaw Yesuf and My friend Mr. Mequannent wale for being with me closely throughout my
study.

Finally, I am grateful thanks to Gondar university department of statistics for permission to use
Survival analysis of the risk factors on women’s with cervical cancer in black lion hospital.

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 LIST OF ABBREVIATIONS
ACS American cancer society
AHR Adjusted hazard ratio
AIC Akaike’s information criteria
AOR Adjusted odd ratio
ASIR Age Specific Incidence Rate
ASMR Age Specific Mortality Rate
BLH Black Lion Hospital
CI Confidence Interval
FIGO Federation of International Gynecology and Obstetrics
GLOBOCAN Global Burden of Cancer
HDI Human development index
HIV Human immune virus
HPV Human Papilloma Virus
HR Hazard ratio
IARC International Agency for Research on Cancer
ICO Institute catalad ’Oncologia
INCTR International Network for Cancer Treatment and Research
MOH Ministry of Health
NCI National cancer institute
RS Relative survival
SCC Squamous Cell Carcinoma
SEER Surveillance, Epidemiology, and End Results
SES Socioeconomic Status
SPSS Statistical Package for Social Scientists
SR Survival Rate
WHO World health organization

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ABSTRACT
Cancer is a group of diseases characterized by the uncontrolled growth and spread of abnormal
cells. If the spread is not controlled, it can result in death. The objective of this thesis was to
identify the best-fitted survival regression model from the pool of existing survival
regression models and to identify factors associated with the survival time of cervical cancer
patients in Black Lion Hospital Addis Ababa, Ethiopia. A retrospective cohort study was
conducted in Black Lion Hospital Addis Ababa, Ethiopia. Information on patients enrolled
December 2014 and had at least one follow-up until January 2017 time period in oncology center
was used in this study. Kaplan-Meier survival curves and Log-Rank tests were used to compare
the survival experience of different category of predictors. Parametric survival models were
employed to examine the effect of explanatory variables on survival times. A total of 518
cervical cancer patients in Black Lion Hospital Addis Ababa, Ethiopia were included in the
study. Out of 518 cervical cancer patients, 49.04% were live in urban area and 50.96 % were live
in rural area.

Using AIC criteria, the parametric PH was found to have the lowest AIC value and hence it is the
best model for predicting survival time of cervical cancer patients in Black Lion Hospital Addis
Ababa, Ethiopia. Among cervical cancer patients the instantaneous risk of death for urban place
of residence is 2.04 times the instantaneous risk of death for rural place of residence, after
keeping all other covariates at some constant level. Presence of HTN (hypertension), the
instantaneous risk of death for patients with HTN have 2.15 greater risk of instantaneous death
than those patients without HTN, after keeping all other covariates at some constant level.

Based on the results parametric models lead to more efficient parameter estimates than Cox
model. Improved the survival of patients was an integral part of controlling cervical cancer. This
can be done by having health education on cervical cancer incorporated in the teaching
curriculum's by the Ministry of education just like it has been done for HIV / AIDS. Carrying
out regular screening programs and community mobilization activities among other channels can
be used to create awareness.

Key words: cervical cancer, Risk factor, survival model.

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 Table of contents

Acknowledgment....................................................................................................iii

LIST OF ABBREVIATIONS................................................................................iv

ABSTRACT.............................................................................................................v

CHAPTER ONE......................................................................................................1

1. INTRODUCTION...............................................................................................1
1.1. BACKGROUND OF THE STUDY...................................................................................................................................1
1.2. STATEMENT OF THE PROBLEM..................................................................................................................................4
1.3. OBJECTIVES OF THE STUDY...................................................................................................................................... 5
1.3.1. General Objectives:....................................................................................................................................5
1.3.2. Specific Objective:......................................................................................................................................5
1.4. SIGNIFICANCE OF THE STUDY...................................................................................................................................5

CHAPTER TWO.....................................................................................................6

2. LITERATUR REVIEW......................................................................................6
2.1. OVERVIEW OF CERVICAL CANCER..............................................................................................................................6
2.2. RISK FACTORS OF SURVIVAL OF PATIENTS WITH CERVICAL CANCER...................................................................................8
2.2.1. Socio-demographic factors........................................................................................................................8
2.2.2. Clinical factors.........................................................................................................................................12
2.3. COX PROPORTIONAL HAZARDS VERSUS PARAMETRIC MODELS.......................................................................................15

CHAPTER THREE...............................................................................................16

3. DATA AND METHODOLOGY......................................................................16

3.1. STUDY AREA....................................................................................................................................................... 16
3.2. DATA................................................................................................................................................................ 16
3.3. INCLUSION AND EXCLUSION CRITERIA.......................................................................................................................16
3.4. VARIABLE OF THE STUDY.......................................................................................................................................17
3.4.1 Dependent variable..................................................................................................................................17
3.4.2 The independent variables........................................................................................................................17
3.5. METHODS OF STATISTICAL ANALYSIS........................................................................................................................18
3.5.1. Survival analysis......................................................................................................................................18
3.5.2. Survival time distribution.........................................................................................................................19
3.5.3. Non-parametric methods........................................................................................................................20
3.5.4. Comparison of Survivorship Functions.....................................................................................................21
3.5.5. Regression Models for Survival Data.......................................................................................................23

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 3.5.6. Strategies for analysis of non proportional data.....................................................................................29
3.5.7. Parametric model....................................................................................................................................30
3.5.8. Parametric Regression Model assessment...............................................................................................33
3.5.9. Comparison of Cox PH and Parametric Models.......................................................................................33

CHAPTER FOUR.................................................................................................35

RESULT AND DISCUSSION..............................................................................35

4. 1. DESCRIPTIVE SUMMARIES AND NON-PARAMETRIC ANALYSIS........................................................................................35
4.2 COX PROPORTIONAL HAZARD MODEL........................................................................................................................38
4.3. PARAMETRIC PROPORTIONAL HAZARD MODEL...........................................................................................................41
4.4. INTERPRETATION OF THE RESULTS...........................................................................................................................43
4.5. MODEL COMPARISON...........................................................................................................................................44
4.6. DISCUSSION........................................................................................................................................................45

CHAPTER FIVE...................................................................................................47

5. CONCLUSION AND RECOMENDATION..................................................47

5.1. CONCLUSION......................................................................................................................................................47
5.2. RECOMMENDATIONS.....................................................................................................................................48

6. REFERENCE....................................................................................................49

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 LIST OF TABLES
Table-1: Results of descriptive measures of categorical predicator variables, BLH, 2014-2017.......................37
Table-2: Results of log rank test for the categorical variables in BLH, 2014-2017............................................38
Table-3 Results of univariate Cox analysis, BLH, 2014-2017.............................................................................39
Table-4: Results of multivariate Cox regression model, BLH, 2014-2017.........................................................39
Table-5: Test of proportional hazards assumption based on schoenfeld residuals BLH, 2014-2017.................40
Table-6: Results of univariate Weibull PH, Exponential and Log- normal PH models BLH, 2014-2017..........42
Table-7: Results of multivariate Exponential PH model, Weibull PH and log normal PH models BLH, 2014-
2017......................................................................................................................................................................42

Appendix A: Data extraction form..................Error: Reference source not found

LIST OF FIGURES
Figure-1: Cumulative hazard plot of the cox-snell residual for multivariate Cox PH model BLH, 2014-2017....41
ANNEX 1: plot of log (-log (survival))) versus log survival time for categorical variables in the fitted model.....55

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 CHAPTER ONE

1. INTRODUCTION

1.1. Background of the study

Cancer is a group of diseases characterized by the uncontrolled growth and spread of abnormal
cells. If the spread is not controlled, it can result in death. Cancer is caused by external factors,
such as tobacco, infectious organisms, and an unhealthy diet, and internal factors, such as
inherited genetic mutations, hormones, and immune conditions. Treatments include surgery,
radiation, chemotherapy, hormone therapy, immune therapy, and targeted therapy (drugs that
interfere specifically with cancer cell growth) (ACS, 2016).

According to WHO report cancer is the second leading cause of death globally, and was
responsible for 8.8 million deaths in 2015. Globally, nearly 1 in 6 deaths is due to cancer and
from this approximately 70% deaths of cancer occurring in low-income and middle-income
countries (Organization, 2015). Around one third of deaths from cancer are due to the 5 leading
behavioral and dietary risks: high body mass index, low fruit intake and vegetable intake, lack of
physical activity, tobacco use, and alcohol use. From these leading risk factors tobacco use is the
most important risk factor for cancer and is responsible for approximately 22% of cancer deaths
(Forouzanfar et al., 2016). Cancers that originate in the female reproductive system includes
cancer of the cervix, breast, ovaries, vagina, vulva and endometrial (ACS, 2011).

Worldwide 874 million women age of 15 years and older are at risk of cervical cancer; 530,232
new cervical cancer cases are diagnosed and 275,008 cervical cancer deaths occur annually.
About 86% of the global cervical cancer burden occurs in less developed countries (De Sanjosé
et al., 2012). The ASIR and ASMR were 18 and10 per 100,000, respectively, in developing
countries and 9 and 3 per 100,000, respectively, in more developed countries. The incidence and
mortality in sub-Saharan Africa are among the highest in the world and accounts for over 70% of
the global cervical cancer burden with 70,000 new cases annually. It is a health concern among
women worldwide as it ranks as the second most common cause of cancer among women

1
(WHO, 2012).The ACS estimates indicates that there will be 12,900 new diagnoses and 4100
cervical cancer-related deaths in the United States in 2015 (Pfaendler and Tewari, 2016).

In Africa, which has a population of 267.9 million women aged 15 years and older at risk of
developing cervical cancer, approximately 80,000 women are diagnosed with cervical cancer
each year, and just over 60,000 women die from the disease. However, cervical cancer incidence
in Africa also varies considerably by region. The highest rates in Africa (ASIR >40 per 100,000)
are all found in Eastern, Southern, or Western Africa(Denny and Anorlu, 2012).Cancer causing
infections such as, Hepatitis C virus, HPV and infection with HIV substantially increases the risk
of cervical cancer (Forouzanfar et al., 2016, Plummer et al., 2016). Infection with hepatitis and
HPV, are responsible for up to 25% of cancer cases in low and middle-income
countries(Plummer et al., 2016).

In 2015, only 35% of low-income countries reported having pathology services generally
available in the public sector. More than 90% of high-income countries reported treatment
services are available compared to less than 30% of low-income countries and the number of
deaths from cervical cancer is nearly 10 times greater in these low-income countries than in
developed regions, and this is mainly due to lack of access to anticancer therapy combined with
late presentation(Organization, 2015). The rates of cervical cancer in developed countries have
decreased dramatically because of cytological screening and DNA testing for high-risk HPV
types (Tewari et al., 2014). In fact, Sub-Saharan Africa has the highest incidence of cervical
cancer in the world, with an incidence rate of 50.9 cases per 100,000 women’s (Nelson et al.,
2016).

The burden of cervical cancer among women in sub-Saharan Africa including Ethiopia is very
high. This is on the fact that knowledge and awareness of patients on the continent are very poor
and mortality still very high. Facilities for the prevention and treatment of cervical cancer are
still very inadequate in many countries in the region. Governments in sub-Saharan Africa must
recognize cervical cancer as a major public health concern and allocate appropriate resources for
its prevention and treatment, and for research. Indeed, cervical cancer in this region must be
accorded the same priority as HIV, malaria, tuberculosis and childhood immunizations (Anorlu,
2008).

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In Ethiopia according to the WHO estimates, there was 7,600 are diagnosed with cervical cancer
and roughly 6,000 women die of the disease each year (WHO, 2011, Abate, 2016). Although
there is no national cancer registry in Ethiopia, reports from a retrospective review showed.
Despite this fact, very few women receive screening services in Ethiopia. Although there is no
national cancer registry, reports from retrospective review of biopsy results have shown that
cervical cancer is the most prevalent cancer among women in the country next to breast cancer,
and low level of awareness, lack of effective screening programs, overshadowed by other health
priorities (such as AIDS, TB, malaria) and insufficient attention to women’s health are one major
determinant for the prognosis of cervical cancer is the stage at which the patient presents
(Alemayehu, 2008).

One major determinant for the prognosis of cervical cancer is the stage at which the patient
presents. Most patients in developing countries including Ethiopia present late with advanced
stage disease, in which treatment may often involve multiple modalities including surgery,
radiotherapy, chemotherapy, and has a markedly diminished chance of success. Several factors
such as educational status, financial capability, location, presence of health care facilities
determine the stage at which patients with cancer present to the health facility(Bailie et al.,
1996).

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1.2. Statement of the problem

Internationally, the burden of cervical cancer falls most heavily on developing nations. About
85% of the cases and 88% of the deaths due to cervical cancer occur in developing nations with
the majorities in sub-Saharan countries (Globocan, 2012).The highest case load of cervical
cancer is in the eastern Africa region (43%) and lowest in the western Africa region (9.8%). The
frequency of cervical cancer death rate is also proportionally higher in the eastern Africa region
and lower in the western Africa region; 44% and 7.2% respectively(Ibrahim et al., 2011).

Ethiopia has a population of 29.4 million women aged 15 and older who are at risk of developing
cervical cancer. Each year an estimated 7095 women are diagnosed with cervical cancer; 4732
die from the disease and it is an important reproductive health problem and is a major cause of
mortality and morbidity in women than any other cancers. The possible contributing factors are
low level of awareness, cost, limited access to screening services and lack of a national cancer
registry(ICO, 2016).

According to the rationale here is, Studying on the survival of cervical cancers patients has
important practical value for patients, providers, and researchers. Cancer survival data is not
widely available in sub-Saharan Africa countries including Ethiopia. Due to this, there are few
studies that are conducted regarding to HPV burden, screening and survival time of cervical
cancer in Ethiopia, despite the high burden and mortality. The proper understanding of prognosis
may help both of the physicians and the patients decide on treatment options, balancing the
personal values for quality versus quantity of life they provide. Furthermore, this few studies on
the survival of cervical cancer patients is based on semi-parametric proportional hazards model.

Therefore, to prevent and control the risk factors that influence on the survival of cervical cancer
patients for the future it is better to assess the determinants of cervical cancer cases, and this
study will assess the survival time among cervical cancer patients and its determinants at Black
Lion hospital using Cox proportional hazard model and parametric proportional hazards model.

4
1.3. Objectives of the study
1.3.1. General Objectives:

To analyze the risk factors that influences the survival time of cervical cancer patients in Black
Lion Hospital Addis Ababa, Ethiopia.

1.3.2. Specific Objective:

 To estimate the survival time of cervical cancer patients.
 To determine the factors that influences the survival of cervical cancer patients.
 To compare Cox PH and parametric PH in explaining the data set.

1.4. Significance of the Study

In order to make a reasonable recommendation in solving the problem of high mortality rate of
patients with cancer of the cervix, it is necessary to understand the survival time of cervical
cancer patients and factors influencing the survival of women’s with cancer of the cervix in the
hospital. From that concrete recommendations may be given to the hospital society and health
program managers for improving the health policies and cancer care strategy of patients with
cervical cancer. Thus, the findings from this research will hope to be useful in providing
information’s about the risk factors or the most influential covariates that have significant
impacts on survival of cervical cancer patients in Black Lion Referral Hospital Addis Ababa,
Ethiopia and to identify death risk extent of patients under these significant factors.

5
 CHAPTER TWO

2. LITERATUR REVIEW

2.1. Overview of cervical cancer

The most common underlying cause of cervical cancer in worldwide countries is infection with
HPV. The prevalence of infection with HPV in women without cervical abnormalities is 11–12%
with higher rates in sub-Saharan Africa (24%), Eastern Europe (21%) and Latin America (16%).
The two most prevalent types are HPV16 (3.2%) and HPV18 (1.4%) (Forman et al., 2012).

Cervical cancer is a cancer arising from the cervix, which is due to the abnormal growth of cells
that have the ability to invade other part of the body. Early on, typically no symptoms are seen.
Later symptoms may include abnormal vaginal bleeding, pelvic pain, or pain during sexual
intercourse (Dhiman et al., 2014). While bleeding after sex may not be serious, it may also
indicate the presence of cervical cancer (Tarney and Han, 2014).The primary underlying cause of
cervical cancer is infection with HPV, specifically two strains HPV16 and HPV 18. There are
two HPV vaccines (Guardrail and Cervarix) that reduce the risk of cancerous or precancerous
changes of the cervix and perineum by about 93% and 62%, respectively.

The vaccines are between 92% and 100% effective against HPV 16 and 18 up to at least 8 years
(Health, 2015).Other risk factors include smoking, a weak immune system, use of birth control
pills, starting sex at a young age, and having many sexual partners (Louie et al., 2009). Diagnosis
is typically by cervical screening followed by a biopsy and medical imaging is then done to
determine whether or not the cancer has spread (McGuire, 2015). Cervical cancer stage is
classified by FIGO staging system, which is based on clinical examination, rather than surgical
findings (Pecorelli et al., 2009).

The five year survival rate in low HDI countries is less than 20% and more than 65% in
developed countries. There are five-fold or greater differences in incidence between world
regions. In those countries for which reliable temporal data are available, incidence rates appear
to be consistently declining by approximately 2% per annum.

6
There is, however, a lack of information from low HDI countries where screening is less likely to
have been successfully implemented. Estimates of the projected incidence of cervical cancer in
2030, based solely on demographic factors, indicate a 2% increase in the global burden of
cervical cancer, i.e., in balance with the current rate of decline. Due to the relative small numbers
involved, it is difficult to discern temporal trends for the other cancers associated with HPV
infection (Forman et al., 2012).

A systematic review of cervical cancer prevention and treatment that included publication
between 2004 and 2014 assess a range of cervical cancer research in Africa. This includes totals
of 380 research articles/reports. The majority (54.6 %) of cervical cancer research in Africa
focused on secondary prevention (i.e., screening). The number of publication focusing on
primary prevention (23.4 %), particularly HPV vaccination, increased significantly in the past
decade. Research regarding the treatment of precancerous lesions and invasive cervical cancer is
emerging (17.6 %), but infrastructure and feasibility challenges in many countries have impeded
efforts to provide and evaluate treatment. Studies assessing aspects of quality of life among
women living with cervical cancer are severely limited (4.1 %). Across all categories, 11.3 % of
publications focused on cervical cancer among HIV-infected women, while 17.1 % focused on
aspects of feasibility for cervical cancer control efforts (Finocchario-Kessler et al., 2016).

In Ethiopia the majority of HPV related cancers of the cervix histological type are squamous cell
carcinoma followed by adenocarcinomas and adenosquamous cell carcinoma. This is due to the
cause of HPV and the prevalence of HPV16 and/or HPV18 among women with cervical cancer
in Ethiopia are 90.8% (Papillomavirus, 2014, ICO, 2016).

A study conducted by (Tadesse, 2016) for the purpose of evaluating preventive mechanisms and
treatment of cervical cancer in Ethiopia, that were attending care in BLH. This qualitative design
study found that due to the inefficient attention paid to cervical cancer, prevention mechanisms
and treatment were found to be largely inadequate and underdeveloped. The lack of proper data
and other competing health care needs have been stated as the main reason behind the lack of
attention paid to cervical cancer. Though steps are currently being taken to expand screening,
pre-cancer treatment and invasive cancer treatment sites, the study found all the steps being
taken to be in preliminary stages.

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Another study done in BLH, Addis Ababa, Ethiopia to estimate economic burden of cervical
cancer among patients and their family members and to determine predictors for variation in
patient related cost of cervical cancer. The average outpatient cost per patient for cervical cancer
was Birr 5,905 ($407.2) (median = 3,000 ($206.9)). Mean direct outpatient cost (Birr 4,845.3
($334.2) takes the largest share compared with the indirect counterpart (Birr 2,173.7 ($150)).
The outpatient cost for almost half of the respondent fails in a range between Birr 6,933 ($478)
and Birr 1,359 ($93.7). Mean inpatient cost for hospitalized patients was Birr 5,863.2 ($404.4).
The average direct inpatient cost was Birr 4,771 ($329) (74% medical costs and 26% non
medical costs). The mean value for total inpatient cost for nearly half of the respondent were in a
range of Birr 7,161($493.9) and 1,936 ($133.5). For every single day increment in inpatient
hospital stay there is equivalent increment of Birr 61.5 ($4.2) on total inpatient patient side cost
(Desalegne, 2011).

2.2. Risk factors of survival of patients with cervical cancer

2.2.1. Socio-demographic factors
Many studies have been reported that socio-demographic factors such as age at diagnosis, marital
status, place of residence, educational level, alcohol use, income level and parity (number of live
birth) etc, was found to be the most powerful predicator of death for cervical cancer patients. A
retrospective cohort study conducted in Brazil for the purpose of estimating the risk factors on
the survival of women’s with cervical cancer using Kaplan-Meier curve and Cox model. The
result of Kaplan-Meier curve and Cox regression showed there were 421 deaths (43.6%) during
the minimum 5-year follow-up, with an overall 5-year survival of 58.8%. Risk factors were place
of residence in the Serrana Region of the State (HR: 1.94; 95%CI: 1.09-3.45) (Mascarello et al.,
2013).

A hospital-based case-control study conducted by (Bayo et al., 2002) employed logistic

regression to identify the risk factors for invasive cervical cancer in Mali. In this study the result
of logistic regression indicates that the risk factors for cervical cancer were parity>10 versus <5
children (OR= 4.8, 95%CI: 1.5-14.7). So, parity (number of live birth) was the most significant
predicators of invasive cervical cancer. And also in a hospital-based study in India conducted by
(Kaverappa et al., 2015a) using Cox regression also found that survival was highest in 35 – 49
years age group (65.8%) and least in > 65 years age group (30.9%).

8
And also survival was higher in urban (57.3%) than rural residents (54.7%). Only 46% illiterate
patients had survived (p = 0.001). Survival in class I socio-economic status was 69.2% where as
in class V it was 46.7%.

(Kaverappa et al., 2015b) conducted a combined prospective and retrospective study in a

tertiary-care cancer hospital in Mysuru, Karnataka, India to determine the socio-demographic
profile of patients with cervical cancer. This study used descriptive analysis using percentage and
proportions to determine the factors. The result of this study showed among the 380 patients with
cervical cancer, 175 (46.1%) were in the age group of 50–64 years. Majority of the patients were
from rural areas (73.9%) and 26.1% were from urban areas. Majority of the patients were Hindus
(93.2%), 249 (65.5%) were illiterate, 237 (62.4%) were married.

In a related combined prospective and retrospective cohort study conducted in Mysuru, India for
the purpose of estimating prognostic factors for the survival of cervical cancer patients. The
result of Kaplan-Meier and the Cox proportional hazards regression model showed age at
diagnosis increases the risk of deaths with older age that is the survival rate was 53.8% among
patients aged < 35 years when followed up for five years. 65.8% and 56.8% of the patients
survived in the 35-49 and 50-64 years age group. Whereas among patients aged more than 65
years the survival was only 30.9%. The median survival time (14 months) was the highest among
patients in the age group of 50- 64 years. Patients aged < 35 years as well as patients aged > 65
years had a median survival time of 6 months (Vishma et al., 2016).

(Nesrin and KILIC, 2011) employed multivariate logistic regression to identify the risk factors
for Cervical Cancer patients from a Hospital-Based Case-Control Study in Istanbul, Turkish 209
patients with histological confirmed cervical cancer were compared with 1050 controls, who
were admitted to the different departments of the same hospital. The result shows the risk factors
for cervical cancer were found to be early age at first diagnosis (OR = 58.07, 95% CI: 27.88-
120.95). However, compared with controls, it was found that cases including higher education
(OR = 0.18, 95% CI: 0.10-0.30), non-married (OR = 0.07, 95% CI: 0.04-0.12) and non-use of
alcohol (OR =0.30, 95% CI: 0.14-0.65) had a decreased risk for cervical cancer.

9
A hospital-based retrospective study from Visakhapatnam City, Andhra Pradesh conducted by
(Kumari et al., 2010) confirmed that aged women’s have lower survival rate than the younger
one. The result in this study indicates that the overall survival of patients were 100%, 85%, 89,
80%, 75%, and 100% and disease free survival were 100%, 64%, 61%, 63%, 44% and 100% for
the patients with the age group of less than 30 years, 40 years,50 years, 60 years, 70 and 80
years.

(Mitiku and Tefera, 2016) Conducted a community based cross-sectional survey in Dessie town,
Northeast Ethiopia to assess women’s knowledge about cervical cancer and associated factors.
This study employed Binary and multiple logistic regressions to assess the risk factors. After
adjusting for covariates, having sufficient knowledge about cervical cancer was positively
associated with better educational level and income. Women with primary education (AOR: 3.4;
95% CI: 2.2–5.1) and those who had secondary and above education (AOR: 8.7; 95% CI: 5.5–
13.7) were more likely to have sufficient knowledge about cervical cancer compared to those
who had no formal education. Furthermore, women earning an average household monthly
income above 1500 Ethiopian birr (ETB) (~75 U.S. dollars) were more likely to have sufficient
knowledge (AOR: 2.3; 95% CI: 1.3–3.9) than women with an average household monthly
income less than 500 ETB (~25 U.S. dollars).

Similarly, a study conducted by (Teame, 2016) determines factors associated with cervical
precancerous lesion among women screened for cervical cancer in Addis Ababa. The bi-variate
result showed that the magnitude of cervical precancerous lesion was 12.8%. Being in the age
group of 40-49 years (44.9%) were significantly associated with cervical precancerous lesion
than being in age group of 30-39 years (39.07%) (AOR=2.40, 95%CI (1.27-4.54)).

A study conducted in Bangladesh on path epidemiology of cervical cancer in national institute of

cancer research using multivariate logistic regression analysis and the results shows that cases
having higher education (OR=1.46, 95% CI: 1.35-6.42), more personal income (OR=0.129, 95%
CI: .02-.24), small family size (OR=0.018, 95% CI: 27.88-120.95) had a decreased risk for
cervical cancer. However, marital status (OR=1.97, 95% CI: 4.21-20.69), age at marriage
(OR=2.57, 95% CI: 11.45-118.29), age at 1st child (OR=9.33, 95% CI: 0.14-0.65), had more risk
for cervical cancer.

10
This study concludes that the majority of the cervical cancer sufferers at NICRH were from
lower-socioeconomic group having less education with a late cancer presentation mostly with
squamous cell carcinoma (Jabeen et al., 2015).

(Sankaranarayanan et al., 1995) conducted a retrospective cohort study on survival and

prognostic factors of cervical cancer patients in Trivandrum, Kerala, India and used Kaplan-
Meier and Cox's proportional hazards regression analysis. The analysis indicates that the overall
5 year observed survival rate was 47.4% (95% CI, 41.6-52.9%). Socioeconomic status,
performance status emerged as independent predictors of survival. Low survival was associated
with low socioeconomic status and poor performance status. (Showalter et al., 2016) conducted
an observational cohort study in Virginia to evaluate receipt of quality cancer care and mortality
after cancer diagnosis among patients with locally advanced cervical cancer. They employed
logistic regression and the result indicates higher quality score included younger age group
versus 66+ years at diagnosis (18–42 [OR]¼12.3, 95% confidence interval: 6.6, 23.0; 42–53
OR¼5.6, CI: 3.3, 9.5; 53–66 OR¼5.5, CI:3.3, 9.1). This implies that older age groups increased
the mortality.

(Muhamad et al., 2015) employed Kaplan Meier analyses and log-rank test to determine the
survival rates of Malaysian women with cervical cancer and associated factors. The Kaplan
Meier curve the median survival time was 65.8 months and the 5-year survival rate was 71.1%.
There were significant differences in survival rates between patients from different age groups
when tested by using the log-rank test. Women less than 45 years old have a better 5-year
survival rate compared to those 45 years old and above (85.2vs 63.8%). Similarly, women aged
less than 45 years old had higher median survival months compared to women aged 45 years old
and above (75.0vs 64.5 months). Similarly, a study conducted by (Mutai et al., 2013) on the
survival of patients with cancer of the cervix in Nairobi, Kenya. Cox regression analysis showed
the age of patients and level of education significantly affects the survival.

A retrospective study done at Rama thibodi hospital, Bangkok, Thailand on age and Survival of
Cervical Cancer Patients with Bone Metastasis and the results shows that the younger age group
had less median overall survival than the older age group, with a statistically significant
difference (21 months, 95% CI 19.93-22.06; 34 months, 95% CI 23.27-44.72, p = 0.021)
(Nartthanarung et al., 2014).

11
Another study conducted in South India using logistic regression showed marital status and
levels of education were the most significant variables i.e. women who were widowed/divorced
(OR=2.08; 95%CI: 1.24-3.50) and had a lower education (OR=2.62; 95%CI:1.29-5.31 for
women with primary school education only) (Kaku et al., 2008).

2.2.2. Clinical factors

Most of the patients with cervical cancer are found to have affected by different clinical factors,
such as, staging, treatment modalities, histological type of cancer etc. Many studies reviewed
these clinical factors as follow:(Salem, 2015)conducted a retrospective cohort study on treatment
outcomes and prognostic factors of Cervical Cancer at South Egypt. The result of Kaplan Meier
and Cox regression showed in the univariate analysis, tumor larger than 4 cm (P =0.033),
advanced stage (p= 0.001) and surgical resection as an initial treatment (p= 0.034) showed
statistically significant decrease in OS. Patients with advanced stage (p= 0.009) had statistically
significant poor DFS on univariate analysis. And also the multivariate analysis showed that
advanced stage was the only independent prognostic factor for poor overall survival and disease
free survival; (HR= 3.237; 95% CI= 1.609-6.513; p= .001) and (HR= 2.694; 95% CI= 1.406-
5.161; p= 0.003) respectively.

A retrospective cohort study conducted in Osaka University found those treatment modalities are
the most significant predicators on survival. The Univariate and multivariate analyses showed
the patients treated with surgery survived significantly longer than those treated with
chemotherapy (P= 0.0318) or palliative care (P= 0.0292). The patients treated with radiotherapy
survived significantly longer than those treated with chemotherapy (P= 0.0004) or palliative care
alone (P= 0.0005) (Mabuchi et al., 2010). Similarly, (Chokunonga et al., 2004) also found that
the type of treatment significantly affects survival of cervix cancer patients in Harare,
Zimbabwe. The result showed that the survival was significantly greater in the first 3 years for
patients who received radiotherapy treatment compared to those that had not.

A study done on the survival of a cohort of women with cervical cancer diagnosed in a Brazilian
cancer center employed Kaplan-Meier curves and a multivariate analysis through Cox model to
assess overall survival of women with cervical cancer and describe prognostic factors associated.
This study showed the 5-year overall survival was 48%. After multivariate analysis, tumor
staging at diagnosis was the single variable significantly associated with prognosis (p<0.001).

12
There was seen a dose-response relationship between mortality and clinical staging, ranging
from 27.8 to 749.6 per 1,000 cases-year in women stage I and IV, respectively (Carmo and Luiz,
2011).

A related study by (Juhan et al., 2013) in Malaysia also found that stage of disease was important
prognostic variables. That is patients who were diagnosed at stage III & IV are at 2.30 times the
risk of death as those in stage I & II.

A retrospective study conducted in Khan Kean University, Thailand for the purpose of
evaluating factors affecting survival of Cervical Cancer Patients Treated at the Radiation Unit.
From multivariate analyses, the factors that statistically affected survival of cervical cancer
patients included stage (p-value<0.001), hemoglobin level (p-value<0.001), interval between
external and intra sanitary radiation (p-value<0.001) and fractionation (p-value=0.024). Stage III
was associated with a 1.65-fold mortality risk compared with stage I (95% CI=1.05-2.59).
Patients with a low hemoglobin level (≤10g/dl.) demonstrated a 1.85-fold mortality risk
compared with patients a value >12 g/dl. (95% CI=1.40-2.44). An interval between external and
intra sanitary radiation >28 days was associated with 2.28-fold mortality risk compared with a
duration of <1 day (95% CI= 1.40-2.44). The fractionation 2 faction was associated with 0.25-
fold mortality risk compared with 1 fraction (95% CI=0.07-0.96) (Pomros et al., 2007).

(Chen et al., 1999) conducted a retrospective analysis to estimate the influence of histological
type on the survival rate of cervical cancer patients in Taiwan. They employed Kaplan–Meier
method, and Cox’s proportional hazards regression analysis and the result of the analysis showed
the 5-year survival rate was lower for patients with adeno carcinoma than for patients with
squamous cell carcinoma (66.5 vs. 74.0%, P= 0.0009). The 5-year survival rates for FIGO stages
I, II, III, and IV squamous cell carcinoma were 81.3, 75.2, 42.7, and 26.1%, respectively, while
for adenocarcinoma they were 75.9, 62.9, 29.2, and 0%, respectively. The difference in survival
rates between squamous cell carcinomand adeno carcinoma was found mainly in stage I (P=
0.0039) and stage II (P= 0.0103), where radiotherapy was used as the primary treatment.

A study conducted by (Intaraphet et al., 2013) in Chiang Mai University on Prognostic Impact of
Histology in Patients with Cervical cancer and the result showed histological type was the most
significant predicators on the survival. Overall, five-year survival was 60.0%, 54.7%, and 48.4%
in patients with Squalors Cell Carcinoma, Adenoma carcinoma and Small Cell Neuron endocrine

13
Carcinoma, respectively. After adjusting for other clinical and pathological factors, patients with
SNEC and ADC had higher risk of cancer-related death compared with SCC patients (HR 2.6;
95% CI, 1.9-3.5 and HR 1.3; 95% CI, 1.1-1.5, respectively). Patients with SNEC were younger
and had higher risk of cancer-related death in both early and advanced stages compared with
SCC patients (HR 4.9; 95% CI, 2.7-9.1 and HR 2.5; 95% CI, 1.7-3.5, respectively). Those with
advanced-stage ADC had a greater risk of cancer-related death (HR 1.4; 95% CI, 1.2-1.7)
compared with those with advanced-stage SCC, while no significant difference was observed in
patients with early stage lesions.

A retrospective study conducted by (Bruno, 1994) in University of North Florida for the purpose
of estimating the survival of cervical cancer patients and the result shows histological type have
prognostic value on the survival of cervical cancer patients. Another study conducted in U.S on
Prognostic model for survival in patients with early stage cervical cancer and the Cox regression
model showed that tumor size, histological type, and lymph node metastasis were independently
associated with the survival of cervical cancer patients (Biewenga et al., 2011).

A hospital-based retrospective study from Visakhapatnam City, Andhra Pradesh conducted by

(Kumari et al., 2010) confirmed that staging, grade of cancer and histological type of cancer was
statistically significant predicators on survival of cervical cancer patients. The Cox regression
model showed For Stage IA, IB, IIA, IIB, IIIB and IVA overall survival were 100%,94%,
94%,81%,42% and 33% and disease free survival were 100%, 87%, 70%,61%,55% and 33%.
The observed survival of patients for grade I is 89%, grade II is 88%, and grade III is 89% and
the disease free survival of patients with grade I is 75% , grade II is 67% , grade III is 54%. OS
and DFS for pathology were 89% and 85% for SCC, and 65% and 70% for ASC.

(Nuranna et al., 2014) conducted a retrospective cohort study which enrolled cervical cancer
patients treated at Cipto Mangunkusumo Hospital, Jakarta. This study revealed that stage III and
IV had lower survival probability (HR 3.27). (Kaverappa et al., 2015a) in India also found that
staging (p = 0.001) are the most significant predicators on the survival. A retrospective hospital-
based study conducted in Nairobi, Kenya on survival of patients with cancer of the cervix and
the result showed the cumulative proportion surviving at the end of the study interval was 0.67 at
stage I, 0.36 at stage II, 0.15 at stage III and 0 at stage IV (Mutai et al., 2013).

14
Another study conducted by (Mascarello et al., 2013) in Brazil showed that women with stages
III and IV at diagnosis showed an increased risk of 4.33 (95%CI: 3.00-6.24) and 15.40 (95%CI:
9.72-24.39), respectively, for lower survival when compared to stage I.

2.3. Cox proportional hazards versus parametric models

A review of literature on survival analysis used in different journals reveals that the Cox
proportional hazard model is the most widely used way of analyzing survival data in clinical
research. Researchers in medical sciences often tend to prefer semi-parametric instead of
parametric models because of fewer assumptions but under certain circumstances, parametric
models give more precise estimates. The main drawback of parametric models is the need to
specify the distribution that most appropriately reflects that of the actual survival times. The
appropriate use of these models offers the advantage of being slightly more efficient, they yield
more precise estimates (with smaller standard error) and to estimate the unknown parameters in
parametric model we often use maximum likelihood procedures and its interpretations are
familiar for researchers (Kleinbaum and Klein, 2012).

The performance between Cox PH and parametric model have been done in the survival of
patients with cancer. (Pourhoseingholi et al., 2007) compared Cox regression and parametric
Models (exponential, weibull and log-normal) in patients with Gastric Carcinoma in Taleghani
hospital, Tehran from February 2003 through January 2007. They used AIC and standardized of
parameter estimates to compare the efficiency of models. In this study the proportional hazards
assumption found to be hold and they reported both Cox PH model and Exponential models are
fitted well in multivariate analysis. Although it seems that there may not be a single model that is
substantially better than others, in univariate analysis the data strongly supported the log normal
regression among parametric models and it can be lead to more precise results as an alternative
to Cox. Similarly, (Moghimi-Dehkordi et al., 2008) compared Cox regression and Parametric
Models (exponential, weibull and log-normal) in patients with stomach cancer in southern Iran.
They used AIC to compare the performance of Cox regression and Parametric Models in the
analysis of stomach cancer data.

The proportional hazards assumption found to be holding and the result showed that the Hazard
Ratio in Cox model and parametric ones are approximately similar, according to AIC; the
Weibull, Exponential models, log- normal model are the most favorable for survival analysis.

15
 CHAPTER THREE

3. DATA AND METHODOLOGY

3.1. Study area

Based on the data obtained from Black Lion Hospital which in Addis Ababa city, the capital of
Ethiopia. Black Lion Hospital is a teaching, central tertiary generalized referral hospital with
approximately 800 inpatients beds. It is the largest and best known public hospital which was
built in the early 1960’s.

The Black Lion Cancer treatment Center was established 20 years ago by Dr. Bogale Solomon
who was at the time the only radiation and medical oncologist in the country. Black Lion
Hospital aspires to become a center of excellence in the diagnosis, treatment and care of patients
with cancer. With the support of Ethiopia’s governmental institutions, None governmental
organizations and international partners, including INCTR, the hospital is hoping to develop a
comprehensive cancer care program, including cancer registry, early detection, prevention,
standard treatment and palliative care.

3.2. Data
The target population of this study was being patients with cervical cancer at black lion hospital,
Addis Ababa was enrolled from December 2014 to January 2017 time period in oncology center.
In this retrospective cohort study the data was employ all cervical cancer patients, diagnosed in
between 2014-2017 and collect the data by reviewing follow-up charts of patients by using
standardized structured questionnaire.

3.3. Inclusion and exclusion criteria

This study considers all cervical cancer patients who were diagnosed and enrolled in BLH during
the required time period (2014-2016) except those patients who have incomplete charts regarding
to important variables, and patients who registered during the required period but their diagnosis
is prior to that, for patients whose follow up time is less than two month was excluded from the
study.

16
3.4. Variable of the study
3.4.1 Dependent variable
The dependent variable (Y) is the survival time of cervical cancer patients, the length of time
from diagnosis start date until the date of death/censored measured in months; survival status
(alive or censored and dead) were used as the dependent variables.

3.4.2 The independent variables

 Age at diagnosis
 Religion of patients
 Place of residence
 Parity (number of live birth)
 FIGO staging of the cervical cancer
 Histological types of cancer
 Histological grade cancer
 Presence of diabetics
 Oral contraceptive
 HIV status of the patients
 Presence of hypertension

17
3.5. Methods of statistical analysis
3.5.1. Survival analysis
Survival analysis is a statistical method for data analysis where the outcome variable of interest
is the time to the occurrence of an event. The event can be death, occurrence of disease, married,
divorce etc. Hence, survival analysis is also referred to as "time to event analysis", which is
applied in a number of applied fields, such as medicine, public health, social science, and
engineering etc. In medical science, time to event can be time until recurrence in a cancer study,
time to death, or time until infection(Lee and Wang, 2003).

Survival time is a length of time that is measured from time origin to the time the event of
interest occurred. Hence, survival data often consists of a response variable that measures the
duration of time until a specified event occurs and a set of independent variables thought to be
associated with the event-time variable. The specific difficulties in survival analysis arise largely
from the fact that only some individuals have experienced the event and other individuals have
not had the event in the end of study and thus their actual survival times are unknown. This leads
to the concept of censoring.

Censoring occurred when we have some information about individual survival time, but we do
not know the survival time exactly. There are three types of censoring: right censoring, left
censoring, and interval censoring. Right censoring is said to occur if the event occurs after the
observed survival time. Right censoring is very common in survival time data, but left censoring
is fairly rare the term "censoring" was be used in this thesis to mean in all instances "right
censoring". Censoring can also occur if we observe the presence of a condition but do not know
where it began. In this case we call it left censoring, and the actual survival time is less than the
observed censoring time. If an individual is known to have experienced an event within an
interval of time but the actual survival time is not known, we have interval censoring. The actual
occurrence time of event is known within an interval of time.

18
3.5.2. Survival time distribution
Let T be a random variable denoting the survival time. The distribution of survival times is
characterized by any of three functions: the survival function, the probability density function or
the hazard function.

These three functions give mathematically equivalent specification of the distributions of the
survival time T. If one of them is known, the other two are determined. The survival function is
most useful for comparing the survival progress of two or more groups. The hazard function
gives a more useful description of the risk of failure at any time point.

3.5.2.1. Survivor Function

The survivor function S(t ); is the probability that the survival time of a randomly selected subject
is greater than some specified time t or the probability of an individual being event-free beyond
timet . In order to find the survival function, suppose T be random variable associated with the
survival times, t be the observed value of the random variable T and f (t ) be the underlying
probability density function of the survival time t . The cumulative distribution function F (t)
represents the probability that an individual selected at random will have a survival time less
than or equal to the specified valuet . Thus, the cumulative distribution function and the survivor
function are given by:

t
F ( t )=P ( T ≤ t )=∫ f ( u ) du , t ≥ 0
0

S ( t )=P (T >t )=1 − F ( t ) , t ≥ 0 (3.1) the relationship between

S(t ) and f (t) is given as

d d
f ( t )= ( 1 − S ( t ) )=− S ( t ) , t ≥ 0
dt dt

3.5.2.2. Hazard function

The hazard function is generally denoted by ℎ ( t )and can be used to express the risk or hazard of
death at timet . It is obtained from the probability that an individual dies in an infinitesimally
small interval (t , ∆ t) given that the individual has survived up to time t i.e. P {t ≤ T < ∆ t∨T ≥ t }.

19
The hazard function is also known as the instantaneous death rate, force of mortality, conditional
mortality rate and hazard rate as it measures the conditional probability of the occurrence of
death per unit time. Hence the hazard function is given as:

P [ t ≤T <t+ ∆ t /T ≥ t ]
h ( t )= lim (3.2)
∆ t →0 ∆t

The hazard function varies from zero indicating no risk to infinity referring the certainty of
failure at that instant. In contrast to the survivor function, which focuses on surviving or not
failing, the hazard function focuses on failing that is the event occurring. Thus, in a way, survival
function and hazard function are complementary to each other. Another function called
cumulative hazard function which measures the total amount of risk that have been accumulated
up to time t can also be used to describe the survival experience.

There is a clearly defined relationship between S ( t )and ℎ ( t )which is given by the formula.

f (t ) f (t) −d
ℎ ( t )= = = lnS ( t ) (3.3)
1− F (t ) s (t) dt

[ ]
t
S ( t )=exp −∫ ℎ [ u ] du =exp ( − H (t) ) , t ≥ 0(3.4)
0

Where H ( t ) =∫ ℎ(u)du the cumulative hazard function, which can be obtained from
0

H ( t ) =− log ( S(t) ) (3.5)

The probability density function of T can be written as

f ( t )=ℎ ( t ) S ( t ) (3.6)

3.5.3. Non-parametric methods

Non-parametric methods require no assumptions about the shape of the hazard function and the
distribution of the survival time. This method is used to estimate survival function and to
compare the survival experience of two or more groups. The Kaplan-Meier estimator is used to
estimate the survival function and log-rank test used to compare survival distribution two or
more groups.

20
3.5.3.1. Kaplan-Meier estimator of the survival function
The Kaplan-Meier estimator proposed by Kaplan and Meier (1958) is the standard non
parametric estimator of the survival function S(t ). Which is also called the product-limit
estimator incorporates information from all observations available, both censored and
uncensored, by considering any point in time as series of steps defined by the observed survival
and censored times (Kaplan and Meier, 1958).

Suppose t 1 , t 2 , …, t n be the survival times of n independent observations andt 1 ≤ t 2 ≤ , …t m , m≤ n be

the m distinct ordered death times. Then the Kaplan-Meier estimator of the survivorship function
(or survival probability) at timet , S ( t )= p(T >t) is defined as:

Ŝ ( t )=∏
t j ≤t
n j− d j
dj jt ≤t
[ ]
=∏ 1 −
dj
nj
(3.7)

Where, n jis the number of individuals who are at risk of dying at timet j, j=1 ,2 , … mwith ^S(t)=1
for t< t1 and d jis the number of individuals who failed (died) at time t j . The variance of the K-M
survival estimator which is also known as the Greenwood’s formula is given by:

dj
var ( Ŝ ( t ) )=(Ŝ(t ))2 ∑ (3.8)
n j (n j −d j)

3.5.4. Comparison of Survivorship Functions

When comparing groups of subjects, it is always a good idea to begin with a graphical display of
the data in each group. The simplest way of comparing the survival times obtained from two or
more groups is to plot the Kaplan-Meier curves for these groups on the same graph. The figure in
general shows if the pattern of one survivorship function lies above another, meaning that the
group defined by the upper curve lived longer, or had a more favorable survival experience, than
the group defined by the lower curve. However, this graph does not allow us to say whether or
not there is a real difference between the groups. Assessing whether or not there is a real
difference between groups can only be done by utilizing statistical tests. There are a number of
methods that can be used to test equality of the survival functions in different groups. One

21
commonly used non-parametric tests for comparison of two or more survival distributions is the
log-rank test(Robins et al., 1986).

Let t 1 ≤ t 2 ≤ , …t m be the m distinct ordered death times across two groups. Suppose that d jfailures
occur at t jand that n jsubjects are at risk just prior tot j ( j=1 ,2 , … , m). Let d ij and nij be the
corresponding numbers in groupi(i=1 , 2). Then the log-rank test compares the observed
number of deaths with the expected number of deaths for group i. Consider the null
hypothesis: S(1)=S(2) i.e. there is no difference between survival curves in two groups. Given
n jand d jthe random variable d 1 j has the hyper geometric distribution

( )( )
dj n j− d j

d1 j n 1 j −d 1j

( ) nj
n1 j

Under the null hypothesis, the probability of experiencing an event at t jdoes not depend on the
dj
group, i.e. the probability of experiencing an event at t j is . So that the expected number of
nj
deaths in group one is

n1 j d j
E ( d 1 j ) =e^ 1 j= ,is the expected number of individuals who experienced an event at time t j in
nj
group 1.

The test statistic is given by the difference between the total observed and expected number of
deaths in group one

m
U L =∑ ( d1 j − v^ 1 j )(3.9)
j=1

Since d 1 j has the hyper geometric distribution, the variance of d 1 j given by

n 1 j n2 j d j (n −d )
^v 1 j=Var ( d 1 j ) = 2
j j
(3.10)
n (n j − 1)
j

^v 1 jis the variance of the number of event occurred at time t jin group 1, d 1 j is the observed
number of failure (event occur) at time t jin group 1, n1 j is the number of individuals at risk of

22
event occur in the first group just before timet j , n2 j is the number of individuals at risk in the
second group just before timet j, d jis the total number of events occurred at t j, n j is the total
number of individuals at risk before timet j.

So that the variance of U L is given by

m
Var ( U L ) =∑ v^ 1 j =V L
j =1

Under the null hypothesis, statistic (3.9) has an approximate normal distribution with zero mean
2
UL 2
and varianceV L. This then follows x.
VL 1

The general form of the test statistic to test the equality of survival curves which can also be used
by several alternatives to the log-rank test, such as the Wilcox on test, may be defined as follows:

∑ w j (d 1 j − e ¿1 j)
Q= j=1 m

∑ w 2j v ¿1 j
j=1

j Is the number of rank-ordered failure times (event times).

Where: w j are weights whose values depend on the specific test?

3.5.5. Regression Models for Survival Data

The most popular model in survival data are Cox regression model and parametric PH model,
which is described as follow.

3.5.5.1. Cox Proportional Hazards Regression Model

Cox (1972) proposed a semi-parametric hazards model for the survival data to see the effect of
explanatory variables on the hazard function (Schoenfeld, 1982, Ruppert et al., 2003). The Cox
proportional hazards model is given by:

ℎ ( t ; x )=ℎ o ( t ) exp ( β 1 x 1 + β 2 x 2+ …+ β p x p ) =ℎo ¿

Where ℎ o ( t ) is called the baseline hazard function, which is the hazard function for an individual
for whom all the variables included in the model are zero, x=(x 1 , x 2 , … , x p)' is the values of the

23
vector of explanatory variables for a particular individual, and β ' =β 1 , β 2 , … , β p is a vector of
regression coefficients.

This model, also known as the Cox regression model, makes no assumptions about the form of
ℎ o ( t )(non-parametric part of model) but assumes parametric form for the effect of the predictors
on the hazard (parametric part of model). The model is therefore referred to as a semi-parametric
model.

The measure of effect is called hazard ratio. The hazard ratio of two individuals with different
covariates x 1and x 2 is
,
exp ⁡(X 1 β)
^ =exp ( ( X 1 − X 2 ) β ) (3.12)
' '
HR= ,
exp ⁡(X 2 β)

This hazard ratio is time-independent, which is why this is called the proportional hazards model.

3.5.5.1.1. Assumption of Cox proportional hazard model

1) The baseline hazard ℎ o ( t ) depends ont , but not the covariates, x 1 , … , x p.
2) The hazard ratio, i.e., e (β¿¿ ' x)¿depends on the covariates, x=(x 1 , x 2 , … , x p)' , but not on
time t .
3) The covariates x i do not depend on timet .

Assumption (2) is what led us to call this a proportional hazards model. To express this
Mathematically, consider two distinct values of the covariate x , say x 1and x 2 in equation (3.12)

HR=exp ( ( X 1 − X 2 ) β )
^ ' '

This equation indicates that the hazard ratio is independent of time t . This shows that the ratio of
the hazard functions for two individuals with different covariate values does not vary with time.

3.5.5.2. Estimation of Cox Regression Model

In Cox proportional hazards model we can estimate the vector of parameters β without having
any assumptions about the baseline hazard ℎ o ( t ) . As a consequence, this model is more flexible
and an estimate of the parameters can be obtained easily.

24
Suppose the survival data based on n independent observations are denoted by the triplet (t i,δ i , x i
) i =1, 2..., n
Where
t i Is the survival time for the ith individual?
δ iIs an indicator of censoring for the ith individual? Given by 0 for censored and 1 for
event experience.
Xi = (Xi1, Xi2.......Xim)' is a column vector of m covariates for individual i.
The full likelihood function for right censored data can be constructed as:
n
L ( β ) =∏ ℎ ( ti , X i , β )δi S ( ti , X i, β ) (3.13)
i=1

Whereℎ(ti , X i , β)=ℎ0 ( ti)e β ' Xi is the hazard function for the ith individual.

( )
S ( ti , X i, β ) = [ so ( ti ) ]exp β is the survival function for the ith individual.
' Xi

It follows that:
n
L ( β ) =∏ [ ℎ0 ( ti ) e β Xi ] [ s o ( ti ) ]
' δi exp ( β )
' Xi

( 3.14 )
i=1

The full maximum likelihood estimator of β can be obtained by differentiating the right hand
side of equation (3.14) with respect to the components of β and the base line hazardℎ0 ( t).
This implies that unless we explicitly specify the base line hazard , ℎ0 (t ), we cannot obtain the
maximum likelihood estimators for the full likelihood. To avoid the specification of the base line
hazard, Cox (1972) proposed a partial likelihood approach that treats the baseline hazard as a
nuisance parameter and removes it from the estimating equation (Blakely and Cox, 1972).

3.5.5.2.1. Partial Likelihood Estimation

Instead of constructing a full likelihood, we consider the probability that an individual
experiences an event at time t igiven that an event occurred at that time.

25
Suppose that data are available for n individuals, amongst them there are r distinct failure times
and n −r right-censored survival times, and assume that only one individual was died at each
ordered failure time, so that there are no ties. The r ordered failure times will be denoted by
t(1)<t(2)<….< t(r), so that t (i)is the ith ordered failure time.
The set of individuals who are at risk at time t (i)is the ith ordered failure (experiences an event)
time, and denoted by R(t (i )). And let x ibe the vector of explanatory variables for an individual
who experiences an event att i.
The partial likelihood function is derived by taking the product of the conditional probability of a
failure at timet (i), given the number of individuals who are at risk of experiencing the event at
timet (i).
Then the probability that the jth individual will experience an event at time t (i) is given by:

exp ( β' X ( i ) )
L p ( β )= ( 3.15 )
∑ exp ( β Xj )
'

j ∈R ( t ( i ) )

Where, the summation in the denominator is over all individuals in the risk set. Thus the partial
likelihood is the product over all event time t (i)for i=1 , 2 ,… , r of the conditional probability
(3.15) to give the partial likelihood function and can be expressed in the form:

[ exp ( β X ( i ) )

]
r '
L Lp ( β ) = ∏ ( 3.16 )
i=1 ∑ exp ( β Xj )
'

j ∈ R (t ( i ) )

The product is over the r distinct ordered survival times.

The corresponding log-partial likelihood function is given by:

i=1 {
log L p ( β )=∑ β' X ( i ) − log
[ ∑
j ∈R (t (i ))
exp ⁡( β ' Xj) (3.17)
]}
The partial likelihood derived above is valid when there are no ties in the data set. But in most
real situations tied survival times are more likely to occur. In addition to the possibility of more
than one experience an event at a time, there might also be more than one censored observations

26
at a time of event. To handle this real-world fact, partial likelihood algorithms have been adopted
to handle ties.
There are three approaches commonly used to estimate regression parameters when there are
ties. These are Efron (1977), Breslow’s approximation and Cox (1972) approximations. The
most popular and easy approach is Breslow’s approximation (Breslow, 1974).

The Breslow approximation is proposed by Breslow and Peto by modifying the partial likelihood
takes the following form:
k
exp( β ¿ ¿ ' s i)
LB ( β )=∏
¿
i=1 { ∑ exp ( β ' x j ) }
di
(3.18)
jϵR (t i )

Whered i is the number of deaths that occurred sequentially at time t i and siis the vector of sums
of each of the m covariates for those individuals who die at the ith death time?

3.5.5.3. Model adequacy for Cox PH model

After a model has been fitted, the adequacy of the fitted model needs to be assessed. The model
checking procedures below are based on residuals. In linear regression methods, residuals are
defined as the difference between the observed and predicted values of the dependent variable.
However, when censored observations are present and partial likely hood function is used in the
Cox PH model, the usual concept of residual is not applicable. A number of residuals have been
proposed for use in connection with the Cox PH model. We have describing three major
residuals in the Cox model: the Cox-Snell residual, the martingale residual, and the Schoenfeld
residual. Then we talk about influence assessment.

3.5.5.3.1. Cox-Snell residuals

The Cox-Snell residual is given by Cox and Snell (Cox and Snell, 1968). The Cox-Snell residual
for the ith individual with observed survival time t i is defined as:

rc i=exp ⁡¿) ^ ^ (t i) = − log S^ (t )

H o (t i ) = H (3.19)
i i i

Where ^
H o (t i) is an estimate of the baseline cumulative hazard function at time t i, the observed
H i(t i) = − log S^ i (t i ),
survival time of that individual. The Cox-Snell residual,rc i, is the value of ^

27
 H i(t i) and ^Si (t i) are the estimated values of the cumulative hazard and survivor functions
where ^
of the ith individual at t i.

If the model was well fitted, the value ^Si (t i) would have similar properties to those of Si (t i) . So
rc i=− log ^Si (t i ) will have a unit exponential distribution, and a test of this assumption provides a
test of model adequacy.

Therefore, we use a plot of H (rc i) versus rc i to check the fit of the model. This gives straight line
with unit slope and zero intercept if the fitted model is correct. Note the Cox-Snell residuals will
not be symmetrically distributed about zero and cannot be negative. This residual is also used to
test overall goodness of fit test.

3.5.5.3.2. Martingale Residuals

The martingale residual for the ith individual is given as:

r mi=δ i −r ci (3.20)

Whereδ i=1 for uncensored observation andδ i=0 for censored observation and the martingale
residuals take values between negative infinity and unity. They have a skewed distribution with
mean zero (Andersen and Gill, 1982). The deviance residuals are a normalized transform of the
martingale residuals (Therneau et al., 1990). They also have a mean of zero but are
approximately symmetrically distributed about zero when the fitted model is appropriate. The
plot of the deviance residuals against the covariates can be obtained. Any unusual patterns may
suggest features of the data that have not been adequately fitted for the model. Very large or very
small values suggest that the observation may be an outlier in need of special attention.

3.5.5.3.3. Schoenfeld residuals

All the above residuals are residuals for each individual. We will describe covariate wise
residuals: Schoenfeld residuals (Schoenfeld, 1982).This is that there is not a single value of the
residual for each individual, but a set of values, one for each explanatory variable included in the
fitted Cox regression model.

The ith partial or Schoenfeld residual for x i, the ith explanatory variable in the model is given by:

r pji = δ i{ x ji -α^ ji }, (3.21)

28
Where x ji is the value of the jth explanatory variable, j=1, 2… p, for the i th individual in the study,
and if individuals in the risk set are indexed by l, then:

∑ X ji exp ⁡( ^β X 1)
l ∈R (t i )
α^ ji =
∑ exp ⁡( ^β X 1 )
lϵR (t i )

And R(t i ) is the set of all individuals at risk at time oft i.

Schoenfeld residuals are also used to check the proportionality of the covariates over time that is
to check the validity of the proportional hazards assumption. If the model fits well then the
residuals are randomly distributed without any systematic pattern around the zero line, reference
line.

3.5.5.4. Testing the proportional hazards assumption

In fitting the Cox model, it is assumed that the hazard ratio between two subjects with different
covariates information is constant over time, i.e., proportionality of hazards. To assess the
proportional hazards assumption we examine different test and graphical techniques have been
developed to check whether the proportional hazards assumption holds.

Cox (1972) proposed a way of checking the proportional hazards assumption by introducing a
constructed time dependent covariate into the model. This is done by specifying a form for the
time by predictor interaction and testing the coefficients of such interactions for significance .i.e.,
adds interaction terms involving time to the model and test for their significance. The Cox model
extended for time-dependent variables can be specified as follows:

p p
h(t,x)=ℎ0 (t)exp(∑ β i X i+∑ γ i X i gi(t)) (3.22)
i=1 i=1

Where, gi(t) is some nonzero function of time corresponding to X i .

To test H0: γ i= 0, i.e., whether PH is adequate, we can use Wald and/or Likelihood Ratio tests. If
the null hypothesis of proportional hazards, i.e. H0: γ = 0 is not rejected, the proportional hazards
assumption is satisfied i.e. β i ' s are not time varying coefficients.

29
A plot of the scaled Schoenfeld residuals as a function of time is used to check the
proportionality assumption for each covariate. In a ‘well-behaved’ model the Schoenfeld
residuals are scattered around zero and a regression line fitted to the residuals has a slope of
approximately zero. The idea behind this test is that if the proportional hazards assumption holds
for a particular covariate, then the Schoenfeld residuals for that covariate will not be related to
survival time.

3.5.6. Strategies for analysis of non proportional data

Suppose that statistic tests or other diagnostic techniques give strong evidence of non
proportionality for one or more covariates. To deal with this we describe two popular methods:
stratified Cox model and Cox regression model with time-dependent variables which are
particularly simple and can be done using available software.

3.5.6.1. Stratified Cox model

One method that we can use is the stratified Cox model, which stratifies on the predictors not
satisfying the PH assumption. The data are stratified into subgroups and the model is applied for
each stratum. The model is given by

ℎig ( t ) =ℎog (t)exp( β ¿ ¿ ' x i g )(3.23)¿

Where grepresents the stratum.

Note that the hazards are non-proportional because the baseline hazards may be different
between strata. The coefficients are assumed to be the same for each stratum g. The partial
likelihood function is simply the product of the partial likelihoods in eachstratum. A drawback of
this approach is that we cannot identify the effect of this stratified predictor. This technique is
most useful when the covariate with non-proportionality is categorical and not of direct interest.

3.5.6.2. Cox regression model with time-dependent variables

Until now we have assumed that the values of all covariates did not change over the period of
observation. However, the values of covariates may change over time t. Such a covariate is
called a time-dependent covariate. The second method to consider is to model non

30
proportionality by time-dependent covariates. The violations of PH assumptions are equivalent to
interactions between covariates and time. That is, the PH model assumes that the effect of each
covariate is the same at all points in time. If the effect of a variable varies with time, the PH
assumption is violated for that variable. To model a time-dependent effect, one can create a time-
dependent covariate X (t), and then βX ( t )=βX ∗ g ( t ) . g(t) is a function of t, logt or Heaviside
function, etc.

3.5.7. Parametric model

The Cox PH model is the most common way of analyzing prognostic factors in clinical data.
This is probably due to the fact that this model allows us to estimate and make inference about
the parameters without assuming any distribution for the survival time. However, when the
proportional hazards assumption is not tenable, these models will not be suitable. In this section,
we will introduce parametric model, in which specific probability distribution is assumed for the
survival times.

The parametric proportional hazards model is the parametric versions of the Cox proportional
hazards model. It is given with the similar form to the Cox PH models. The key difference
between the two kinds of models is that the baseline hazard function is assumed to follow a
specific distribution when a fully parametric PH model is fitted to the data, whereas the Cox
model has no such constraint. The coefficients are estimated by partial likelihood in Cox model
but maximum likelihood in parametric PH model. Other than this, the two types of models are
equivalent. Hazard ratios have the same interpretation and proportionality of hazards is still
assumed. In this study the following common parametric models are considered.

3.5.7.1. Weibull PH model

Suppose that survival times are assumed to have a Weibull distribution with scale parameter λ
and shape parameter γ, so the survival and hazard function of a W (λ,γ) distribution are given by

S(t ) = exp [ − ( λ t )γ ] , ℎ ( t )=λγ ( t )γ −1 (3.24)

With λ,γ > 0. The hazard rate increases when γ> 1 and decreases when γ < 1 as time goes on.
When γ = 1, the hazard rate remains constant, which is the special exponential case.

31
Under the Weibull PH model, the hazard function of a particular patient with covariates
'
x=(x 1 , x 2 , … , x p) is given by

ℎ ( t ; x )= λγ ( t ) γ −1 exp ( β 1 x 1 + β 2 x 2+ …+ β p x p ) =λγ ( t )γ − 1 e(β ¿¿' x)(3.25 )¿

We can see that the survival time of this patient has the Weibull distribution with scale parameter
λ and shape parameter γ: Therefore the Weibull family with fixed γ possesses PH property.

This shows that the effects of the explanatory variables in the model alter the scale parameter of
the distribution, while the shape parameter remains constant.

From equation (3.25), the corresponding survival function is given by

S ( t ; x )=exp ¿ ¿
After a transformation of the survival function for a Weibull distribution, we can obtain the
formula:

log { − logS (t ) }=log λ+γ logt (3.27)

The plot of log { − logS (t) } versus log ⁡(t)should give approximately a straight line if the
Weibulldistribution assumption is reasonable. The intercept and slope of the line will be rough
estimate of log λ and γ respectively. If the two lines for two groups in this plot are essentially
parallel, this means that the proportional hazards model is valid. Furthermore, if the straight line
has a slope nearly one, the simpler exponential distribution is reasonable.

Another approach to assess the suitability of a parametric model is to estimate the hazard
function using the non-parametric method. If the hazard function were reasonably constant over
time, this would indicate that the exponential distribution might be appropriate. If the hazard
function increased or decreased monotonically with increasing survival time, a Weibull
distribution might be considered.

3.5.7.2. Exponential PH model

The exponential PH model is a special case of the Weibull model when γ = 1. The hazardfunction
under this model is to assume that it is constant over time. The survival andhazard function are
written as

32
 S ( t )=exp ( − λt ) ,ℎ (t )= λ(3.28)

Under the exponential PH model, the hazard function of a particular patient is given by

( β¿¿' x)(3.29)¿
ℎ ( t ; x )= λ exp ( β 1 x 1+ β2 x 2+ …+ β p x p ) =λ e

In the other way, for an exponential distribution, there islogS ( t ) =− λt thus we can consider the
graph of logS ( t ) versust . This should be a line that goes through the origin if exponential
distribution is appropriate.

3.5.7.3. The Log Normal Regression Model

The log-normal model may take censored time dependent variable that allows the hazard rate to
increase and decrease (Aalen et al., 2008). The log-normal model assumes that ε N(0; 1). Let h(t)
be the hazard function of T for equation (3.29) when β = 0 i.e β 0=β 1=… β p=0.Then, it can be
shown that h(t) has the following functional form:

ℎ ( t )=
ϕ( δ )
log ( t )

(3.30)

[ 1− Φ( δ )]
log ( t )

( )
2 t
1 −t 2 1 −u
( )
Where, ϕ t = exp is the probability density function, andΦ ( t ) ∫ exp du is the
√2 π 2 −∞ √2 π 2
cumulative distribution function of the standard normal distribution. Then, the log-hazard
function of T at any covariate value X can be expressed as:

( )
t
=log ℎ0 ( t e − β x ) − β ' x
'

logℎ (3.31)
X

Obviously we no longer have a proportional hazards model. If the baseline hazard function is
desired, it can be obtained from equation (3.29) by setting x = 0. The survival function S(t/x) at
any covariate x can be expressed as:

S ( t ⎹ x ) =ϕ [ β∗0 + β ∗1 x 1+ …+ β ∗p x p − α log ( t ) ] (3.32)

1 β
Where,α = , β∗j = j forj=0 , 1.. … p, This the final survival model with intercept depending
δ δ
with t.

33
3.5.8. Parametric Regression Model assessment
Every step during model fitting uses the upcoming statistical procedures and later at the end we
checked all the assumptions needed for the model. One of the statistical procedures that are used
to fit the final model is: Deviance (D) is twice the difference of the likelihoods for the full model
(with higher covariates) and the reduced model (with lower covariate/s) (Hosmer and
Lemeshow, 1989)of adding a new independent variable to a parametric regression model is
tested by subtracting the deviance of the model with the new parameter from the deviance of the
model without the new parameter, the difference is then tested against a chi-square distribution
with degrees of freedom equal to the difference between the degrees of freedom of the old and
new models.

D= {( β p ) − L ( β q ) } (3.33)
Where, p and q are number of covariates such that, p>q .
Finally, those factors significant at 5% level of significance included in the final multivariate
parametric regression model.

3.5.9. Comparison of Cox PH and Parametric Models

Different models can be compared on the basis of the variables selected and their coefficients in
each model, Comparison of Model Estimate and on AIC used in this research.

3.5.9.1. Comparison of Model Estimate

If the models being compared have a similar set of covariates that have entered in the respective
final models, it can be interpreted as all models are equally good or bad as far as the
identification of important covariates associated with the outcome.

The precision of the regression coefficients is another criterion that can be used to compare
different models. The smaller the standard error, the more precise an estimate is expected to be.
A model with more precise coefficients can be considered as a more precise model.

3.5.9.2. Comparison based on Akaike’s information criteria.

For the aim of comparison among parametric and semi parametric models we used Akaike
Information Criterion(AIC) and standardized of parameter estimates.AIC proposed by (Akaike,

34
1974)may also be used when comparing the variability of different parametric models. The AIC
of a model may be defined a

AIC=−2≪+2 ( c+ k +1 ) (3.34)

Where ¿ , c , k denotes the log-likelihood, number of covariates and the number of model-specific
ancillary parameters respectively. A lower value of AIC suggests a better model.

3.5.9.3. Ethical consideration

Ethical clearance was obtained from the ethical review committee of University of Gondar
College of natural and computational sciences. The names of the subjects were not extracted to
ensure privacy of patient information and confidentiality was maintained throughout the
data collection process and analysis. Approval and permission was also obtained from the
administrative officers of BLAK LION, referral hospitals.

35
 CHAPTER FOUR

4. RESULT AND DISCUSSION

This section presents the result of statistical analysis and discussions carried out to answer the
basic research questions and the objectives of the study. Data management and analysis was
done using SPSS and STATA statistical Software.

4. 1. Descriptive summaries and non-parametric analysis

From the total of 518 cervical cancer patients, the minimum age is 18 and the maximum age is
80. The mean age of the patients was 48.61 years with (SD=11.728). From the patients
considered the majority of women’s have more than four Childs. The summary statistics for the
categorical predicator variables such as, residence, marital status, religion, stage, grade, oral
contraceptive use, diabetic, hypertension and HIV are presented below.

The descriptive summary shows a death proportion seems lower for urban women’s (5.02%)
than for rural women’s (11.00%). The married group showed the highest percentage (10.04%)
with respect to death proportions than the other three groups and patients whose religion are
orthodox have highest percentage of death (9.27%) than the others religion groups. Stage III
patients have the highest death proportion (7.72%) as compared to the other groups while stage I
patients show the lowest death rate. The patient whose histological type has Squamous cell
carcinoma was the highest percentage of death (12.36%) than the other types and well differentiated
histological grade patients have highest death proportions (7.53%) than the other grades. A patient who
took oral contraceptive was the highest death proportions (9.27%) and patients who have diabetic
were lower death proportion (1.54%) than the patients who have no diabetics. The death
proportion of patients who have no hypertension was highest (12.55%) than the patients who
have hypertension and HIV negative patients have the highest proportion of death (10.62%) than
the other groups. All the results have been summarized in Table 1 below.

36
Table-1: Results of descriptive measures of categorical predicator variables, 2014-2017
Covariates Category Status

Censored (%) Death (%)

Residence of patients Urban 228(44.02) 26(5.02)
Rural 207(39.97) 57(11.00)
Religion of patients Muslim 151(29.15) 31(5.98)
Orthodox 243(46.91) 48(9.27)
Protestant 39(7.53) 4(0.77)
Catholic 2(0.39) 0(0.00)
Stage of cancer at diagnosis Stage I 34(6.56) 3(0.58)
Stage II 145(27.99) 14(2.70)
Stage III 176(33.98) 40(7.72)
Stage IV 80(15.44) 26(5.02)
Histological type of cancer Squamous cell carcinoma 250(48.26) 64(12.36)
Adenocarcinoma 129(24.90) 13(2.51)
Adenosquamous cell carcinoma 56(10.81) 6(1.16)
Others 0(0.00) 0(0.00)
Histological grade of cancer Well differentiated 117(22.59) 39(7.53)
Moderately differentiated 155(29.92) 25(4.83)
Poorly differentiated 163(31.47) 19(3.67)
Oral contraceptive use No 254(49.03) 35(6.76)
Yes 181(34.94) 48(9.27)
Diabetic status of patients No 406(78.38) 75(14.48)
Yes 29(5.60) 8(1.54)
Hypertension status No 390(75.29) 65(12.55)
Yes 45(8.69) 18(3.47)
HIV status of patients Negative 244(47.10) 55(10.62)
Positive 42(8.11) 15(2.90)
Unknown 149(28.76) 13(2.51)

Differences in all key variables were determined using log rank (χ2) test and assessed the
equality of survival functions for the different categorical variables. The null hypothesis to be
tested is that there is no difference between the probabilities of an event occurring at any time
37
point for each population. According to the test results residence, FIGO stage, histological type,
histological grade, OCP use, hypertension and HIV status were a statistically not equal in
experiencing the death event, whereas Marital status, religion and presence of diabetics are
statistically the same in experiencing the event death. The STATA result has been presented in
table 2 below.

Table-2: Results of log rank test for the categorical variables in BLH, 2014-2017
Variable Chi-square Pr>Ch-square

Religion 1.56 0.669

Presence of diabetics 0.66 0.417
Residence 11.28 0.0008
FIGO stage 9.72 0.0211
Histological type 8.02 0.0181
Histological grade 5.64 0.0591
Oral contraceptive use 7.16 0.0070
Presence of hypertension 9.56 0.0020
HIV status 13.45 0.0012

4.2 Cox proportional hazard model

The univariate Cox proportional hazards regressions models are fitted for every covariates as
shown in table 4.3 to check covariates affecting survival of patients with cervical cancer, before
proceeding to higher models. We considered including the predicators in the multivariate model
if the test for the Univariate analysis has a p-value less than or equal to 0.05. The result of log
rank and univariate Cox model identified similar significant predicators at 5% level.

Consequently, the significant variables for building a multivariate Cox model are age at first
diagnosis, place of residence, FIGO stage at diagnosis, histological type, histological grade, and
Oral contraceptive use, presence of hypertension co-morbidity and HIV status of the patients.
The hazard ratio, 95% CI and standard errors for each variable is given below in table 3.

38
Table-3 Results of univariate Cox analysis, BLH, 2014-2017.
Variables HR SE p-value 95% CI
Lower Upper
Age 1.024 0.0094 0.009 1.006 1.042
Religion 0.888 0.160 0.511 0.624 1.265
Residence 2.159 0.512 0.001 1.357 3.435
Parity 0.971 0.042 0.494 0.893 1.056
FIGO stage 1.519 0.212 0.003 1.155 1.997
Histological type 0.609 0.117 0.010 0.417 0.888
Histological grade 0.725 0.101 0.020 0.553 0.951
Oral contraceptive use 1.792 0.399 0.009 1.157 2.772
Presence of diabetics 1.348 0.502 0.422 0.649 2.799
Presence of hypertension 2.223 0.594 0.003 1.317 3.754
HIV status 0.337 0.099 0.022 0.562 0.956

The significant variables at 5% level were considered in the model. Among the predicator
variables considered for building multivariate Cox, the forward stepwise procedure picked up six
variables age at diagnosis, place of residence, FIGO stage, histological type, histological grade
and presence of hypertension. The multivariate Cox model based on this significant variable was
summarized in table 4 below.

Table-4: Results of multivariate Cox regression model, BLH, 2014-2017.

Variable Coef(β) Haz. Ratio Std. Err. P-value [95%Conf.Interval]

39
Age 0.028 1.028 0.009 0.003 1.009 1.048
Residence
1 0.706 2.027 0.490 0.003 1.262 3.256
FIGO stage
1 0.478 1.614 1.044 0.460 0.454 5.734
2 0.979 2.661 1.617 0.107 0.808 8.761
3 1.410 4.097 2.545 0.023 1.213 13.840
Histological type
1 -0.639 0.527 0.164 0.040 0.286 0.972
2 -0.768 0.464 0.201 0.075 0.199 1.081
Histological grade
1 -0.664 0.515 0.136 0.062 0.306 0.865
2 -0.810 0.445 0.127 0.005 0.253 0.779
1.hypertension 0.804 2.236 0.615 0.003 1.304 3.835

Adequacy of the fitted model that is the assumptions of proportional hazards and the goodness of
fit were assessed. We used the schoenfeld residuals to test the PH assumptions. The correlation
(ρ) between schoenfeld residuals and survival time for each covariate was presented in table 5
below.
Table-5: Test of proportional hazards assumption based on schoenfeld residuals BLH,
2014-2017
Variable Rho(ρ) Chi2 DF p-value

Age at diagnosis 0.13036 1.07 1 0.3008

Place of residence -0.02107 0.04 1 0.848
FIGO stage 0.10068 0.83 1 0.364
Histological type 0.08839 0.69 1 0.4065
Histological grade 0.03967 0.14 1 0.711
Presence of hypertension -0.09950 0.78 1 0.377
Global test 3.73 6 0.713

40
The results from table 5 indicate that all variables satisfied the PH assumption as the correlation
between schoenfeld residuals and survival time is not significant at 0.05 levels. The plot of
scaled schoenfeld residuals versus analysis time were also checks the PH assumption. The result
of plot of scaled schoenfeld residuals versus survival time in the annex 1 are more or less random
and LOESS smoothed curves have basically zero slope which is an indication of no evidence of
non proportionality.
The proportional hazard assumptions was also tested based on the (1og (-log (survival))) plot
versus log (survival time), which is called a log-cumulative hazard plot. The plot of (1og (-log
(survival))) plot versus log (survival time) were used to check the PH assumption for all the
categorical variables included in the fitted model (annex 1). The graphs for each of the
categorical variables display lines that appeared to be roughly parallel for place of residence and
presence of hypertension, thus proportional hazard assumption was met. There was an interaction
between FIGO stage, histological type and histological grade with time indicating possible
violation of PH assumption. However the overall Schoenfeld global test of the full model
satisfies the PH assumption (chi2 (6) = 3.73, Prob>chi2=0.713) as presented in table 4.5 above.
Plot of the cox-snell residuals was applied to test the overall fit of the model. In this method cox-
snell residuals were plotted against the cumulative hazard of cox-snell residuals as shown in
figure 1. The figure reveals that the overall fit of the Cox model is good. However there is little
evidence of a systematic deviation from the straight line at the right, thus the result of the graph
indicates the model fit the data well.

Figure-1: Cumulative hazard plot of the cox-snell residual for multivariate Cox PH model
BLH, 2014-2017
2
1.5
1
.5
0

0 .5 1 1.5 2
Cox-Snell residual

H Cox-Snell residual

41
4.3. Parametric proportional hazard model
Univariate PH model was applied in a similar manner as applied in a Cox PH model for
Exponential, Weibull and Log-normal PH models. The results of the univariate parametric PH
models are presented in table 6. In the three models variables significant at 5% level in the
univariate analysis were taken as candidate variables for their multivariable analysis.

Table-6: Results of univariate Weibull PH, Exponential and Log- normal PH models BLH,
2014-2017
Covariates Weibull PH Exponential PH Log-normal
HR SE P-value HR SE P-value HR SE P-value
Age 1.02 0.009 0.009 1.03 0.01 0.004 0.04 0.01 0.014
Residence 2.20 0.52 0.001 2.14 0.51 0.001 0.45 0.13 0.001
Religion 0.90 0.16 0.568 0.88 0.16 0.475 0.06 0.104 0.546
Parity 0.97 0.04 0.417 0.98 0.04 0.657 0.01 0.024 0.586
FIGO Stage 1.49 0.21 0.004 1.52 0.21 0.002 0.43 0.078 0.081
Histological type 0.61 0.12 0.011 0.59 0.01 0.008 0.28 0.100 0.003
Histological grade 0.73 0.09 0.020 0.68 0.09 0.006 0.17 0.079 0.031
OCP use 1.82 0.41 0.007 1.75 0.39 0.012 0.27 0.134 0.041
Diabetics 1.33 0.49 0.446 1.37 0.51 0.399 0.18 0.23 0.433
Hypertension 2.19 0.58 0.003 2.11 0.56 0.005 0.53 0.17 0.001
HIV status 0.74 0.09 0.024 0.73 0.18 0.019 0.18 0.08 0.016

From table 6 the Exponential PH, Weibull PH and log normal PH model picked up the same
variables namely age, residence, FIGO stage, histological type, histological grade and presence
of hypertension (HTN) as selected by Cox PH model. The hazard ratio and the corresponding
95% CI with standard error for the given models are given in table 7.
More or less the given models had the same HR with almost identical standard errors in
estimating the significant variables at 95% CI.

Table-7: Results of multivariate Exponential PH model, Weibull PH and log normal PH

models BLH, 2014-2017.
Covariates Weibull PH Exponential PH Log-normal

42
 HR SE P-value HR SE P-value coef SE P-value
Age 1.03 0.01 0.003 1.03 0.01 0.004 -0.02 0.005 0.017
Residence 2.04 0.49 0.008 1.89 0.45 0.007 -0.39 0.13 0.003
FIGO stage 1.57 0.22 0.001 1.53 0.21 0.002 -0.22 0.08 0.006
Histological type 0.64 0.13 0.019 0.63 0.12 0.017 0.25 0.10 0.011
Histological grade 0.65 0.06 0.002 0.63 0.18 0.001 0.23 0.08 0.005
Presence of HTN 2.15 0.59 0.005 2.03 0.55 0.009 -0.49 0.17 0.003

The three parametric survival model Weibull, Exponential and Log-normal models HR, SE and
P-value are obtained in the above.

4.4. Interpretation of the Results

Residence: Among cervical cancer patients the instantaneous risk of death for urban place of
residence is 2.04 times the instantaneous risk of death for rural place of residence, after keeping
all other covariates at some constant level. This does suggest urban place of residence patients
have excess risk of instantaneous death than their counterpart rural place of residence.

FIGO stage: The hazard ratio in Table 7 shows that among cervical cancer patients the
instantaneous risk of death for FIGO stage three is 1.57 times the instantaneous risk of death
for FIGO stage one, keeping all other covariates at some constant level. Similarly, among
cervical cancer patients, the instantaneous risk of death for FIGO stage four is 2.01 times the
instantaneous risk of death for FIGO stage of the reference group, keeping all other covariates at
some constant level.

Histological type: Among cervical cancer patients, the instantaneous risk of death for
adenocarcinoma (non keratinizing) status are 0.64 times the instantaneous risk of death for
squamous cell carcinoma, after keeping all other covariates at some constant level respectively.

Histological grade: Among cervical cancer patients, the instantaneous risk of death for
moderately differentiated grade 0.65 times the instantaneous risk of well differentiated grade,
after keeping all other covariates at some constant level.

43
Presence of HTN (hypertension), The instantaneous risk of death for patients with HTN have
2.15 greater risk of instantaneous death than those patients without HTN, after keeping all other
covariates at some constant level.

4.5. Model comparison

Akaike Information Criterion (AIC) was used to assess these models properly. For a better
judgment, thus, Akaike information criterion can be used. Akaike information criterion is used to

44
measure the goodness of statistical models’ fitness, and the smaller it is, the better it is. The
smaller the AIC is, the more efficacious of the model. The result of AIC is given in table 8
below.

Table-8, Comparison based on the Results of the Akaike Information Criterion (AIC) b/n
the Cox Proportional Hazard and Parametric proportional Models BLH, 2014-2017.
Models AIC
Cox 314.3
Exponential 193.9
Weibull 190.4
Log-normal 140.3

Most cancer researchers tend to use Cox semi-parametric model rather than parametric models.
Therefore, parametric models such as exponential, Weibull and log-normal can be better choices
in such situation.
A major objective of this paper is to compare Cox semi-parametric and parametric survival
models in modeling the survival time of cervical cancer patients. So, in this study the results of
Cox semi-parametric model and parametric models were compared in modeling the survival time
of cervical cancer patients to assess these models, Akaike information criterion (AIC) were used.

Although most researchers in medical and cancer fields have made use of Cox semi-parametric
models in the survival time of cervical cancer patients, results of parametric models have often
been more reliable and have had less bias. As parametric models do not need proportional
hazards assumption (PH) in similar situations and they consider a specific statistical distribution
for time to the occurrence of the outcome, they have a better fitness. A parametric model was
also being credible alternatives to Cox semi-parametric model where proportional hazard
assumption is not made. In addition, fully parametric models may offer some advantages.

4.6. Discussion
A major objective of this paper is to investigate the comparative performance of Cox semi-
parametric and parametric survival models in modeling the survival time of women’s with

45
cervical cancer. So, in this study the results of Cox semi-parametric model and parametric
models were compared in modeling the survival time of cervical cancer patients. To assess these
models, Akaike information criterion (AIC) revealed that parametric models had better fitness.
This finding is consistent with the findings obtained from most studies carried out on patients
with gastric cancer (Orbe et al., 2012; Nardi and Schemper, 2013; Dehkordi, 2017;
Pourhoseingholi et al., 2017).
Based on asymptotic results, parametric models lead to more efficient parameter estimates than
Cox model. When empirical information is sufficient, parametric models can provide some
insights into the shape of the baseline hazard.
Most cancer researchers tend to use Cox semi-parametric model rather than parametric models in
modeling the cancer patients. A systematic review on cancer journals indicates that only 5% of
studies in which Cox model has been used for modeling cervical cancer cases, investigated the
required assumptions for this model. The absence of proportional hazards assumption causes the
estimations to be unreliable and biased. Moreover, studies conducted in this scope demonstrate
that either proportional hazards assumption is made or not, parametric models are more efficient
(Orbe et al., 20; Patel et al., 2016).

Therefore, parametric models such as exponential, Weibull, log-normal can be better choices in
such situations. Considering a particular statistical distribution for time to the occurrence of next
state and requiring no assumption of proportional hazards (PH), these models provide fitness for
data. A major objective of this paper is to investigate the comparative performance of Cox semi-
parametric and parametric survival models in modeling cervical cancer patients.

In addition, fully parametric models may offer some advantages. Based on the results parametric
models lead to more efficient parameter estimates than Cox model. With a decrease in sample
sizes, relative efficiencies may further change in favor of parametric models. When empirical
information is sufficient, parametric models can provide some insights into the shape of the

46
baseline hazard. So, in this study the results of Cox semi-parametric model and parametric
models were compared in modeling cervical cancer cases. To assess these models, Akaike
information criterion (AIC) mode estimates were was used.

This finding is consistent with the findings obtained from most studies carried out on patients of
cervical cancer (Orbe et al., 2012; Nardi and Schemper, 2013; Dehkordi, 2016; Pourhoseingholi
et al., 2016).

47
 CHAPTER FIVE

5. CONCLUSION AND RECOMENDATION

5.1. Conclusion
This was a three-year (2014-2017) retrospective cohort study based on 518 cervical cancer
patients in Black Lion Hospital Addis Ababa, Ethiopia. The purpose of the study was to identify
the best-fit parametric survival regression model from the pool of existing parametric survival
models (exponential, Weibull, Log-Logistic, and log normal), and to determine factors
associated with the survival time of cervical cancer patients in Black Lion Hospital Addis Ababa,
Ethiopia. It has been found that 16% of the considered patients were died and the remaining 84%
were censored at the end of the study.

Although most researchers in medical and cancer fields have made use of Cox semi-parametric
model into account, based on the findings of this research results of parametric models have
often been more reliable and have had less bias. As parametric models do not need proportional
hazards assumption (PH) in similar situations and they consider a specific statistical distribution
for time to the occurrence of next state, they have a better fitness.

Parametric models were also being credible alternatives to Cox semi-parametric model while
proportional hazard assumption is not made. In addition, fully parametric models may offer some
advantages. Based on the results parametric models lead to more efficient parameter estimates
than Cox model. With a decrease in sample sizes, relative efficiencies may further change in
favor of parametric models. When empirical information is sufficient, parametric models can
provide some insights into the shape of the baseline hazard.

48
5.2. RECOMMENDATIONS
 Based on the finding of this study the following recommendations are given.
 Survival time of cervical cancer through regular programs of women and prompt
comprehensive treatment should be taken up to improve the overall survival of the
patients.
 Improved the survival of patients were an integral part of controlling cervical cancer.
This can be done by having health education on cervical cancer incorporated in the
teaching curriculums by the Ministry of education just like it has been done for HIV /
AIDS. Carrying out regular screening programs and community mobilization activities
among other channels can be used to create awareness.
 Information on the availability of the HPV vaccine is some health facilities is unknown to
many Ethiopians. Therefore awareness on the survival of cervical cancer will reduce the
high mortality of patients with cancer of the cervix among women. Government
intervention to the increase the survival and to decrease the burden of the cervical cancer
treatment on the patients is very necessary.
 Decentralizing cancer treatment by the national government is an important intervention.
This will reduce the number of patients who have to wait before they undergo especially
curative treatment for those diagnosed at advanced stages because as a result of long
queues, their conditions are worsened.
 Further research on the survival time and the effect of treatment on the disease should be
carried out to give more insight into the survival time of the disease and disease
management.

49
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ANNEX 1: plot of log (-log (survival) versus log survival time for categorical variables in
the fitted model
6

6
4

4
-ln[-ln(Survival Probability)]
-ln[-ln(Survival Probability)]
2

2
0

0
1 1.5 2 2.5 3 3.5
-2

1 1.5 2 2.5 3 3.5 ln(analysis time)

ln(analysis time)
figosta = stage I figosta = stage II
residen = urban residen = rural figosta = stage III figosta = stage Iv

Kaplan-Meier survival estimates

1.00
0.75
0.50
0.25
0.00

0 10 20 30 40
analysis time

histolo = squamous cell carcinoma histolo = adenocarcinoma

histolo = adenosquamous cell carcinoma (non keratinizing)

55
 Kaplan-Meier survival estimates
1.00

Kaplan-Meier survival estimates

1.00
0.75

0.75
0.50

0.50
0.25

0.25
0.00

0 10 20 30 40

0.00
analysis time
0 10 20 30 40
grade = well differentiated grade = moderately differentiated analysis time
grade = poorly differentiated OCP = no OCP = yes

Kaplan-Meier survival estimates

1.00
0.75
0.50
0.25
0.00

0 10 20 30 40
analysis time

hyperte = no hyperte = yes

56
57
58