The kidneys are two bean-shaped organs found on the left and right sides of the body in vertebrates. They filter the blood in order to make urine, to release and retain water, and to remove waste. They also control the ion concentrations and acid-base balance of the blood. Each kidney feeds urine into the bladder by means of a tube known as the ureter.

Kidney failure (renal failure) is a condition where the kidneys are no longer filtering the blood of unwanted waste in the blood stream as well as they should. There are two primary types of kidney failure, acute and chronic. Acute kidney failure is current and often sudden issues where the kidneys are not working as well as they usually do. Chronic kidney failure (renal failure), the focus of this article, is also known as end-stage renal disease or ESRD. It is a condition where the kidneys lose their ability to filter waste and excess water from the bloodstream to convert into urine.In both cases, there is usually an underlying cause.

CKD also known as chronic renal disease is progressive loss in kidney function over a period of months or years. Professional guidelines classified the severity of CKD in five stages, with stage 1 being the mildest and usually causing few symptoms and stage 5 being a severe illness with poor life expectancy if untreated. Stage 5 CKD is often called end-stage kidney disease, end-stage renal disease, or end-stage kidney failure, and is largely synonymous with the now outdated terms chronic renal failure or chronic kidney failure; and usually means the patient requires renal replacement therapy, which may involve a form of dialysis, but ideally constitutes a kidney transplant. Individuals with ESRD would die within a few weeks or months if not sustained by some form of dialysis therapy or a kidney transplant. The term ‘dialysis’ refers to a treatment option that is suggested for people diagnosed with end-stage renal failure.

CKD is now recognized as a public health priority worldwide. According to the 2010 Global Burden of Disease study that ranked the causes of death worldwide in 1990 and 2010, CKD climbed the list from 27th to 18th position over two decades(Zhang and Rothenbacher, 2008). According to WHO report, 2003, the prevalence of impaired kidney function was estimated to range between 10% to 20% of the adult population in most countries worldwide(Organization, 2003). However, a recent study suggests that the incidence of kidney disease is increasing globally(Stanifer et al., 2014).

The National Kidney Foundation estimates that 20 million Americans have chronic kidney disease and at least a further 20 million people have an increased risk(National, 2002, Johnson et al., 2004). In 2011, 113,136 patients in the United States started treatment for ESRD(Control and Prevention, 2014). The increase in growth of the population with ESRD is partially related to the under recognition of earlier stages of CKD and the risk factors for its development(Gouda et al., 2011).

Lack of national registries and community-based studies in Africa makes a challenge to know its prevalence in the continent. ESRF has become a major health problem in SSA. By 2020, the burden of diabetes and CVD will have increased in Africa alone, with concomitant increases in the prevalence of CKD and ESRD(Schena, 2000). There are limited data on the prevalence and incidence of ESRF in SSA due to lack of renal registries. In Nigeria a study reported an increase of hospital admissions because of ESRF from 6 to 16 % between the years 1989 and 2003(Arogundade et al., 2011). Hypertension is a leading cause of ESRF in Senegal and Ghana(Diouf et al., 1999, Matekole et al., 1993) while chronic glomerulonephritis is the leading cause in South Africa and Ivory Coast(Du Toit et al., 1994, Diallo et al., 1996) . Chronic kidney disease is at least 3-4 times more frequent more Africa than developed countries. Chronic kidney disease affects mainly young adults aged 20–50 years in SSA and is primarily due to hypertension and glomerular diseases, unlike developed countries where chronic kidney disease presents in middle-aged and elderly patients and is predominantly due to diabetes mellitus and hypertension(Arogundade and Barsoum, 2008). The prevalence of kidney disease is more in blacks than whites’ counterparts (Tarver-Carr et al., 2002). The higher prevalence among Africans has been attributed to genetic predisposition, low socio-economic status and inequities in access to healthcare(Wong et al., 2002).

The health status of the Ethiopian is extremely poor. Ethiopia’s main health problems are communicable diseases caused by poor sanitation and malnutrition. These problems are exacerbated by the shortage of trained nurses and clinicians and of health facilities. In 2000, there were 103 hospitals and 338 medical centers in Ethiopia. There are only two medical schools in Ethiopia and Ethiopians share fewer than three physicians per 100,000 people(Tuso, 2009). Poland has 200 dialysis centers; Spain has 400. By comparison, Ethiopia with a population twice that of Poland and Spain combined has only two dialysis centers and two nephrologists. The country is challenged by emigration with many educated professionals leaving Ethiopia for a better economic opportunity in the West(Tuso, 2009)

In developing countries, such as Ethiopia, chronic disease is a growing problem. Like many other chronic diseases, the incidence of chronic kidney disease (CKD) in Ethiopia is rising because of increased risk factors such as high blood pressure and diabetes mellitus(Moeller et al., 2002). Given the limited financial and human resources available in our country, a valid estimate of CRF magnitude needed to inform resource allocation and prevention programs. Moreover, the scarcity and high cost of dialysis and kidney transplantation oblige for early the identification and management of associated factors(Pinho et al., 2015).

Since early recognition may help in the prevention of CKD progression and improve survival, surveillance programmers are being promoted worldwide(Radhakrishnan et al., 2014). From this perspective, proper epidemiological information about CKD at the national and regional level is fundamental to allow the main stakeholders, the patients, general practitioners and nephrologists, and the health system funding bodies to design and implement appropriate Prevention policies.

ESRD requiring RRT is the common final pathway for CKD. The population of patients on RRT has doubled in the last two decades. Globally, the number of patients receiving RRT was estimated to be over 1.8 million in 2004, with less than 5 % of this population residing in SSA (Grassmann et al., 2005).RRT is the mainstay of care for patients with end stage renal disease (ESRD). Dialysis as an option of RRT prolongs survival, reduces morbidities and improves quality of life. However, despite many technical advances, morbidities and mortalities of patients on dialysis remain unacceptably high and their quality of life is often poor(System, 2002).

Although maintenance dialysis methods have now successfully prolonged the life of patients, mortality remains high(Hsu et al., 2004). Approximately 9–13% of patients on hemodialysis in India die within 1 year(Rao et al., 1998). The adjusted rates of all‑cause mortality are 6.3–8.2 times greater for dialysis patients than the general population(Collins et al., 2013).

Treatment options for CKD are not readily available for most countries in sub-Saharan Africa. The region contributes to less than 5% of patients on RRT worldwide(Bleyer et al., 1996, Barsoum, 2006, Akinsola et al., 2004, Naicker, 2003).Dialysis and transplant programs in this part of the world are dependent on the availability of external funding and donors. As a result, only less than 5% of patients with diagnosed ESRD are able to get treatment for longer than 3 months(Arogundade and Barsoum, 2008). Common independent predictors of survival are age, race, serum albumin at the start of dialysis, activity level at the start of dialysis, and presence of certain comorbidities such as heart failure and cancer(Bleyer et al., 1996). For many years the magnitude of ESRD in Ethiopia has not been studied. The use of dialysis in the country as a treatment strategy for ESRD dates less than a decade. In addition, access for dialysis is limited and is a highly unaffordable for the general public. Each dialysis session costs about $100 (1700 Birr) excluding the costs for other supportive cares. Because of the low socio-economic status, dialysis is thus considered as luxury care in the country. There is currently no dialysis center in Public hospitals in Ethiopia with a population surpassing 85 million. In addition, there is no national strategy for prevention and care of patients with CKD(Shibiru et al., 2013).

We investigated the outcome of hemodialysis and the factors which had an impact on survival. Patient survival is a key index to the overall adequacy of treatment in most chronic diseases. Analyses of survival of patients undergoing hemodialysis are very important, as it may offer clues and ideas for prolonging the survival of ESRD patients.

1.2. Statement of the problem

If kidneys fail it needs treatment to replace the work they normally do. The treatment options are dialysis or kidney transplantation each treatment has benefited and drawback. No matter which treatment is chosen, you will need to make some change in your life, include how you eat and plan your activities.

When the kidneys fail completely, kidney transplantation is another option other than dialysis. Fortunately, human being can function with only one kidney, so relative and other donor is option. However, it is necessary to find a donor that has similar tissue and blood type, which means that finding are a kidney may still be difficult. Most people who need a kidney transplant must also be on dialysis until a much is found. At the same time, dialysis costs a lot of money.

Patients who are on dialysis also face different problem that may end up with losing life. No study has been conducted in our country that report the potential factor for the death of renal patients hemodialysis patients .knowing the causes of the death of renal failure patients will help in taking appropriate care for that problem. This enables to give due attention to these problem so that we can prolong the life of hemodialysis patients.

Since the aim of HD is improve the health of renal failure individuals, it would be essential to study survival time and associated risk factor of renal HD patients. Thus assessment of survival on patients receiving HD has paramount important. Therefore, the present study is to determine factor influencing survival among patients on hemodialysis in saint General hospital.

1.3 Objective of the study

1.3.1 General Objective

The main Objective of the study is to investigate survival pattern and assess risk factors for poor outcome of patients on maintenance hemodialysis for end stage renal disease.

1.3.2 Specific objective

The specific objective of the study is:

To estimate the survival time of renal failure patients receiving dialysis.
To estimate median survival time for the patients.
To determine the factors and/or covariates that affect the survival of renal failure patients treated with dialysis.
To recommend for the concerned body

1.4 Significance of the study

Chronic renal failure is not only the individual issue but also family and community problem. Therefore, assessing survival and associated factors helps to tackle the problem. The disease especially if the patient reaches end stage of renal disease, family face challenge due to dialysis fee. Most of dialysis service given from private institution this makes the problem devastating. Therefore, the result of this study has the following advantage.

The results of this study might provide information to government and other concerned bodies in setting policies, strategies and further investigation for reducing death to renal failure patient.
The results help donors and government to understand risk factors that influence the death of renal failure patients.
The study could provide base-line data for detail and further studies in the future.

CHAPTER TWO

2. LITERATURE REVIEW

When your kidneys stop working waste can no longer be removed from your blood, meaning you have kidney failure. Kidney failure is also called end-stage renal disease (ESRD) or Stage 5 CKD. (Renal is a medical term for kidney, meaning “having to do with the kidneys.”) When you have ESRD you need dialysis or a kidney transplant to survive.Chronic kidney disease has become a major health concern globally, especially in developing countries with a marked burden in Sub-Saharan Africa (Naicker, 2009). This concern is largely due to the rising prevalence of risk factors such as type 2 diabetes, hypertension, and the HIV pandemic, the enormous cost implication of its treatment, its role in cardiovascular morbidity and mortality and the fact that the disease largely afflicts the economically productive younger age groups (Naicker, 2009, Barsoum, 2006). The database of patients available in the ‘Renal Registry’ enables analysis of the influence of different factors on patient survival. These factors either reflect patient case mix [e.g. age, gender, ethnicity, underlying diagnosis & other co-morbidity] or are dependent on treatment [e.g. hemoglobin, mode of dialysis, phosphate level].

When someone’s kidneys fail, the only options are dialysis or a kidney transplant. Because there aren’t enough donor kidneys to give transplants to everyone who needs one, many people must turn to dialysis. In dialysis, a machine takes over many of the jobs of the kidneys, such as filtering excess fluid and waste. In the United States, almost 400,000 people undergo dialysis every year, according to the U.S. National Institute of Diabetes and Digestive and Kidney Diseases. In 2008, fewer than 18,000 people received a kidney transplant, according to NIDDK. It may not remove enough fluid, and levels of important nutrients can get out of balance for people on dialysis, according to background information in one of the studies. In addition, people on dialysis have to eat a limited diet. Previous research has suggested that longer dialysis sessions seem to provide a benefit without increasing the risks of complications.Researchers compared the health of 746 patients who received hemodialysis treatments at a clinic three nights per week for about eight hours each night to 2,062 similar patients who received conventional dialysis care. As with the other studies, the researchers saw a significant benefit from the longer dialysis sessions. During a two-year follow-up period, those on night-time dialysis had a 25 percent reduced risk of dying. The night-time group also had benefits such as lower weight, blood pressure and blood phosphorous levels. (Dialysis patients have difficulty maintaining proper phosphorous levels, putting them at risk of serious complications such as heart disease. Diet and medications help to control these levels(Singh et al., 2006)

(Prabha and Prasad, 2016) employed cox regression analysis to determine the factors influencing survival among patients on maintenance hemodialysis. A total of 198 patients with end‑stage renal disease who were started on hemodialysis (8 h/week) were studied. Follow‑up was censored at the time of death or at the end of the 2‑year study period, whichever occurred first, by using data from India tertiary care hospital. This study revealed that mortality among hemodialysis patients remained high mostly due to sepsis and ischemic heart disease. Patient survival was better with good native kidney urine output, adequate serum albumin, absence of LVH and ejection fraction >50% on two‑dimensional echocardiography, compliance to dialysis, and interdialytic weight gain <3 kg. Comprehensive predialytic nephrology care prevents mortality and improves survival among hemodialysis patients.

According to (Zeleke, 2016) who used logistic regression model to examine The Magnitude of Chronic Renal Failure and its associated factors among patients. He used the data at St. Paulo’s Hospital, Addis Ababa, Ethiopia. He obtained that chronic renal failure common in all age group and common among male than females. Chronic renal failure magnitude among patients with hypertension and kidney infection had statistical significance.

(Fiseha et al., 2014) Used data from butajira hospital, southern Ethiopia among 214 randomly selected diabetic adults. The aim of this study was to determine the prevalence of CKD and its associated risk factors among diabetic adults attending Butajira hospital of Southern Ethiopia based on estimated GFR. Significant risk factors for CKD in the study subjects when using either the MDRD or C-G equation were older age, longer duration of diabetes, family history of kidney disease, and poor glucose control (P < 0.05).

(Marinovich et al., 2012) applied the Cox model to assess the association between income and survival of patients after adjusting for age, sex, diabetes, comorbidities, initial laboratory results, and first vascular access by using data in Argentine Registry of Chronic Dialysis. Low or no income of patients at the time of entry into HD is an independent risk factor for immediate lower survival.

(Lynn et al., 2002) Also Used cox proportional hazard model and data from retrospective cohort study of 168 patients in London (UK) to examine Hypertension as a determinant of survival for patients treated with hemodialysis. The result showed that Seventy-one patients died and the median survival was 4.2 years (5.6 on HD, 2.2 on CAPD, P _ 0.0001). High and low BP values at the start of dialysis were associated with the highest mortality. Hypertension was the risk factor for survival and patients with mid-range BP values survived the longest.

(Eleftheria, 2014) Identify Causes and complications of chronic kidney disease in patients on dialysis in the University Hospital of Heraklion between September 2009 and September 2010. Data were analyzed with descriptive statistical analysis, t-test, Kaplan Maier analysis and Cox regression analysis. The variable considered were sex, age, cause of ESRD, presence or not of diabetes mellitus, duration and type of dialysis, type of vascular access, number and causes of hospitalizations in the nephrology ward, length of stay in each admission, type of infections and the corresponding pathogens.The major cause which seems to be responsible for the occurrence of chronic kidney disease is diabetic kidney disease (19.5%), followed by glomerulonephritis (18,7%). The major causes of hospitalization were infections (37.9%), including bacteremia due to central catheter infection (40.4%), peritonitis in PD patients (19.1%), gastroenteritis (12.8%), respiratory tract infections (12.8%), urinary tract infections (6.4%) and other infections (such as cholangitis, skin infections etc) 8.5%. Cardiac problems as a reason for hospitalization included pulmonary edema (57.1%), faint episodes, pulmonary embolism, decompensated heart failure and myocardial infarction (7.1% each).

A study conducted in University of Erlangen-Nuremberg, Germany showed that cardiovascular disease (CVD) is a significant complication in chronic kidney disease (CKD) and a major cause of death in dialysis patients. Clinical studies have shown that anemia is associated with reduced survival in patients with renal disease, heart failure or both. There is also evidence that, even in otherwise healthy individuals, anemia is independently associated with an increased risk of CVD (Strippoli et al., 2004).

(Urrutia et al., 2015) also used Weibull Distribution model to analyze the Survival Analysis of Patients with End Stage Renal Disease. The data were obtained from the records ofV. L. Makabali Memorial Hospital with respect to time t (patient’s age), covariates such as developed secondary disease (Pulmonary Congestion and Cardiovascular Disease), gender, and the event of interest: the death of ESRD patients. They reported that hazard rate increases and survival rate decreases of ESRD patient diagnosed with Pulmonary Congestion, Cardiovascular Disease and both diseases with respect to time. It also shows that female patients have a greater risk of death compared to males.

(Fabian et al., 2015) conduct study on Morbidity and mortality of black HIV-positive patients with end-stage kidney disease receiving chronic haemodialysis in South Africa. Retrospective study compared the incidences of vascular and infectious morbidity and mortality in black HIV-positive patients with those in a group of HIV-negative patients matched for ethnicity, age and gender. All the patients were receiving chronic hemodialysis in the medically insured healthcare sector of SA. This study has shown that black HIV-positive patients receiving chronic HD in a healthcare-funded environment in SA have excellent overall survival in spite of higher hospital admission rates and higher infectious morbidity compared with HIV-negative patients. The incidences of tuberculosis and hospital admission rates for vascular access-related infections were significantly higher in the HIV-positive group than the HIV-negative group. The HIV-positive group had significantly lower albumin (p<0.05) and hemoglobin levels (p<0.01), but this did not impact on mortality. Survival in both groups was excellent. In the HIV-positive group, viral suppression rates weresuboptimal with <50% of patients on antiretroviral therapy completely virally suppressed

A study conducted by(Tong et al., 2016) to examine mortality and associated risk factor in dialysis patients with cardio vascular disease in Asian dialysis patients. Prospective cohort study, on the mortality and risk factors were investigated in 591 dialysis patients who were recruited from two dialysis centers from May 1, 2009 to May 1, 2014. The Cox proportional hazards regression assessed adjusted differences in mortality risk. A multivariate analysis was also performed, comparing the CVD and non-CVD groups. Result show that A total of 591 patients were enrolled in this study (mean age, 52.05 ± 16.46 years [SD]; 61.8% men; 20.8% with CVD), with a median follow-up of 21.9 (maximum, 72) months. The cumulative hazard of mortality was significantly higher in CVD patients (hazard ratio [HR], 1.835; 95% confidence interval [CI], 1.023-3.293; P=0.042) than in their non-CVD counterparts after adjusting for various confounders. On multivariate Cox analysis, stroke (HR, 4.574; 95% CI, 2.149-9.736; P<0.001) was an independent predictor of all-cause mortality in the CVD group. In the non-CVD group, diabetes mellitus (HR, 2.974; 95% CI, 1.560-5.668; P=0.001) and elevated high-sensitivity C-reactive lipoprotein (hs-CRP) (HR, 1.017; 95% CI, 1.005-1.030; P=0.005) were independent predictors of all-cause mortality.

Many researchers found that there is an inverse relationship between patients with and without prior stroke. Beater survival is seen among renal failure patients who haven’t prior stroke.

In Taiwan National Health Insurance Research Database (NHRI-NHIRD-99182) was used and all adult patients (≥18 yr.) with end stage renal disease (ESRD) who started maintenance HD between January 1, 1999, and December 31, 1999, were selected. The patients were followed from the first reported date of HD to the date of death, end of dialysis or December 31, 2008. A Cox’s proportional hazard model was applied to identify the risk factors for all-cause mortality.

The aim of this study was to assess risks for mortality between patients with and without prior stroke undergoing chronic hemodialysis (HD). After adjusting for age, sex and other covariates, the patients with prior stroke were found to have a 36 % increased risk of mortality compared to those without prior stroke (HR 1.36, 95% CI: 1.22-1.52). The cumulative survival rates among HD patients without prior stroke were 96.0 per cent at the first year, 68.4 per cent at the fifth year, and 46.7 per cent at the ninth year, and 92.9, 47.3 and 23.6 per cent, respectively, in those with prior stroke (log-rank: P<0.001). The findings showed that prior stroke was an important predictor for all-cause mortality and poor outcome in patients undergoing chronic HD (Chien et al., 2013).

CHAPTER THREE

3. DATA AND METHODOLOGY

This section describes the data and methods used in this study to come up with the development of a survival model and estimate the probability of surviving all causes of death for a specified time interval calculated from the cohort of ESRD cases.

3.1 Source of Data

The source of data for this study is Saint Geberial general hospital. The hospital is located in Addis Ababa, Ethiopia. It is the first private Hospital established in 1995 and one of the dialysis centers in the country. The hospitals serve as a teaching and medical center for the population of Addis Ababa and the country as well. Saint Geberial general hospital launched dialysis treatment service in 2000 E.C for renal failure patients who fulfill the criteria to use the treatment. The data will collected by using pretested structured questionnaire that consisted of characteristics related to demographic profiles, causes and risk factors of CKD, clinical conditions of patients at initiation and last session of dialysis and treatments given. These are collected by reviewing patients’ medical records and dialysis registration book.

3.2 Study design

This is a retrospective analysis of patients’ clinical data on maintenance hemodialysis for end stage renal disease (ESRD) at saint geberial general hospital. The cohort is followed from 2005 May 1 E.C to 2008April 30 E.C and the data was secondary since it is collected from records chart.

3.3 Measurement of variable

3.2.1 Definition of variables

The response (dependent) variable is continuous and describes the length of treatment time in month. The explanatory (independent) variables of interest in this analysis include socio-economic, demographic, and characteristics of disease and treatment profiles.

3.2.2 The Response Variable

The response variable for the

0=once per week

1=two times per week

2= three times per week

Status of hypertension

(Hypertension)

0=no

1=yes

Status of diabetes

(Diabetes)

1=no

2= yes

Infection

0=no

1=yes

Stroke

0= no

1=yes

Anemia

0=no

1=yes

Cardiac problem

(Cardiac)

X10

0=no

1=yes

BMI

X11

0=BMI<18.5

1=between 18.5 and 25

2=between 25 and 30

3= above

Duration of

dialysis per session

X12

0= 3 hour

1 = 3^1/2 hour

4 = hour

HIV

X13

0= HIV positive

1= HIV negative

3.3 Methods for data Analysis

3.3.1 Survival Data Analysis

Survival analysis is defined as a branch of statistics which deals with data related to time to an event. This topic is also called reliability analysis in engineering and duration analysis in economics or sociology. The term survival analysis applies to techniques in which the data being analyzed represent the time it takes for a certain event to occur. The use of survival analysis, as opposed to the use of different statistical methods, is most important when there is no time-to-event record. In reality such situation can occur due to the following reasons:

When an individual survive beyond the study period or the individual does not experience the event.
Lost to follow-up, that is, an individual may drop out, transfer to other place, etc.
Deaths due to other causes different from that/those specified in the study.

Therefore, survival data are almost always incomplete. The statistical terminology for such data is censoring. Censoring is common in survival analysis and it is considered as an important feature of survival data. Survival analysis is well suited to for such data which are very common in medical research since studies in medical areas have a special feature that follow-up studies could start at a certain observation time and could end before all experimental units had experienced an event. The most common encountered form of a censored observation is one in which observation begins at the defined time, say t=0, and terminates before the outcome of interest is observed. Since the incomplete nature of the observation occurs in the right tail of the time axis, such observations are said to be right censoring. The other mechanism that can lead to incomplete observation of time is truncation. A truncated observation is one which is incomplete due to a selection process inherent in the study design.

There are obviously many potential life models that overcome such incomplete observations. In some situations there may be reasons to select a particular family of models; the model my fit data on hand well, past experience may have shown the model to give a good description of lifetime distribution from similar populations, there may be a knowledge of the underlying aging or failure process that suggests the validity of the model, and so on. In situations in which no family of models is singled out as being particular appropriate, the choice of the model is frequently made on the basis of considerations such as: the convenience of mathematically handling the model, the statistical methods available in connection with the model and the degree of complication of calculations involved in using the model.

Three additional points should be mentioned in connection with the choice of the model. Firstly, for any chosen particular model it has to fit the available data upon appropriate tests. Second, one should be aware of the consequences of departures from the assumed model on inferences made. Finally, although there is a lot of work based on lifetime distributions of parametric models, there are many situations in which it is desirable to avoid strong assumptions about the model. Nonparametric or distribution-free procedures are important in this case (Lawless, 1982).

Several methods have been developed for the analysis of survival data. Some of these are:

Descriptive statistics which include life tables, survival distribution, and Kaplan-Meier survival function estimation which are used for the estimation of the distribution of survival time from a sample.
Nonparametric tests are available for comparing the survival experience between two or more groups. The most common and widely used of these tests are the log-rank test, Generalized Wilcoxon test and Peto-Prentice test.
The multivariate Method uses Cox-proportional hazards model. It is considered as the most interesting survival modeling in the interest of examining the relationship between survival and one or more predictors. Covariates may be categorical or continuous. In addition the model has the capability of including both time-dependent and time-independent variables

3.3.1.1 Descriptive Methods for Survival data

In any applied setting, a statistical analysis should begin with a thoughtful and thorough description of the data. In particular, an initial step in the analysis of a set of survival data is to present numerical or graphical summaries of the survival times in a particular group. Routine applications of standard measures of central tendency and variability will not yield estimates of the desired parameters when the data include censored observations. In summarizing survival data, the two common functions applied are the survivor function and the hazard function.

1. Survivor function S (t)

The survivor function is defined to be the probability that the survival time of a randomly selected subject is greater than or equal to some specified time. Thus, it gives the probability that an individual surviving beyond a specified time. Moreover, the distribution of survival time is characterized by three functions: (a) the survivorship function, (b) the probability density function, and (c) the hazard function.

Let T be a random variable associated with the survival times, tbe the specified value of the random variable T and

ithindividual.

δi

= an indicator of censoring for the

ithindividual given by 0 for censored and 1 for event/death

= a vector of covariates for individual i

Xi2 ,Xi2, . . . ,Xip.

The full likelihood for right censored data can be constructed as

β=

∏i=1nλ(ti,Xi,β)δiS(ti,Xi,β) (3.13)

Where

λ(ti,Xi,β)

λ0tieβ’Xiis the hazard function for individual i.

Sti,Xi,β

S0ti)

eβ’Xiis the survival function for individual i.

It follows that

β=

∏i=1nλ0tiexp

(β’Xi)δiS0(ti)exp

β’Xi(3.14)

The full maximum likelihood estimator of β can be obtained by differentiating the right hand side of t equation (3.14) with respect to the components of

βand the base line hazard

λ0t

This implies that unless we explicitly specify the base line hazard,

λot, we cannot obtain themaximum 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.

Partial likelihood

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

tigiven that an event occurred at that time.

Let

Ridenote the set of individuals at risk at time just prior to

ti. Assume that for the present case there is only one failure at time

ti, i.e, no ties. The probability that individual i with covariates

Xiis the one who experience the event at time

ti.

=P(individual i has experience an event at time

ti/one event at time

ti)

λt,Xi∑jεRtiλt,Xj

(3.15)

And under the proportional hazards assumption on using equation (3.12), the ratio

λ0texpβ’Xi∑jεRtiλ0texpβ’Xj

(3.16)

Shows the contribution to the partial likelihood at each death time

tiby the individuals with covariate

Xiin the risk set

Rti. Where

Ritis the overall subjects in the risk set at time

ti.

By eliminating the base line hazards function, in the numerator and denominator, equation

(3.16) becomes

expβ’xi∑jεRtiβ’Xj

(3.17)

Thus the partial likelihood is the product over all failure time

tifor i = 1, 2…m of the

Conditional probability (3.13) to give the partial likelihood the partial likelihood is the product over all failure time

tifor i = 1, 2,…, m of the conditional probability (3.17) to give the partial likelihood.

β= ∏i=1mexpβ’Xi∑jεRtiexpβ’Xi(3.18)

The product is over the m distinct ordered survival times and

Xidenotes the value of the covariate for the subject with ordered survival time

ti.The log partial likelihood function is

β=

∑i=1mβ’Xi-ln∑jεRtiexpβ’Xj(3.19)

We obtain the maximum partial likelihood estimator by differentiating the right hand side of (3.19) with respect to the component of β, setting the derivative equal to zero and solving for the unknown parameters.

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 death at a time, there might also be more than one censored observations at a time of death.

To handle this real-world fact, partial likelihood algorithms have been adopted to handle ties.

There are three approaches in common to estimate regression parameters when there are ties. The most popular and easy approach is Breslow’s approximation.

The Breslow approximation

This approximation is proposed by Breslow and Peto by modifying the partial likelihood takes the following form

β=

∏i=1mexpβ’Si∑IεRtiexpβ’XIdi (3.20)

Where

Sithe sum of covariates over

disubjects at time

The number of deaths occurred at time

Now the partial log likelihood of (3.20) is given as

β=

∑i=1mβ’Si-diln∑IεRtiexpβ’XI (3.21)

We obtain the Breslow maximum partial likelihood estimator, adjusted for tied observation, by differentiating equation (3.21 ) with respect to the component of β and setting the derivative equal to zero and solving for the unknown parameters.

3.3.2.4 Interpretation of the coefficients of the Cox-regression model

The estimated coefficients for the predictor variables represent the slope or rate of change of a function of the outcome variable per unit of change in the predictor variable by keeping the remaining predictor variables fixed (Hosmer-Lemeshow, 1989). Thus interpretation involves two issues, determining the functional relationship between the outcome variable and the covariate and appropriately defining the unit of change for the predictor variable (Hosmer- Lemeshow, 1989).

The estimated regression coefficients

βí’sreflect linear and non-linear relationships andthey will be interpreted as the change in the log-hazards ratio for every unitincrease/decrease, depending on the variable change in

Xiholding other predictors constant.

For example, for a dichotomous covariate with value 1 and 0, the hazard ratios of being in the category of interest for the

jthsubject, becomes

λ0texpβi*1́λ0texpβi*0́=

expβífixing the other covariates constant. It is interpreted as the hazard rate, or rate of death in our case, among subjects with

ithcovariate value equals 1 is

expβítime higher than subjects with

ithcovariate value equals zero, i = 1,2,…, p and j = 1,2,…, n . For covariates having L levels

(L>2), similarly interpretations can made by taking one of the L-levels as a reference category.

3.3.2.5 Variable selection procedure

A major reason for using the Cox model instead of the Logrank test is that the former easily allows for multivariable analysis.An important issue is how to decide on which variables are to be included in a Cox model.The methods available to select a subset of the covariates to include in a proportional hazards regression model are essentially the same as those used in the other regression models, like purposeful selection, stepwise (forward selection and backward elimination) and best subsets selection. When the number of variables is relatively large, it can be computationally expensive to fit all possible models. In this situation, automatic routines for variable selection that are available in many software packages might seem an attractive prospect. These routines are based on forward selection, backward elimination or a combination of the two known as the stepwise procedure (Collet, 2003). Thus, instead of using automatic variable selection procedures, the following general strategy for model selection is recommended by Collet (2003).

1. The first step is to fit models that contain each of the variables one at a time. The values of -2log

L̀for these models are then compared with that for the null model. The null model is a model to determine which variables on their own significantly reduce the value of this statistic.

2. The variables that appear to be important from step 1 are then fitted. In the presence of certain variables others may cease to be important. Consequently, those variables that do not significantly increase the value of -2log

Ĺwhen they are omitted from the model can now be discarded. We therefore compute the change in the value of -2log

Ĺwhen each variable on its own is omitted from the set. Only those that lead to a significant increase in the value of -2log

Ĺare retained in the model. Once a variable has been dropped, the effect of omitting each of the remaining variables in turn should be examined.

3. Variables that were not important on their own, and so were not under consideration in step 2, may become important in the presence of others. These variables are therefore added to the model from step 2, one at a time, and any that reduce -2log

Ĺsignificantly are retained in the model. This process may result in terms in the model determined at step 2 ceasing to be significant.

4. A final check is made to ensure that no term in the model can be omitted without significantly increasing the value of -2log

Ĺand that no term not included significantly reduces -2log

Ĺ.

When using this selection procedure, rigid application of a particular significance level should be avoided. In order to guide decisions on whether to include or omit a term, the significance level should not be too small. A level of around 20% – 25% is recommended (Hosmer et al, 2008).

3.3.3Assessment of model adequacy (Model Checking)

The adequacy of the model needs to be assessed after the model has been fitted to observed survival data. Model-based inferences depend completely on the fitted statistical model. For these inferences to be valid the fitted model must provide an adequate summery of the data upon which it is based. Many model checking procedure are based on quantities known as residual. Residuals are values that can be calculated for each observation and have a feature that their behavior is known, at least approximately when the fitted model is satisfactory. When the cox regression model has been fitted to the survival time and the liner component of the model contains p explanatory variable , X1, X2, . . . , Xp

Then, the cox snell residual for the

ithindividual, i=1,2, …, n is given by

rCi

expβxíHotwhere

H0tis the estimated cumulative base line hazard function at time

tithen the observed time of that individual the cox snell residual have properties that have quite dissimilar to those of residual used in liner regression analysis . They will not be symmetrically distributed above zero and they cannot be negative. Furthermore , when an appropriate test has been fitted they have highly skewed distribution .censored observation lead to residual that cannot be regarded to the same footing as residual derived from uncensored observation. Therefore to take an account for censored, the modified cox Snell(martingale residual) for the

ithindividual is given as

rMi=

δi-rCiwhen

δi =0 for censored observation

δi=1 foruncensored observation.

In large sample the martingale residual uncorrelated with one another and has an expected value zero. In this respect, thy have properties similar to those possessed to by residual encountered in liner regression analysis. However, the martingale residuals aren’t symmetrically distributed about zero.

Plot of residual against explanatory variable can be used to indicated whether any particular variable needs to be transformed prior into incorporated it in the model. When the residual are plotted against explanatory variable that are not in the fitted cox regression model they don’t show an obvious relationship, then it can be suggested the variable is not needed in model. Hence in the plots of the martingale residual against the value of explanatory variable, if most of the point fall horizontally about zero then the fitted model is taken as satisfactory.

3.3.3.1 Checking for linearity of continuous covariates

As described above to check the linearity of continuous covariates we plot hazard against the midpoint of the classes and also using plots of martingales residual but for these particular study the plots of martingale residualis used. Thus to check linearity we plot martingales residual against the exclude covariate and see if the resulting plot is a straight line then it show linearity.

3.3.3.2 Checking for proportionality assumption

In order to use cox model, we must check the assumption of weather the effects of covariate on hazard ratio remain constant over time. These critical assumptions of proportional hazard model and must be checked for each covariate.

Schoenfeld residuals are useful to check the proportionality of the covariates over time, that is, to check the validity of the proportional hazards assumption.to checkproportionality assumption for each covariate, we plot the secaledschoenfeld residual on the y- axis against log of survival time on the x axis ,If the model fits well then the residuals are randomly distributed without any systematic pattern around the zero line, the reference line .

The

ithSchoenfeld residuals for

Xjthe

jthexplanatory variable in the model, is given by

rpji

ciXji-ají where

Xjiis the value of the

jthexplanatory variable, j = 1, 2, ……, p, for the

ithIndividual.

ají

∑IεRtiXjiexpβ’XÍ∑IεRtiexpβ’XÍ and

Rtiis the set of all individuals at risk at time

ti.

3.3.4 Model assessment

DFBETA.Dfbetas.is one of the method of checking whether there is an influential observation in the data or not. If the absolute value of dfbeta is greater than

2sqrtnthen it indicates there is an influential observation otherwise not. Where n is the number of observations used in the analysis Dfbeta is a useful measure to assess the influence of each point on the estimated

Coefficients

β̃j’S. This measure is analogous to that used in regular linear regression. Large values suggest we inspect corresponding data points. The measure dfbetas is dfbeta divided by the s.e (

β̃j).

Coefficient of determination

Several authors have proposed methods for computing an

R2statistic for Cox regression. One method due to Nagelkerke (1991) defines the

R2statistic as

= 1-exp

-2nlnLβ̃-lnLO=

1-exp

2nlnLO-lnLβ̃(3.22)

Where lnL

β̃and lnL

Odenote the likelihoods for the Cox regression models with and without the covariates, respectively.

The

R2given by this definition have the following properties:

1. It has the same interpretation as the

R2in linear regression. Specifically, it measures the proportion of variation explained by the model, or rather, 1-

R2is the proportion of unexplained variation.

2. For a given model, it achieves the largest value at the maximum likelihood estimates.

3. It is independent of the units used for the response and predictor variables

CHAPTER FOUR

4.1 Expected outcome

At the end of the research the following point will be expected.

The predictive ability of the model (cox proportional hazard model) survival of renal failure patient’s receiving dialysis based on the selected explanatory variable or factor will expect to be realized (explained).

Survival pattern of renal failure patients receiving dialysis in saint geberial general hospital would be showed.

By using the survival curve the probability of renal failure patients who continued to dialysis at any given time would be estimated.

4.3 TENTATIVE WORK PLAN IN 2017

No.	Activities	2017
		Jan				Feb.				Mar.				Apr.				May				June
		Week				Week				Week				Week				Week				Week
		1	2	3	4	1	2	3	4	1	2	3	4	1	2	3	4	1	2	3	4	1	2	3	4
1	Title selection
2	Proposal preparation, submission to advisors & finalization
3	Training of enumerators
4	Data collection, monitoring & gathering finished data
5	Data editing, entry & analyses
6	Report writing
7	Submission of the draft report to Advisors
8	Finalizing the report
9	Submission of the final report to department
10	Presentation of results to concerned bodies

4.3 BUDGET BREAKDOWN

Stationary requirements
S.No.	Item	Unit	Quantity	Unit price	Total price(Birr)
1	80gm printer paper	Pack	6	125	750.00
2	Pen	Pcs	10	5	50.00
3	Pencil	Pcs	1	1.00	1.00
4	Flash Disk	Pcs	1(16GB)	300.00	300.00
5	Transparency	Sheet	150	3.00	450.00
6	Notebook	Pad	4	15.00	60.00
7	Stapler	Pcs	1	30	30.00
8	Internet service	Hr	20	15	300.00
9	CD RW	Pcs	5	25	125.00
Sub total					2066.00

Wage for enumerators
S.No.	Title			Rate (Birr)		Number		Duration		Total (Birr)
1	Training of enumerators (data collectors)			100.00/day		4 enumerators 1 coordinator		3 days		1,500.00
2	Tea & coffee during training			25.00/person		5		3days		375.00
3	Per diem for data collectors(card reviewing)			20.00/card		4 enumerators				10,000.00
4	Secretarial services/data entry			80.00/day		2 clerks		15 days		2,400.00
5	Coordinator			80.00/day		1 coordinator		15 days		1,200.00
Sub-total										15475.00
Transport cost
Traveler		From – to	Unit		Traveling days		Unit price		Total(ETB)
Investigator		Gondar-ADDISE Ababa	Days		6		530		3180.00
Sub-total									3180.00

Miscellaneous expenses
Expense category	Unit	Quantity	Unit Price	Total (ETB)
Typing of proposal	Page	40	7	280.00
Binding proposal	Piece	4	10.00	40.00
Printing proposal	page	260	1.50	390.00
Document Binding	piece	10	10.00	100.00
Printing documents	page	1000	1.500	1500.00
Photocopying	Page	2000	.50	1000.00
Typing of the thesis	Page	150	4.00	600.00
Mobile card	Pcs	5	100	500
Sub-total				4,410.00

Summary of Budget breakdown
S.No	Expense category	Total(Birr)
1	Stationery	2,066.00
2	Wage to enumerators	15,475.00
3	Miscellaneous expense	4,400.00
4	Transport	3,180.00
5	Contingency (10%)	2,513.10
Grand-total		27,644.10

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