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1.1              INTRODUCTION

Cancer is a potentially fatal disease caused mainly by environmental factors that mutate genes encoding critical cell-regulatory proteins. The resultant aberrant cell behavior leads to vital organs resulting in disseminated disease, commonly a harbinger of imminent patient death (Malcolm, 2001).

Breast cancer is now the commonest malignancy affecting women in Nigeria. It is likely to become an important public health issue in the next millennium. Recent years have witnessed an explosion in knowledge about the basic sciences of the disease, including the genetic basic and the pathology. These changes are leading to revisions in the management of the disease with a positive impact on prognosis. In this review, the recent developments in the various aspects of breast cancer are reviewed with reference to how they affect the disease in this environment (Adebamowo, et al., 2000).

Cancer is the second leading cause of death in the United States. About one-half of all men and one-third of all women in is the US will develop cancer during their lifetimes. Today, millions of people are living with cancer or have had cancer (America Cancer Society, 2012).

Over the next 25 years there will be a dramatic increase in the number of people developing cancer. Globally 10 million new cancer patients are diagnosed each year and this will be 20 million by the year 2020.

Cancer is now the public most feared disease. Billions of dollars are spent annually on cancer research by the drug industry, cancer charities and governments, but a cure for cancer appear elusive, and yet we are in the midst of a revolution in our ability to image part of the body, painlessly and fine details (Sankrithi et al., 1991). Cancer is a group of diseases characterized by unregulated division and spread of cells. The cancerous cells may occur in liquids, as in leukemia. Most, however, occur in solid tumors that originally appear in various tissues in various parts of the body. By their original locations they are classified into various types of cancer, such as lung, colon, breast, prostate cancer, etc. localized tumors can be removed by surgery or irradiating with high survival rates. As cancer progresses, however, it metastasizes invading the surrounding tissues, entering the blood stream, spreading and establishing colonies in distant parts of the body.ony a third of patients with metastasized cancer survive more than five years. Invasive distension spreading crab- like from a tumor in the breast were described by Hippocrates. From the crab, Karkinos in Greek and cancer in Latin, came the name of its inducing agents, carcinogens (Dervan, et al., 2004).

The causes of serious ill health in the world are changing. Infection as a major cause is giving way to non-communicable diseases such as cardiovascular disease and cancer. In 1996 there were 10 million new cancer cases and 12 million deaths. Part of the reason for this is that life expectancy is steadily rising and most cancers are more common in an ageing population. More significantly, a globalization of unhealthy lifestyles, particularly cigarette smoking and the adopting of many features of the modern western diet (high fat, low fibred content) will increase cancer incidence (Malcolm, 2001).

Survival analysis is a class of statistical methods designed to study the occurrence and timing of events. The methods were developed for studying the time from initiating events (such as birth, diagnosis of a disease, state of a treatment etc.) to some terminal events (such as response to treatment, relapse, death etc.) these methods are mostly applied in medical sciences. However, the methods were successfully applied to many different kinds of even across disciplines. Examples include the manufacturing or engineering sectors (how long it takes a machine to fail), social sciences (how long a marriage will last), finance (the time it takes the price of stock in stocks market to drops) and so on. Sometimes other names are used to refer to this class of methods such as “ duration analysis”, “failure time analysis”, “event history analysis”, “transition analysis”, but the basic techniques are the same as in the underlying idea i.e understanding the pattern of events in time and what factors cause those events to occur. Distensions spreading crab-like from a tumor In the breast were described by Hippocrates. From the crab, karkinos in greek and cancer in latin, came the name of the disease and the name of its including agents, carcinogens (Dervan, et al., 2004).

Survival analysis measures the probability of how long it take a given outcome to occur for a group of similar individuals known as failure times (Cox and Oates, 1984). Survival analysis method also measures the probability that the given event in question will last the next point in time (Gokovali et al, 2007). Survival analysis studies are well known to occur in medical sciences particularly in cancer studies. Depending on the question of the studies, one is interested in the risk group i.e which group of patients or components is more likely to experience the events; or time predictions. The starting time from a defined point to the occurrence of a given event is called survival time (Berwick et al, 2004) and the analysis of such group data is called survival analysis (Altman, 1977).

In order to understand the survival analysis; the concept of event has to be understood.

According to Blossfeld et al, (1989) an event is a change in state as defined by one or more qualitative variables within the relevant state space. Examples are death, marriage; promotion etc. survival analysis is the core of any study of time to a particular events, such as death, infection or diagnosis of a particular disease. It is therefore fundamental to most epidemiological cohort studies. Survival data can be thought of as being generated by what is called a “failure time process”. A failure time process consist of units, such as individuals, government, countries and so on that are observed at some starting points, such as individuals, government, countries and so on that are observed at some stating  point in time. These units are in some states. For example, the individual is healthy, the government is in power, a country is at peace and so on, and is observed over time. At any given point in time, these unit are at “risk” of experiencing some events, where an event essentially represents a change or transition to another state. For example, the individual dies, the government falls from power, a country is at war etc. after the event is experienced, the unit is either no longer observed or it is at risk of experiencing another kind of event. In some circumstances, units are not observed in experiencing an event; that is no transition is made from one state to another while the unit is being observed. For example, the individual remains healthy, the government remains in power, the country remains at peace and so on. These cases are called “censored” somce we do not observe the subsequent history of the unit after the last observation point. Censoring is endemic to survival analysis data. It is defined as the loss of observation on the life time variable of interest in the process of an investigation. In survival data, censoring frequently occurs for many reasons. In clinical trials, the effectiveness of new medical treatment for a particular disease is investigated. A patient for example, may be lost to follow up due to migration or health problems. Censoring occurs when a subject does not have an event during the observation time, meaning that we cannot observe what has happened subsequently on the subject.

According to kilenbaum and klien (2005), there are generally three reasons why censoring may occur; when a person does  not experience the event before the study ends; when a person is lost to follow-up during the study period; when a person withdraws from the study because of death (if death is not the event of interest) or some other reason. There are different types of censoring. They are right censoring, it left censoring and interval censoring. Right censoring is the most common type of censoring, it occurs when the observation is terminated. In other words, it occurs when a subject leaves the study before an event occurs. For example, consider the patients in a clinical trial for the study of effect treatments on stroke occurrence. The study ends after five years, those patients who have no strokes by end of the five yars are said to be right censored. Also, in a study of divorce, couples that do not divorce during observational period are right censored. Left censoring rarely occur, it happens when an event is known to have occurred before some particular time, but the exact time is unknown. For example, infection with some sexually transmitted disease such as HIV/AIDS.

Another example is in a study of first marriage, if a person is known only to have married before age 20, that person’s marriage age is left censored. For interval of time but the individual or subject is known to have experienced an event within an interval of time but the actual survival time is not known, then an interval of time. For example, infection with sexually-transmitted diseases such as HIV/AIDS with regular testing. e.g. annually.

Another feature of survival data is” truncation”. Truncation refers to complete lack of information about the occurrence of the event. It is a condition other than the event of interest that is, for example, used to screen respondents or patients (Klein and moeschberger, 1997).

Right-truncation occurs, but is less frequent. Klein and Moeschberger (1997) provided the example of the examination of an episode from HIV infection until the development of AIDS.

If the sample only includes those who have developed AIDS prior to the end of the study, those HIV-infected individuals who have not yet progressed to AIDS are excluded from the sample. Another type of truncation is interval or gap truncation, which is similar to left truncation. This could occur in a clinical study if, for example, a patient is under observation for the first 3 months of the study, drops out for 2 months and then rejoins the study again for the last 7 months. Dropping out of the study for 2 months creates an interval or gap in the period of observation. Both left and interval truncations are dealt with during analysis by omitting the subject from all individual in the study (in a binary-outcome analysis) during the truncation period (or gap) due to the fact that they could not have experienced the event during those periods.

1.2        Statement of the Problem

Weibull, weibull-pareto and weibull distribution models are parametric models. These models are mostly used in the analysis of survival data in clinical research. It has not been established which model among the three that is most efficient in the analysis of survival data. This study therefore, compared the three models towards establishing that would be most suitable for the analysis of survival data in clinical research.

1.3        Motivation

The research topic is researchable and one of the interesting, changeable compounded topic. I am motivated because of the compounded nature of models.

1.4       Scope of the Study

This is a study that dealt with women who were diagnosed will breast cancer in Federal Medical Center Gusau. The range of women ages is 20 years and above.

1.6    Aim and objectives

Cancer disease differs, as the models used for cancer studies also differs. This study aim to investigate weibull distribution model in assessing the best comparative the best comparative model that fits breast cancer data in clinical research.

The specific objectives were to:

i.                    Fit the three models used in the survival analysis using data on breast cancer.

ii.                  Evaluate the models used the study of survival analysis using model comparison.

iii.                Select the best model using Alaike information criteria.

1.7     History of Cancer Disease

Human cancer is probably an old as human race. The word cancer came from the father of medicine, Hippocrates a Greek physician. Hippocrates used the Greek words, “carrions” and “carcinoma” to describe tumor thus, calling cancer “Karkinos”. These Greek terms actually were words that describe a “crab”, which Hippocrates thought a tumour resembled. Tumour is abnormal mass of new tissue growing in or on the body, causing cancer disease; it destroys parts of the body, often causing death. Although, Hippocrates was certainly not the first to discover the disease. The history of cancer began much earlier. Cancer is one of the ten causes of death of the world population. World health organization (WHO)’s International Agency for Research on Cancer also found the number of cancer-related deaths increased from 7.6 million in 2008 to 8.2 million in 2012. The most commonly diagnosed types of cancer were lung cancer, breast cancer and colorectal cancer, which made up 13 percent, 11.9 percent and9.7 percent of the total, respectively (WHO, 2012).

1.7.1  Causes of Cancer Disease

Normally, the body makes new cells when they are needed for the growth or repair of damage parts of the body. This cells growth is controlled by a group of genes that works together. When one or more of these genes is damaged (or mutated), too many cells are produced. These excess cells clump together to form a tumor resulting in cancer. Genes can be mutated by bad chemicals in a person’s environment, like tobacco smoke, but more often, damage to growth control genes occurs spontaneously in only a few cells of the body, that is why a tumor is typically found or at least begins in just one spot.

Cancer is not just one disease, but a large group of almost 100 diseases. Its two main characteristics are uncontrolled growth of cells in he human body and the ability of these cells to migrate from original site and spread to distant sites. If the spread is not controlled, cancer can result in death. (American Cancer Society, 2012).

1.7.2 Types of Cancer

Cancer has the potential to affect every organ in the body. The cells within malignant tumor have the ability to invade neighboring tissues and organs, thus, spreading the disease. It is also possible for the cancerous cells to break free from the tumor and ent4er the blood stream, in turn spreading the disease to the organs. This process of spreading is called metastasis.

Some to the different types of cancer are:

Blood cancer, bone cancer, brain cancer, breast cancer, digestive/gastrointestinal cancer, endocrine cancer, respiratory cancer, skin cancer, prostate cancer, cervical cancer.

1.7.3    Diagnosis of Cancer

Diagnosis begins with physical examination and a complete medical history. The doctor observe, feel and palpate (apply pressure by touch) different parts of the body in order to identify any variations from the normal size. As detect thyroid cancer, the doctor will observe the front of the neck for swelling. A doctor may conduct a thorough examination of the skin to pelvis is used to detect cancers of the ovaries, uterus, cervix and vagina. Breast examination includes visual observation where the doctor looks for any discharge, unevenness, discoloration or scaling, he palpates both breasts to feel for masses or lumps.

For males inspection of the rectum and the prostate is also included in the physical examination. The doctor inserts a gloved finger in to the rectum and rotates it slowly to feel for any growths, tumors or other abnormalities. If the doctor detects an abnormality on physical examination, or the patient has some symptom that could be indicative of cancer, the doctor may order diagnostic tests.

A blood test for cancer is easy to perform, usually inexpensive and risk-free. Blood tests can be either specific or non-specific. Often, in certain cancers, te cancer cells release particular proteins (called tumor makers) and blood tests can be used to detect the presence of these tumor makers. Blood tests are generally more useful in monitoring the effectiveness of the treatment, or in following the course of the disease and detecting re-occurrence of the disease.

1.7.4    Treatment of Cancer

Treatment and prevention of cancers continue to be the focus of a great deal in cancer research. Research in to new cancer therapies included cancer targeting gene therapy, virus therapy and a drug that stimulate apoptosis or self-distraction of cancer cells, but not healthy of cancer treatment is to remove all or reduce as much of the tumor as possible and prevent the recurrence or spread of the primary tumor. If the cancer is very aggressive and a cure is not possible, then the treatment should be aimed at relieving symptoms and controlling the cancer for as long as possible. Cancer treatment can take many different forms, and it is always tailored to the individual patient. The decision of which the type of treatment is the most appropriate depends on the type and location of cancer, the extent to which it has already spread the patient’s age, sex, general health status and personal treatment preferences.

The major types of treatment are:

Surgery, radiation, chemotherapy, immunotherapy, hormone therapy and bone-marrow transplantation (America Cancer Society, 2012).

Surgery:- surgery is the removal of a visible tumor and is the most frequently used cancer treatment. It is most effective when a cancer is small and confirmed to one area of the body.

Radiation: radiation kills tumor cells. Radiation is used alone in cases where tumor is unsuitable for surgery. Most often, it is used in conduction with surgery and chemotherapy. Radiation can either be external form of radiation, the radiation is aimed at the tumor from outside the body. In internal radiation, (also known as brachytherapy), a radioactive substance in the form of pellets or liquid is paced at the cancerous site by means of a pill, injection in a sealed container.

Chemotherapy: this is the use of drugs to kill cancer cells. It destroys the hard-to-detect cancer cells that have spread and are circulating in the body.

Immunotherapy: this uses the body’s own immune system to destroy cancer cells. This form of treatment is being intensively studies in clinical trials and is not widely available to most cancer patients.

Hormone therapy: hormone therapy Is a standard treatment for some types of cancer that are hormone-dependent and grow faster in the presence of a particular hormone. These include cancer of the prostate, breast and uterus. Hormone therapy involves blocking the production or action of these hormones. As a result, the growth of the tumor slow down and survival may be extended for several months or years.

Bone marrow transplantation: the bone morrow is the tissue within the bone cavities that contains blood-forming cells. Healthy bone marrow tissue replenishes the blood supply and is essential to life. Sometimes the amount of drugs or radiation needed to destroy cancer cells also destroys bone marrow. Replacing bone marrow with healthy cells counteracts this adverse effect. A bone marrow transplant is to removal of marrow from one person to the transplant of the blood-forming cells either to the same person or to someone else.

1.8       Breast Cancer

Breast cancer is a type of cancer originating from breast tissue, most commonly from the inner lining of milk ducts or the lobules that supply the ducts with milk (sariego, 2010). Cancers originating from ducts are known as ductal carcinomas, while those originating from lobules are known as lobular carcinomas. Breast cancer occurs in humans and other mammals. While the overwhelming majority of human cases occur n women, male breast cancer can also occur. Breast cancer is the most frequent cancer in women while it is the second one in all humans. Although its prevalence changes in different societies, it is known that one out of 8-10 women in western society would have breast cancer during their life span. The mortality rate of breast cancer was calculated as 3%. The prevalence of the disease is especially higher in the North America and European countries than the rest of the world (Stewart and Kleihues, 2003).

In 1990, the world health organization (WHO) conducted a study in which 796,000 breast cancer cases were reported out of which 314,000 deaths occurred. In 2002, 1,152,000 new cases and 411,000 deaths were detected in  a study, conducted by international agency on cancer for research (IARC) under WHO administration. According to all phases of the disease, the five year survival rate has been reported as 73% un developed countries and 52% in developing countries. The significant difference between those two values can be explained by early diagnosis via mammography scans and better treatment in development countries. Breast cancer is a disease found mostly in females, and it is a genetic transmission disease, causing by abnormal.

Hormones, obesity and food with high fats and spreading of cancer from other part of organs to breast (wingo, et al 1995). Therefore breast cancer is considered as a major health issue worldwide (Harichi, et al 2001).

1.9       Definition of terms

Breast: is a protruding organs on the upper front of a woman’s body which as secrete milk after childbirth.

Cancer: is a disease caused by an uncontrolled division of abnormal cells in a part of the body.

Breast cancer: is an uncontrolled growth of breast cells.

Tumor: simply refers to a mass. This is general term that can refer to benign (generally harmless) or malignant (cancerous).

Surgery: is the especially of medicine that treats disease and disorders by cutting, removing or changing the body with an operative that opens the body for therapy.

Radiation: is the emission of energy as electromagnetic waves or as moving subatomic particles, especially high-energy particles which cause ionization.

Chemotherapy: is the treatment of disease by the use of chemical substances, especially the treatment of cancer by cytotoxic and other drugs.

Immunotherapy: is the prevention or treatment of disease with substances that stimulate the immune response.

Hormone therapy: hormone therapy medicines are whole body (system) treatment for hormone-receptor-positive breast cancers.

Bone marrow transplant: is a procedure to replace damaged or destroyed bone marrow with healthy bone marrow stem cells. Bone marrow is the soft, fatty tissue inside your bones.

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