Fossil Fuels As A Source Of Energy - 2044 Words

Since the evolution of science, many people have become solely dependent on a variety of technologies to supply their essential needs of life. A key technology that people have a high level of dependency on is fossil fuels. Fossil fuels are a source of energy people use in their everyday life as a way to get light, electricity, and to keep warm. Fossil fuels are perceived as a nuclear energy, which has been around for decades. Initially, scientists perceived this type of energy as affordable and safe; however, in the late 20th century, danger of nuclear plants began to threat regions of United States. Due to the increase of global warning from the burning of fossil fuels, climate scientists and environmental experts are considering ways to replace nuclear energy (Ferguson). Since the world uses fossil fuels as a source of energy supply, it would be beneficial if the world considered using alternatives means of energy sources once all the present energy has been used up. The world wou ld greatly benefit from these alternatives since the production of present energy is polluting America. Yet with the world being greatly overpopulated and having insufficient supplies of resources, scientists all across the nation are thinking of ways to replace fossil fuels with alternative energies. Therefore, the purpose of this paper is to explicate alternatives people could use as a source of energy instead of being merely dependent on fossil fuels, and the advantages and disadvantages ofShow MoreRelatedFossil Fuels : The Source Of Energy1709 Words   |  7 Pagessociety fossil fuels are the primary source of energy for most of the industrialized world. Utilizing fossil fuels has been vital to the industrialization development. Throughout industrialization of many parts of the world, energy has been needed at a much higher density then before and fossil fuels have fulfilled that need. Coal, gas, and oil are the three major sources of fossil fuels in the world. Despite other me ans of energy, such as wind power, hydroelectric power and so on, fossil fuels are stillRead MoreFossil Fuels : The Source Of Energy2902 Words   |  12 PagesAlthough fossil fuels are the main source of energy on Earth, there are several other forms of energy that are gaining in popularity. Alternative energy, or renewable energy, is a more environmentally and economically friendly source of energy. There are four main forms of alternative energy; solar, wind, nuclear, and hydroelectric. Each source has several different advantages over fossil fuels as well as disadvantages of use and durability. Using these renewable sources as the main provider of energyRead MoreRenewable Energy Sources For Fossil Fuels1240 Words   |  5 Pagesas fossil fuels in order to provide us energy. Almost everything we use nowadays consumes power in some form, and in tandem we rely on energy. Fossil fuels have become the go to resource for providing power. Fossil fuels include natural resources such as coal, petroleum, and natural gas. These fossil fuels fall under the non-renewable category because they take thousands of years in order to form naturally and cannot be replaced as fast as they are being consumed. Another non-renewable energy sourceRead MoreAlternative Energy Sources For Fossil Fuels2676 Words   |  11 Pages Alternative Energy Sources Emily Lazovich Gwynedd Mercy University Abstract Fossil fuels can be easily found around the globe and the production of these fuels may be cost-effective. Although fossil fuel is harmful to the environment, the United States is continuing to use fossil fuel as a source of energy. In addition to this, once the fossil fuels have all been used up, there is no chance of obtaining more. There are many types of alternative energy sources in the world thatRead MoreFossil Fuel And Alternative Sources Of Energy1218 Words   |  5 Pages Energy Policy Jameisha Lyttle Gwynedd Mercy University Abstract The United States government, as well as many others around the world, have relied on fossil fuel as an energy source for a long period of time. The extraction, production, and development of these sources have contributed to the many issues with the environment. In addition to this, fossil fuel will not exist forever because there is a limited amount on earth and it cannot be restored. For this reason, the UnitedRead MoreAlternative Sources Of Energy For Fossil Fuel1432 Words   |  6 Pages In this day and age, finding an alternate source of energy to fossil fuel is essential. Humans are using up fossil fuels, such as coal and oil, faster than they can be made naturally.This means that there will be a time when all of the fossil fuels will have been used to power . To prevent a world without energy, many alternative sources have been harnessed. Six different pathways for energies were found: solar power, biomass, geothermal power, hydropower, wind power, and nuclear power. All o fRead MoreAlternative Energy Sources Of Fossil Fuels1701 Words   |  7 Pages the world has run on fossil fuels. Fossil fuels are critical to global energy infrastructure due to their inherent advantages and generate significant economic value as a result. However, the negative economic and environmental implications of fossil fuels demands a permanent transition towards alternative energy. The world will continue to investigate alternative energy sources and must commit to them to avoid long-term environmental degradation. Ultimately, fossil fuels are on the way out, butRead MoreFossil Fuels : An Alternative Source Of Energy1715 Words   |  7 PagesIntroduction: Fossil fuels have been keeping our country running for quite a long time, throughout our history. The reason why fossil fuels have been so instrumental in our production of energy is the increase in technology. Technology has brought the world ways to dig into the earth and extract oil, which we have been doing quite a bit more of as late. The problem with this increase in drilling and digging for fossil fuels is that there is only so much of it, and cannot be created, or reused. OnceRead MoreAlternative Energy Sources For Fossil Fuels1874 Words   |  8 Pagesconsuming energy. Currently the majority of this energy comes from fossil fuels (i.e. coal, natural gas, and oil). Fossil fuels made up eighty-seven percent of the energy consumed worldwide in 2012 (Gonzalez Lucky). There are many people who do not believe there is an energy crisis, or that there is anything wrong with depending on fossil fuels, however fossil fuels are non-renewable, which means once they are gone we are una ble to create more. In addition, the carbon that is located in fossil fuelsRead MoreFossil Fuels And Alternative Energy Sources1682 Words   |  7 PagesMost fossil fuels such as oil, natural gas and coal are considered nonrenewable resources in that their use is not sustainable because their formation takes billions of years (Investopedia, 2014). As the nonrenewable resources become more and more scarce, the cost to obtain them will continue to gradually rise (Investopedia, 2014). Eventually, the price will become so high that users will no longer be able to afford them, forcing the change from fossil fuels to alternative energy sources (Investopedia)

The Effects of Global Warming on Our Planet Essay - 576 Words

The Effects of Global Warming on Our Planet Global warming, professionally also called the climate change represents nowadays a critical global issue posing a serious potential threat. This simply means that the average temperature of our planet is slowly rising. This however is not due to the natural causes as it was in the past but due to people and their activities, which permit the so-called greenhouse gases to be emitted into the atmosphere. This has already taken its toll in terms of altering the weather and subsequently the conditions of the whole planet and might also have consequences for the future. Therefore this essay will, in the next few sections explore the impacts that global†¦show more content†¦A further contribution to problems is also a refusal of certain countries to ratify Kyoto agreement, an agreement to reduce emissions. As a result, gases gathered in the atmosphere form a layer around our planet which functions as a greenhouse thus warming the planet. There are several implications emanating from this. First of all, the temperatures rise considerably. According to statistics in last two hundred years the temperatures increased by 0.6 degrees (Velhora, 2004). This led to a further series of interlocked issues e.g. melting and retreating glaciers and rising sea levels. Large areas of ice help to control the world?s temperature by reflecting the sun?s rays. However, reduction of ice sheets exposes more areas of water, which absorbs the heath from the sun reducing areas of ice still further (Johnston, 2005). In addition, rising sea levels also led to an excessive erosion of cliffs (Hall, 2005). Climate change also affected the species distribution. Due to the warming certain insects and plants expand their range (Hall, 2005) thus reducing the space of other species. As a consequence of spring coming earlier trees are blooming earlier as well as earlier nesting birds risking that the chicks will hatch before their usual food supply is available (Henderson, 2005). Considering what further effects a global warming might have it is crucial to takeShow MoreRelatedThe Effects Of Global Warming On Our Planet1396 Words   |  6 Pages There is no doubt that global warming becomes one of the most dangerous, serious and popular issues in the 21st century. It is possible to identify the probable and effective solutions by means of the population around the world to reduce negative effects on our planet. Joseph and Roy (2014) points out 97% of the scientists and professionals are trying to discover the best explanations, which can prevent our world from violent disasters that can damage the lives and wealth of all nations and animalsRead MoreGlobal Warming and Its Effect on Our Planet2763 Words   |  12 PagesIntroduction Nowadays, Global warming is an incontrovertible fact, which proves that our planet and its climate are in trouble. Well global warming is a term that denotes a slow warming of the earth’s regular temperature. It was also named exclusively man-made effects, in particular carbon dioxide. Carbon dioxide has largely increased during the past forty years, and scientists concluded that the average earth temperature has increased solely based on man-made activities suchRead MoreThe Effects Of Global Warming On Our Future On A Hotter Planet1829 Words   |  8 Pages21st, global warming rates have increased by unprecedented amounts. As the Earth’s changing climate becomes a pertinent issue for nature and human society, climate scientists continue to predict the effects that rising temperatures will have on the whole planet in the future. Notably, in 2008, environmental activist Mark Lynas examined aspects of global warming, like rising sea levels, natural disast ers, and overall temperature changes in his book â€Å"Six Degrees: Our Future on a Hotter Planet.† LynasRead MoreThe Effects Of Global Warming On Our Planet s Ecosystem1173 Words   |  5 PagesMother Earth is burning as we speak; humanity has killed our precious Earth. Global-warming is a vicious killer that was created by the humans on this Earth, and there s no way to cure it. We, as humans, have the power to cleanse the Earth, but instead we destroy it. Heat is absorbed by carbon dioxide and greenhouse gases. A greenhouse gas absorbs thermal radiation emitted by the Earth s surface. As the sun s energy reaches the Earth’s surface, some of it is released into space, some is absorbedRead MoreThe Issue Of Global Warming1338 Words   |  6 PagesOver the past years, the controversial issue of global warming has been primarily brought to the attention of the public. Global warming is generally assumed to be the main cause of rising average global temperature. The cli mate on the Earth is changing and there is no big surprise. It is believed that global warming is caused by many natural and manmade activities, which is affecting the planet by the seconds, minutes, hours, days, and years. Many may not even care about this serious issue, butRead MoreThe Potential Cause Of Global Warming1689 Words   |  7 PagesThe potential causes of global warming are debated about by many scientists. Many scientists believe that global warming is natural while others believe it to be caused by mostly humans. Global warming may be completely natural for many reasons. First, Earth tends to go through cycles of heating and cooling and this wouldn’t be the first time our planet has begun to heat up unexpectedly. Second, nobody can directly correlate humans with global warming, we may emit CO2 but that doesn’t mean we causedRead More The Severe Effect of Global Warming Essay1266 Words   |  6 PagesGlobal Warming When we think of global warming, we think about Air pollution, rise of temperature, melting glaciers, carbon dioxide emissions and so no. But even though we know that these factors could lead to a global catastrophe, very often we do not realize what king of severe effect the global warming could have on our planet. Imagine that you are placed into the future. It is some where around 2050. You begin to live in this new world, but the planet is not the same any more. You hear aboutRead MoreGlobal Warming: The Release of Greenhouse Gases986 Words   |  4 Pagesthe truth about global warming. It seems that everyone else has been tagging along as well. It has become a great concern that people aren’t aware of what global warming actually is, and citizens leave it up to politics to decide for them. So, What is Global Warming? There is a process that occurs in our atmosphere called the Greenhouse Effect. The natural release of greenhouse gasses from our planet is done to keep our planet warm. What occurs is these gasses are released into our atmosphere, inRead MoreClimate Change And Global Warming1630 Words   |  7 PagesClimate Related Threats Global warming will lead to uncontrollable devastation such as famine, war, and economic instability. Climate change will accelerate the dislocation of hundreds of millions of people and the extinction of many species. The negative effects of climate change are obvious on every continent. Professor Le Quere, director of the Tyndall Centre for Climate Change Research at the University of East Anglia said, The human influence on climate change is clear. The atmosphere andRead MoreThe Warming Of The Arctic Antarctic And Greenland Ice Sheets Have Lost 5.5 Trillion Tons Of Ice1262 Words   |  6 PagesThe Earth’s climate is constantly changing, and unfortunately it’s not for the better. Our planet that everybody calls home has a complex environment engulfed with diversity. These complexities also differ among location, which result in warm and cold regions. The regions also shift temperatures according to the location of our planet orbiting our sun. There is definitely a n overall trend around the world that our climate is increasing in temperature. Even if it’s too slight to be noticeable, it’s

Greek and Roman Cultures Free Essays

Alicia Battles AIU-Online Cultural Topics November 11, 2012 Abstract In this assignment I will compare and contrast Greek and Roman Culture. I will discuss the likes and differences of their government, geographic terrain, economics, trade practices, art, architecture, philosophies, and religious beliefs. Greek Terrain- city states separated by hilly countryside and all near water Art- ideal artistic form (Superior to Roman art) Economy- grew wheat, produced, wine and olive oil; thought trading was degrading Social classes- slaves, freedmen, metics, citizens, women; women were not considered citizens Government- kings originally ruled, then oligarchy, then democracy Religion- cupid God of Love, Ares God of war, based on human personality traits, Love, Honor, Hatred, Dignity, also their roles in life determined what they were god of; Zeus: sky/weather, Hades: death, Poseidon: sea, aquatics; Physical life was of importance instead of eventuality of the afterlife; Each god had characteristics that determined their actions; Deities were important for progression of life but mortals were just as Both Geographic Terrain- Mediterranean countries Economy- based on agriculture, worked mines, had slaves, produced wine and olive oil, coinage, divided by wealth Religion- same gods but different names and traits Government- originated by kings Philosophy- slowly emerged out of religious awe into curiosity about the principles and elements of the natural world. We will write a custom essay sample on Greek and Roman Cultures or any similar topic only for you Order Now When Greek population moved to their cities interest changed to social living. Roman Terrain- Rome was inland, and on one side of the Tiber River Art- realistic portraits for decoration Economy- imported wheat, farmers, and also engaged in trade Social Classes- slaves, freedmen, plebeians, patricians Women were considered citizens Government- Kings originally ruled, then mixed republican form, then emperors Religion- Eros god of love, Mars god of martial fertility, Deities named after objects; mortals did good deeds to be rewarded in the afterlife; they strove to gain their place with the gods in heaven Religion- gods not gender specific so their individual characteristics were not central to the myths; myths based in brave, heroic deeds of gods not mortals as mortal life was not important after death; Not individualistic; a warrior found sacred; actions more important than words; gods had no physical mportant as it was their contribution in society that mattered in the end; Individualistic: individuals had more consequences for their actions than that of a group Physical work not as important as creativity Gods were beautiful, bodies, muscles, eyes and hair made them more beautiful. Architecture- Buildings made of wood, clay, or mud bricks, limestone, marble, terracotta, plaster , and bronze; buildings were of the type of religious, funerary, domestic, civic, or recreational themes ppearance; Architecture- Rome adopted most of its architecture from Greek architecture References: http://www. britannica. com/EBchecked/topic/1350843/Western-philosophy/16256/Shifts-in-the-focus-and-concern-of-Western-philosophy http://www. differencebetween. com/difference-between-greek-and-vs-roman-archit ecture/ http://www. diffen. com/difference/Greek_Gods_vs_Roman_Gods http://ancienthistory. about. com/od/greecevsrome/ss/GreecevsRome_8. htm How to cite Greek and Roman Cultures, Essay examples

Failure of Leadership-Free-Samples for Students-Myassignmenthelp

Question: Discuss about the Failure of Leadership. Answer: Introduction: Leaders can be defined as the individuals who take on the responsibility of guiding a group of subordinates in order to help them meet the objectives of organizations. The leaders influence and encourage the subordinates in ways by which they can effectively overcome different barriers that come in their ay and reach their goals (Hill Bartol, 2016). Leaders are responsible for helping them realize their potential and make them work beyond their capacity to reach the zenith of success. One of their main weapons is their potential to motivate the employees that help them to overcome different stress and help them deliver their best work (Hojat et al., 2015). Researchers are of the opinion that in order to develop leadership skills, every individual need to reflect regularly on both their positive and negative traits (Saeed et al., 2017). This would help strengthen their positive aspects, overcome different barriers, and modify their negative traits to provide guidance that helps every organization to achieve their mission and vision (Priest Gass, 2017). This assignment will reflect how failed leadership situation helped me to enhance my skills of communication and team management skills helping me for preparing myself for a bright future. The first step of Gibbs reflective cycle is the description of the event. During the placement months, I was assigned the position of a team leader to manage a team of about eight people. I was given an assignment to complete within an assigned date. I called each of the individual of the team and allocated their respective task. One of the members tried to provide me a suggestion stating that rather than assigning one piece of work to one member. I should allocate one place of work to two members that would reduce the chances of failing to meet the deadlines. I did not listen to him completely and cut him out stating that since I am the leader, my orders need to be adhered to. I tried to be very strict with them so that they do not waste their time in gossiping and not doing their work. I did not allow anyone to talk with each other on the floor to maintain discipline. One of the members could not submit me the work and missed the deadline that I had given her. I could not control m y anger and shouted on her following which she never continued me directly on the floor. Moreover, when one of the members came to me and asked me that he was not able to complete their work due to personal issues, I blamed him stating that these are all excuses that he was making for not completing the work. The next day he put forward a resignation letter that made me quite nervous. I became so nervous that I lost my confidence and could not manage the team effectively. Moreover, there arose many situations where huge fights took place between the subordinates where each blamed each other for failure of completion of work. All these resulted in the failure of the assignment and my mentor severely criticized me. The second step mainly says what the individuals was feeling and thinking during the incidences. When I was given the responsibility to complete the assignment with the help of teamwork, I thought that if I have to make the work complete successfully, I need to be quite strict with the subordinate. I thought, if I allow them to communicate and interact on the floor, they would spend most of the time of the day in informal interactions that may result them in failing to meet the requirement. I also thought that they are making excuses as they had wasted their time and required more time to complete the work. I thought if I allow them more time, the assignment will not be completed within time and would thereby fail. The pressures of meeting the deadlines made me nervous and therefore I shouted in anger on the individual who came to me for help. I could not control my emotions that time. I became quite nervous when one of them submitted his resignation, as I could not understand what m istake I had made that resulted in taking him such a big decision. The failure of the entire project made me quite upset and I felt both confused and upset about the reasons that had resulted in failure of the teamwork. The third step of the cycle is the evaluation stage that mainly involves stating what was good and bad about experiences. Many negative factors were associated with the incident. Due to my improper leadership, the subordinates develop a very negative feeling about me. They developed a feeling that I was rude and they decided never to work under my guidance. This created a very negative image of mine that affected my career. Such negative image in the very beginning of my career had the potential to affect my future prospects. Moreover, I lost my self-confidence entirely and could not gain courage to overcome the negative vibes that I was receiving. My mentor who had trust on me and provided me with the opportunity to exhibit my leadership trait was also very upset about the bad performance that I had put forward. I felt very sad for letting down his expectations. However, the positive aspect of the incident was that this incident helped me to realize that my leadership traits were no t up to the mark and I do not have proper knowledge about how to manage a team and lead a team towards success. Therefore, it helped me to realize that I need to work more on my leadership skills and team working skills so that I can become successful in my future leadership projects. The fourth important step is called the analysis step. This step helps individuals to make senses from the situations. After discussing with my mentors as well as after going through several research articles, I realized the mistakes that I had conducted in my leadership. I realized that I do not have proper communication skills. I am an impatient listener and I do not have effective feedback giving and listening skills. Cutting out subordinates in middle of their suggestions make them feel disrespected as they feel that they do not have power or acceptance in the organization (Chuang, Jackson Jiang, 2016). They feel that their suggestions are not respected and this affects employee and teams morale that in turn affects human relations. Moreover, I neither allowed the employees to communicate among them nor arranged for any meetings with effective and constructive feedback giving and receiving sessions in the team. Due to lack of effective communication and encouragement of communic ation from my side, bonding and relationship did not develop. Researchers are of the opinion that rapport building is one of the most importance aspects of teamwork that strengthened human relations in workplace (Kozlowski et al., 2015). The stronger the relationship between employees, the better is productivity as employees not only shared work burden but also engages in informal discussion that releases pressure (Scully, 2015). Emotional turmoil in employees can be handled effectively by proper communication that prevents burnout (Hargett et al., 2017). Besides, I also realized that I have poor emotional intelligence. I have poor self-regulation skills for which I cannot control my emotions properly. Therefore, when I became angry I could not keep myself calm and shouted on the employee that affected her self-respect. Researchers are of the opinion that individuals who have higher self regulation capability can maintain trustworthiness and integrity, openness to change and enjoy c omfort with ambiguity (Hojat et al., 2015). I also did not have poor empathy for which I could not connect with the pain and emotion of the employee who could not complete the work due to personal issues. In place, I was rude with him which made him upset. He felt that the organization does not trust him and cannot pay importance to the concerns and issues he is facing. I also could not motivate and inspire them to work and my leadership trait was more autocratic than transformational. Researchers suggest that transformational leadership in the 21st century is essential to bring out the best productivity where motivation and leading by example is most important (Carter et al., 2015). I was unnecessarily strict with them that affected their self-esteem, their morale and made them burnout easily. Therefore, they were not able to exhibit effective teamwork and even failed to meet the productivity and deadline. The next step is called the conclusion phase where the individual needs to state what else he should have done in the incidents. I should have exhibited proper listening skills and should not have cut down the employees in midst of their suggestions. I should have been empathetic to both the employees who could not complete their work and should have tried to understand their issues and helped them in return. I should have inspired all the members to communicate with each other and arrange or meetings where I would have motivated them to work beyond their capabilities to meet the goals. I should have provided more importance to rapport building among the employees so that they can establish good bonds with each other and show effective teamwork. I should not have been strict with them and in place be friendlier with them by sharing their concerns and guiding them with the work where they were stuck. This would have led to success of the assignments (Dubrin et al., 2015). The next step is called the action plan stages that help individuals to prepare with the action plan that they would apply if the events occur again. When I get such leadership projects form next time, the most important aspect I would pay importance to is rapport building between the employees and effective communication with the employees and among the employees. Researchers are of the opinion that rapport building enhances human relations and helps to overcome stress, pressure, anxiety and emotional turmoil (Matthews McLees, 2015). This aspect also enhances productivity. Moreover, I will arrange for effective constructive feedback sessions every week so that employees can open up to about their concern and disclose their suggestions for each other in a constructive manner. Such sessions would help in developing relationship among the employees (Schaik et al., 2014). Moreover, I will also work on my emotional intelligence attributes so that I can emotionally connect with my subord inates and motivate them to perform the best. From the entire discussion above, it had been easily understood the three aspects which are very important for effective teamwork and leadership helping in developing human relations at workplace. These are effective communication skills, proper rapport building in teamwork and high emotional intelligence. Every leader should develop the mentioned attributes so that they can help their subordinates meet the organization goals and reach the zenith of success References: Carter, D. R., Seely, P. W., Dagosta, J., DeChurch, L. A., Zaccaro, S. J. (2015). Leadership for global virtual teams: Facilitating teamwork processes. InLeading global teams(pp. 225-252). Springer, New York, NY. Chuang, C. H., Jackson, S. E., Jiang, Y. (2016). Can knowledge-intensive teamwork be managed? Examining the roles of HRM systems, leadership, and tacit knowledge.Journal of management,42(2), 524-554. DuBrin, A. J. (2015).Leadership: Research findings, practice, and skills. Nelson Education. Hargett, C. W., Doty, J. P., Hauck, J. N., Webb, A. M., Cook, S. H., Tsipis, N. E., ... Taylor, D. C. (2017). Developing a model for effective leadership in healthcare: a concept mapping approach.Journal of Healthcare Leadership,9, 69. Hill, N. S., Bartol, K. M. (2016). Empowering leadership and effective collaboration in geographically dispersed teams.Personnel Psychology,69(1), 159-198. Hojat, M., Michalec, B., Veloski, J. J., Tykocinski, M. L. (2015). Can empathy, other personality attributes, and level of positive social influence in medical school identify potential leaders in medicine?.Academic Medicine,90(4), 505-510. Kozlowski, S. W., Grand, J. A., Baard, S. K., Pearce, M. (2015). Teams, teamwork, and team effectiveness: Implications for human systems integration.The handbook of human systems integration, 535-552. Matthews, R., McLees, J. (2015). Building effective projects teams and teamwork.Journal of Information Technology and Economic Development,6(2), 20. Priest, S., Gass, M. (2017).Effective Leadership in Adventure Programming, 3E. Human Kinetics. Saeed, F., Wall, A., Roberts, C., Riahi, R., Bury, A. (2017). A proposed quantitative methodology for the evaluation of the effectiveness of Human Element, Leadership and Management (HELM) training in the UK.WMU Journal of Maritime Affairs,16(1), 115-138. Schaik, S. M., O'brien, B. C., Almeida, S. A., Adler, S. R. (2014). Perceptions of interprofessional teamwork in low?acuity settings: a qualitative analysis.Medical education,48(6), 583-592. Scully, N. J. (2015). Leadership in nursing: The importance of recognising inherent values and attributes to secure a positive future for the profession.Collegian,22(4), 439-444. Weinstein, J., Morton, L. H. (2015). Collaboration and teamwork.

JULIE Its my fathers fault that I cant trust men Essays

JULIE: Its my fathers fault that I cant trust men Some Background Data: Julie is interested in exploring her relationships with men. She says that she cannot trust me because I am a man and that she cannot trust men because her father was an alcoholic and was therefore untrustworthy. She recalls that he was never around when she needed him and that she would not have felt free to go to him with her problems in any case, because he was loud and gruff. She tells me of the guilt she felt over her fathers drinking because of her sense that in some way she was causing him to drink. Julie, who is now 35 and unmarried, is leery of men, convinced that they will somehow let her down if she gives them the chance. She has decided in advance that she will not be a fool again, that she will not let herself need or trust men. Although Julie seems pretty clear about not wanting to risk trusting men, she realizes that this notion is self-defeating and would like to challenge her views. Though she wants to change the way in which she perceives and feels about men, somehow she seems to have an investment in her belief about their basic untrustworthiness. She is not very willing to look at her part in keeping this assumption about men alive. Rather, she would prefer to pin the blame on her father. It was he, who taught her this lesson, and now it is difficult for her to change, or so she reports. Jerry Corey's Way of Working with Julie from an Adlerian Perspective Even if it is true that her father did treat her unkindly, my assessment is that it is a basic mistake for her to have generalized what she believes to be true of her father to all men. My hope is that our relationship, based on respect and cooperation, will be a catalyst for her in challenging her assumptions about men. At one point in her therapy, I ask Julie if she knows why she is so angry and upset with men. When she mentions her father, I say: Hes just one man. Do you know why you react in this way to most men even today? If it is appropriate to her response, I may suggest: Could it be that your beliefs against men keep you from having to test your ability to be a true friend? or, could it be that you want to give your father a constant reminder that he has wrecked your life? Could you be getting your revenge for an unhappy childhood? Of course, these interventions would come after we had been working together for a time and trust was established. As part of the assessment process I am interested in exploring her early memories, especially those pertaining to her father and mother, the guiding lines for male and female relationships. We will also explore what it was like for her as a child in her family, what interpretation she gave to events, and what meaning she gave to herself, others, and the world. Some additional questions that I will pose are: a.What do you think you get from staying angry at your father and insisting that he is the cause of your fear of men? b.What do you imagine it would be like for you if you were to act as if men were trustworthy? And what do you suppose really prevents you from doing that? c.What would happen or what would you be doing differently if you trusted men? d.If you could forgive your father, what do you imagine that would be like for you? For him? For your dealings with other men? e.If you keep the same attitudes until you die, how will that be for you? f.How would you like to be in five years? g.If you really want to change, what can you do to begin the process? What are you willing to do? My relationship with Julie is the major vehicle with which to work in the sessions. A male counselor who emphasizes listening, mutual respect, honesty, partnership, and encouragement will give her a chance to examine her mistaken notions and try on new behaviors. A lifestyle assessment will help her see the broad

womens lib essays

womens lib essays Throughout the years, women have been seen as someone to have children, someone to cook, someone to clean, and someone who does not deserve rights. Because two women, Elizabeth Stanton and Susan B. Anthony, fought for equal rights, women today have an equality that was once thought impossible. They began by educating women on the rights they should have, then forming the National Womans Suffrage Association, and finally, together, Elizabeth Cady Stanton, and Susan B. Anthony would change the way that the United States viewed women, they would give them the right to vote. Elizabeth Cady Stanton started the fight for womens rights at a convention in Seneca Falls, New York 1848. She spoke out on the so-called equal rights that women had, saying It is the duty of the women of this country to secure to themselves their sacred right to the elective franchise. With that great statement Elizabeth Cady Stanton showed that women do have an opinion and they want to voice it. As her speech progressed she spoke about the inalienable rights that the constitution granted to all Americans; and how these rights were not given equally to women. Her radical new ideas sparked a controversial battle that would last well into the next century. Elizabeth Cady Stanton was one of the first women to wear bloomers and not a dress around her town and home, causing her husband (a judge) much ridicule and embarrassment. In 1851 at another convention in Seneca Falls, she met Susan B. Anthony, a woman as passionate about the fight for women to vote as she was; oddly enough, they met while Stanton was wearing bloomers. The women immediately became friends, and started full force to gain equal rights for women. Elizabeth Cady Stanton wrote most of the speeches delivered by Susan B. Anthony. Elizabeth Cady Stanton became the woman behind the scenes, and as the years progressed so did their fight. ...

Case Study Essay Example | Topics and Well Written Essays - 250 words

Case Study - Essay Example One of the filmmaking characteristics that differs American cinema from French cinema is that French filmmaking is somewhat dull and sloppy whereas American filmmaking involves such characteristics, which are able to attract a vast majority of public towards the cinema. â€Å"The actions of characters in American cinema are largely done to reveal a general character trait which distinguishes itself from French cinema† (Smith). Another difference between the cultures of two countries is that French art and entertainment industry is closely linked to the political parties of France whereas in the United States, there is no such influence of politics on the entertainment industry. France is the third largest foreign market for the American movies whereas in the United States, foreign markets are able to capture less than 2 percent of the box office. Therefore, we can say that at present, American film market is really dominating the French market and it has the potential to invad e rest of the European film markets as well in the near future. Works Cited Smith, Jonathan. â€Å"Differences Between American and French Cinema.† Wordpress.com, 09 Jul. 2007 Web. 27 Dec. 2010.

Global Strategies to Eliminate Hunger Essay Example | Topics and Well Written Essays - 750 words

Global Strategies to Eliminate Hunger - Essay Example According to the World Food program (2013), food security is a situation where a household has access to food for consumption. Most developed countries such as the United States of America, and China have highly invested in ways to ensure availability food supply to their population (Shapouri, 2010). They ensure that their household s do not live in fear of starvation. Finances have been channeled to projects and researches to help in the production of better strains of agricultural products. Technologically, laboratories and other research institution have been issued with state of the art technology to provide hybrids for most crops. This ensures food security, which involves storage of surplus foods in case of any risks. These risks involve economic meltdowns, natural disasters, and wars. Storage of surplus foods for the future ensures a country’s self-sufficiency (Shapouri, 2010). On the other hand, developing and non-developed countries have also started initiatives and p rograms to help increase food production (Lawrence, Lyons & Wallington, 2010). This has been implemented through financial and technological help from the already developed countries. However, even with this set initiatives, there have been increased cases of hunger and starvation. This is mostly evident in third world countries. Efforts to guarantee food security in most countries have had several setbacks irrespective of increased technological know-how and financial aids. ... For example, in Sudan, conflicts in Darfur region have lasted for a decade and led to displacements of millions of people. This has led to demand for extra food since the camps are in non-productive area. In some situations during war, the enemy may destroy the food reserves to cause defeat. To eradicate hunger in this situation, avoiding wars may prevent hunger since individuals will invest in other ideas to increase food production. Wars and civil conflicts may lead individual governments to channel more funds into purchasing armory and paying military (Peacock, 2012). In case wars are stopped, the funds could be used to invest in new and advanced ways of agricultural production. Moreover, global peace facilitate efforts geared to eradicate hunger rather than countries seeking to advance war ammunitions. Increased diseases such as HIV Aids, cancer, malnutrition have also contributed to cases of hunger and starvation (Lawrence, Lyons & Wallington, 2010). These diseases are mostly fo und in under developed countries due to poverty. Deaths from the diseases lead to loss of labor that provides psychical and mental work force in agricultural farms. In counties such as those in Africa, there are higher mortality rates due to the increased spread of HIV Aids, which leave most of the children as orphans. With increased medical bills, there are reduced funds to purchase and invest in food security. This increases the rates of hunger and starvation in these countries. The economies also suffer a fall in the countries’ Gross National Product due to increased funds being allocated health services. Focusing on how to reduce mortality rates due to major diseases will lead to an increased and strong work force. Investing in agriculture with the labor force will increase the

Integrated Marketing Communication To Build Brands Essay

Integrated Marketing Communication To Build Brands - Essay Example To find a relationship between IMC, market orientation (MO), learning orientation (LO), brand orientation (BO) and brand performance 1000 questionnaires were mailed to 1000 organizations in Australia. MO has a direct positive relationship but LO do not have the relationship. Again BO has the relationship Both IMC and BO have a direct positive relationship with brand performance. IMC has a significant role to play in promoting the performance of the brand in the market. Conceptual approach redefining and supporting the empirical relationship could have been done.To find a relationship between IMC, market orientation (MO), learning orientation (LO), brand orientation (BO) and brand performance 1000 questionnaires were mailed to 1000 organizations in Australia. MO has a direct positive relationship but LO do not have the relationship. Again BO has the relationship Both IMC and BO have a direct positive relationship with brand performance. IMC has a significant role to play in promoting the performance of the brand in the market. Conceptual approach redefining and supporting the empirical relationship could have been done.Laric & Lynagh (2010) Role of IMC in sustainability marketing Based on operations of various firms and organizations, the ways as to how they tackle challenges by IMC Conceptual Approach Role of sustainability is very essential in organizations and IMC plays an effective part in enhancing it The key focus of the research was on sustainability and it has been marked as an important concept for organization. Both sustainability and IMC are important for organizations as they are correlated. A more in-depth analysis could have made the findings more viable. To examine the linkage between IMC and revenue generation. Earlier literature about IMC have been analyzed and propositions formulated and model has been developed Conceptual Approach. Internal marketing has an important role to play in organizations for generating revenue. Internal marketing enha nces the relationships among brand orientation, market orientation, and IMC. Both internal marketings, as well as intra-organizational marketing in the form of IMC, are important for organizational performance Propositions once developed are better evaluated by an empirical approach. To examine the effect of customer and competitor orientation and inter-functional coordination on the brand orientation that in turn affect to brand performance in SMEs. The hypothesis was developed and questionnaires were mailed to 4502 SMEs in Finland regarding the topic. Empirical Approach Customer orientation along with inter-functional coordination has an effect on brand orientation but competitor orientation does not have the relationship. The constructs of IMC has a direct impact on the brand performance.   Brand orientation and market orientation are directly related to the positive performance of the brand. More focus on the core concept of IMC should have been made. To focus on the concept o f IMC as a relationship-building strategy Random sample of communicating professionals from 1000 non-profit organizations were selected and the quantitative online survey was conducted.

Decision Tree for Prognostic Classification

Decision Tree for Prognostic Classification Decision Tree for Prognostic Classification of Multivariate Survival Data and Competing Risks 1. Introduction Decision tree (DT) is one way to represent rules underlying data. It is the most popular tool for exploring complex data structures. Besides that it has become one of the most flexible, intuitive and powerful data analytic tools for determining distinct prognostic subgroups with similar outcome within each subgroup but different outcomes between the subgroups (i.e., prognostic grouping of patients). It is hierarchical, sequential classification structures that recursively partition the set of observations. Prognostic groups are important in assessing disease heterogeneity and for design and stratification of future clinical trials. Because patterns of medical treatment are changing so rapidly, it is important that the results of the present analysis be applicable to contemporary patients. Due to their mathematical simplicity, linear regression for continuous data, logistic regression for binary data, proportional hazard regression for censored survival data, marginal and frailty regression for multivariate survival data, and proportional subdistribution hazard regression for competing risks data are among the most commonly used statistical methods. These parametric and semiparametric regression methods, however, may not lead to faithful data descriptions when the underlying assumptions are not satisfied. Sometimes, model interpretation can be problematic in the presence of high-order interactions among predictors. DT has evolved to relax or remove the restrictive assumptions. In many cases, DT is used to explore data structures and to derive parsimonious models. DT is selected to analyze the data rather than the traditional regression analysis for several reasons. Discovery of interactions is difficult using traditional regression, because the interactions must be specified a priori. In contrast, DT automatically detects important interactions. Furthermore, unlike traditional regression analysis, DT is useful in uncovering variables that may be largely operative within a specific patient subgroup but may have minimal effect or none in other patient subgroups. Also, DT provides a superior means for prognostic classification. Rather than fitting a model to the data, DT sequentially divides the patient group into two subgroups based on prognostic factor values (e.g., tumor size The landmark work of DT in statistical community is the Classification and Regression Trees (CART) methodology of Breiman et al. (1984). A different approach was C4.5 proposed by Quinlan (1992). Original DT method was used in classification and regression for categorical and continuous response variable, respectively. In a clinical setting, however, the outcome of primary interest is often duration of survival, time to event, or some other incomplete (that is, censored) outcome. Therefore, several authors have developed extensions of original DT in the setting of censored survival data (Banerjee Noone, 2008). In science and technology, interest often lies in studying processes which generate events repeatedly over time. Such processes are referred to as recurrent event processes and the data they provide are called recurrent event data which includes in multivariate survival data. Such data arise frequently in medical studies, where information is often available on many individuals, each of whom may experience transient clinical events repeatedly over a period of observation. Examples include the occurrence of asthma attacks in respirology trials, epileptic seizures in neurology studies, and fractures in osteoporosis studies. In business, examples include the filing of warranty claims on automobiles, or insurance claims for policy holders. Since multivariate survival times frequently arise when individuals under observation are naturally clustered or when each individual might experience multiple events, then further extensions of DT are developed for such kind of data. In some studies, patients may be simultaneously exposed to several events, each competing for their mortality or morbidity. For example, suppose that a group of patients diagnosed with heart disease is followed in order to observe a myocardial infarction (MI). If by the end of the study each patient was either observed to have MI or was alive and well, then the usual survival techniques can be applied. In real life, however, some patients may die from other causes before experiencing an MI. This is a competing risks situation because death from other causes prohibits the occurrence of MI. MI is considered the event of interest, while death from other causes is considered a competing risk. The group of patients dead of other causes cannot be considered censored, since their observations are not incomplete. The extension of DT can also be employed for competing risks survival time data. These extensions can make one apply the technique to clinical trial data to aid in the development of prognostic classifications for chronic diseases. This chapter will cover DT for multivariate and competing risks survival time data as well as their application in the development of medical prognosis. Two kinds of multivariate survival time regression model, i.e. marginal and frailty regression model, have their own DT extensions. Whereas, the extension of DT for competing risks has two types of tree. First, the â€Å"single event† DT is developed based on splitting function using one event only. Second, the â€Å"composite events† tree which use all the events jointly. 2. Decision Tree A DT is a tree-like structure used for classification, decision theory, clustering, and prediction functions. It depicts rules for dividing data into groups based on the regularities in the data. A DT can be used for categorical and continuous response variables. When the response variables are continuous, the DT is often referred to as a regression tree. If the response variables are categorical, it is called a classification tree. However, the same concepts apply to both types of trees. DTs are widely used in computer science for data structures, in medical sciences for diagnosis, in botany for classification, in psychology for decision theory, and in economic analysis for evaluating investment alternatives. DTs learn from data and generate models containing explicit rule-like relationships among the variables. DT algorithms begin with the entire set of data, split the data into two or more subsets by testing the value of a predictor variable, and then repeatedly split each subset into finer subsets until the split size reaches an appropriate level. The entire modeling process can be illustrated in a tree-like structure. A DT model consists of two parts: creating the tree and applying the tree to the data. To achieve this, DTs use several different algorithms. The most popular algorithm in the statistical community is Classification and Regression Trees (CART) (Breiman et al., 1984). This algorithm helps DTs gain credibility and acceptance in the statistics community. It creates binary splits on nominal or interval predictor variables for a nominal, ordinal, or interval response. The most widely-used algorithms by computer scientists are ID3, C4.5, and C5.0 (Quinlan, 1993). The first version of C4.5 and C5.0 were limited to categorical predictors; however, the most recent versions are similar to CART. Other algorithms include Chi-Square Automatic Interaction Detection (CHAID) for categorical response (Kass, 1980), CLS, AID, TREEDISC, Angoss KnowledgeSEEKER, CRUISE, GUIDE and QUEST (Loh, 2008). These algorithms use different approaches for splitting variables. CART, CRUISE, GUIDE and QUEST use the sta tistical approach, while CLS, ID3, and C4.5 use an approach in which the number of branches off an internal node is equal to the number of possible categories. Another common approach, used by AID, CHAID, and TREEDISC, is the one in which the number of nodes on an internal node varies from two to the maximum number of possible categories. Angoss KnowledgeSEEKER uses a combination of these approaches. Each algorithm employs different mathematical processes to determine how to group and rank variables. Let us illustrate the DT method in a simplified example of credit evaluation. Suppose a credit card issuer wants to develop a model that can be used for evaluating potential candidates based on its historical customer data. The companys main concern is the default of payment by a cardholder. Therefore, the model should be able to help the company classify a candidate as a possible defaulter or not. The database may contain millions of records and hundreds of fields. A fragment of such a database is shown in Table 1. The input variables include income, age, education, occupation, and many others, determined by some quantitative or qualitative methods. The model building process is illustrated in the tree structure in 1. The DT algorithm first selects a variable, income, to split the dataset into two subsets. This variable, and also the splitting value of $31,000, is selected by a splitting criterion of the algorithm. There exist many splitting criteria (Mingers, 1989). The basic principle of these criteria is that they all attempt to divide the data into clusters such that variations within each cluster are minimized and variations between the clusters are maximized. The follow- Name Age Income Education Occupation Default Andrew 42 45600 College Manager No Allison 26 29000 High School Self Owned Yes Sabrina 58 36800 High School Clerk No Andy 35 37300 College Engineer No †¦ Table 1. Partial records and fields of a database table for credit evaluation up splits are similar to the first one. The process continues until an appropriate tree size is reached. 1 shows a segment of the DT. Based on this tree model, a candidate with income at least $31,000 and at least college degree is unlikely to default the payment; but a self-employed candidate whose income is less than $31,000 and age is less than 28 is more likely to default. We begin with a discussion of the general structure of a popular DT algorithm in statistical community, i.e. CART model. A CART model describes the conditional distribution of y given X, where y is the response variable and X is a set of predictor variables (X = (X1,X2,†¦,Xp)). This model has two main components: a tree T with b terminal nodes, and a parameter Q = (q1,q2,†¦, qb) ÃÅ' Rk which associates the parameter values qm, with the mth terminal node. Thus a tree model is fully specified by the pair (T, Q). If X lies in the region corresponding to the mth terminal node then y|X has the distribution f(y|qm), where we use f to represent a conditional distribution indexed by qm. The model is called a regression tree or a classification tree according to whether the response y is quantitative or qualitative, respectively. 2.1 Splitting a tree The DT T subdivides the predictor variable space as follows. Each internal node has an associated splitting rule which uses a predictor to assign observations to either its left or right child node. The internal nodes are thus partitioned into two subsequent nodes using the splitting rule. For quantitative predictors, the splitting rule is based on a split rule c, and assigns observations for which {xi For a regression tree, conventional algorithm models the response in each region Rm as a constant qm. Thus the overall tree model can be expressed as (Hastie et al., 2001): (1) where Rm, m = 1, 2,†¦,b consist of a partition of the predictors space, and therefore representing the space of b terminal nodes. If we adopt the method of minimizing the sum of squares as our criterion to characterize the best split, it is easy to see that the best , is just the average of yi in region Rm: (2) where Nm is the number of observations falling in node m. The residual sum of squares is (3) which will serve as an impurity measure for regression trees. If the response is a factor taking outcomes 1,2, K, the impurity measure Qm(T), defined in (3) is not suitable. Instead, we represent a region Rm with Nm observations with (4) which is the proportion of class k(k ÃŽ {1, 2,†¦,K}) observations in node m. We classify the observations in node m to a class , the majority class in node m. Different measures Qm(T) of node impurity include the following (Hastie et al., 2001): Misclassification error: Gini index: Cross-entropy or deviance: (5) For binary outcomes, if p is the proportion of the second class, these three measures are 1 max(p, 1 p), 2p(1 p) and -p log p (1 p) log(1 p), respectively. All three definitions of impurity are concave, having minimums at p = 0 and p = 1 and a maximum at p = 0.5. Entropy and the Gini index are the most common, and generally give very similar results except when there are two response categories. 2.2 Pruning a tree To be consistent with conventional notations, lets define the impurity of a node h as I(h) ((3) for a regression tree, and any one in (5) for a classification tree). We then choose the split with maximal impurity reduction (6) where hL and hR are the left and right children nodes of h and p(h) is proportion of sample fall in node h. How large should we grow the tree then? Clearly a very large tree might overfit the data, while a small tree may not be able to capture the important structure. Tree size is a tuning parameter governing the models complexity, and the optimal tree size should be adaptively chosen from the data. One approach would be to continue the splitting procedures until the decrease on impurity due to the split exceeds some threshold. This strategy is too short-sighted, however, since a seeming worthless split might lead to a very good split below it. The preferred strategy is to grow a large tree T0, stopping the splitting process when some minimum number of observations in a terminal node (say 10) is reached. Then this large tree is pruned using pruning algorithm, such as cost-complexity or split complexity pruning algorithm. To prune large tree T0 by using cost-complexity algorithm, we define a subtree T T0 to be any tree that can be obtained by pruning T0, and define to be the set of terminal nodes of T. That is, collapsing any number of its terminal nodes. As before, we index terminal nodes by m, with node m representing region Rm. Let denotes the number of terminal nodes in T (= b). We use instead of b following the conventional notation and define the risk of trees and define cost of tree as Regression tree: , Classification tree: , (7) where r(h) measures the impurity of node h in a classification tree (can be any one in (5)). We define the cost complexity criterion (Breiman et al., 1984) (8) where a(> 0) is the complexity parameter. The idea is, for each a, find the subtree Ta T0 to minimize Ra(T). The tuning parameter a > 0 governs the tradeoff between tree size and its goodness of fit to the data (Hastie et al., 2001). Large values of a result in smaller tree Ta and conversely for smaller values of a. As the notation suggests, with a = 0 the solution is the full tree T0. To find Ta we use weakest link pruning: we successively collapse the internal node that produces the smallest per-node increase in R(T), and continue until we produce the single-node (root) tree. This gives a (finite) sequence of subtrees, and one can show this sequence must contains Ta. See Brieman et al. (1984) and Ripley (1996) for details. Estimation of a () is achieved by five- or ten-fold cross-validation. Our final tree is then denoted as . It follows that, in CART and related algorithms, classification and regression trees are produced from data in two stages. In the first stage, a large initial tree is produced by splitting one node at a time in an iterative, greedy fashion. In the second stage, a small subtree of the initial tree is selected, using the same data set. Whereas the splitting procedure proceeds in a top-down fashion, the second stage, known as pruning, proceeds from the bottom-up by successively removing nodes from the initial tree. Theorem 1 (Brieman et al., 1984, Section 3.3) For any value of the complexity parameter a, there is a unique smallest subtree of T0 that minimizes the cost-complexity. Theorem 2 (Zhang Singer, 1999, Section 4.2) If a2 > al, the optimal sub-tree corresponding to a2 is a subtree of the optimal subtree corresponding to al. More general, suppose we end up with m thresholds, 0 (9) where means that is a subtree of . These are called nested optimal subtrees. 3. Decision Tree for Censored Survival Data Survival analysis is the phrase used to describe the analysis of data that correspond to the time from a well-defined time origin until the occurrence of some particular events or end-points. It is important to state what the event is and when the period of observation starts and finish. In medical research, the time origin will often correspond to the recruitment of an individual into an experimental study, and the end-point is the death of the patient or the occurrence of some adverse events. Survival data are rarely normally distributed, but are skewed and comprise typically of many early events and relatively few late ones. It is these features of the data that necessitate the special method survival analysis. The specific difficulties relating to survival analysis arise largely from the fact that only some individuals have experienced the event and, subsequently, survival times will be unknown for a subset of the study group. This phenomenon is called censoring and it may arise in the following ways: (a) a patient has not (yet) experienced the relevant outcome, such as relapse or death, by the time the study has to end; (b) a patient is lost to follow-up during the study period; (c) a patient experiences a different event that makes further follow-up impossible. Generally, censoring times may vary from individual to individual. Such censored survival time underestimated the true (but unknown) time to event. Visualising the survival process of an individual as a time-line, the event (assuming it is to occur) is beyond the end of the follow-up period. This situation is often called right censoring. Most survival data include right censored observation. In many biomedical and reliability studies, interest focuses on relating the time to event to a set of covariates. Cox proportional hazard model (Cox, 1972) has been established as the major framework for analysis of such survival data over the past three decades. But, often in practices, one primary goal of survival analysis is to extract meaningful subgroups of patients determined by the prognostic factors such as patient characteristics that are related to the level of disease. Although proportional hazard model and its extensions are powerful in studying the association between covariates and survival times, usually they are problematic in prognostic classification. One approach for classification is to compute a risk score based on the estimated coefficients from regression methods (Machin et al., 2006). This approach, however, may be problematic for several reasons. First, the definition of risk groups is arbitrary. Secondly, the risk score depends on the correct specification of the model. It is difficult to check whether the model is correct when many covariates are involved. Thirdly, when there are many interaction terms and the model becomes complicated, the result becomes difficult to interpret for the purpose of prognostic classification. Finally, a more serious problem is that an invalid prognostic group may be produced if no patient is included in a covariate profile. In contrast, DT methods do not suffer from these problems. Owing to the development of fast computers, computer-intensive methods such as DT methods have become popular. Since these investigate the significance of all potential risk factors automatically and provide interpretable models, they offer distinct advantages to analysts. Recently a large amount of DT methods have been developed for the analysis of survival data, where the basic concepts for growing and pruning trees remain unchanged, but the choice of the splitting criterion has been modified to incorporate the censored survival data. The application of DT methods for survival data are described by a number of authors (Gordon Olshen, 1985; Ciampi et al., 1986; Segal, 1988; Davis Anderson, 1989; Therneau et al., 1990; LeBlanc Crowley, 1992; LeBlanc Crowley, 1993; Ahn Loh, 1994; Bacchetti Segal, 1995; Huang et al., 1998; KeleÃ…Å ¸ Segal, 2002; Jin et al., 2004; Cappelli Zhang, 2007; Cho Hong, 2008), including the text by Zhang Singer (1999). 4. Decision Tree for Multivariate Censored Survival Data Multivariate survival data frequently arise when we faced the complexity of studies involving multiple treatment centres, family members and measurements repeatedly made on the same individual. For example, in multi-centre clinical trials, the outcomes for groups of patients at several centres are examined. In some instances, patients in a centre might exhibit similar responses due to uniformity of surroundings and procedures within a centre. This would result in correlated outcomes at the level of the treatment centre. For the situation of studies of family members or litters, correlation in outcome is likely for genetic reasons. In this case, the outcomes would be correlated at the family or litter level. Finally, when one person or animal is measured repeatedly over time, correlation will most definitely exist in those responses. Within the context of correlated data, the observations which are correlated for a group of individuals (within a treatment centre or a family) or for on e individual (because of repeated sampling) are referred to as a cluster, so that from this point on, the responses within a cluster will be assumed to be correlated. Analysis of multivariate survival data is complex due to the presence of dependence among survival times and unknown marginal distributions. Multivariate survival times frequently arise when individuals under observation are naturally clustered or when each individual might experience multiple events. A successful treatment of correlated failure times was made by Clayton and Cuzik (1985) who modelled the dependence structure with a frailty term. Another approach is based on a proportional hazard formulation of the marginal hazard function, which has been studied by Wei et al. (1989) and Liang et al. (1993). Noticeably, Prentice et al. (1981) and Andersen Gill (1982) also suggested two alternative approaches to analyze multiple event times. Extension of tree techniques to multivariate censored data is motivated by the classification issue associated with multivariate survival data. For example, clinical investigators design studies to form prognostic rules. Credit risk analysts collect account information to build up credit scoring criteria. Frequently, in such studies the outcomes of ultimate interest are correlated times to event, such as relapses, late payments, or bankruptcies. Since DT methods recursively partition the predictor space, they are an alternative to conventional regression tools. This section is concerned with the generalization of DT models to multivariate survival data. In attempt to facilitate an extension of DT methods to multivariate survival data, more difficulties need to be circumvented. 4.1 Decision tree for multivariate survival data based on marginal model DT methods for multivariate survival data are not many. Almost all the multivariate DT methods have been based on between-node heterogeneity, with the exception of Molinaro et al. (2004) who proposed a general within-node homogeneity approach for both univariate and multivariate data. The multivariate methods proposed by Su Fan (2001, 2004) and Gao et al. (2004, 2006) concentrated on between-node heterogeneity and used the results of regression models. Specifically, for recurrent event data and clustered event data, Su Fan (2004) used likelihood-ratio tests while Gao et al. (2004) used robust Wald tests from a gamma frailty model to maximize the between-node heterogeneity. Su Fan (2001) and Fan et al. (2006) used a robust log-rank statistic while Gao et al. (2006) used a robust Wald test from the marginal failure-time model of Wei et al. (1989). The generalization of DT for multivariate survival data is developed by using goodness of split approach. DT by goodness of split is grown by maximizing a measure of between-node difference. Therefore, only internal nodes have associated two-sample statistics. The tree structure is different from CART because, for trees grown by minimizing within-node error, each node, either terminal or internal, has an associated impurity measure. This is why the CART pruning procedure is not directly applicable to such types of trees. However, the split-complexity pruning algorithm of LeBlanc Crowley (1993) has resulted in trees by goodness of split that has become well-developed tools. This modified tree technique not only provides a convenient way of handling survival data, but also enlarges the applied scope of DT methods in a more general sense. Especially for those situations where defining prediction error terms is relatively difficult, growing trees by a two-sample statistic, together with the split-complexity pruning, offers a feasible way of performing tree analysis. The DT procedure consists of three parts: a method to partition the data recursively into a large tree, a method to prune the large tree into a subtree sequence, and a method to determine the optimal tree size. In the multivariate survival trees, the between-node difference is measured by a robust Wald statistic, which is derived from a marginal approach to multivariate survival data that was developed by Wei et al. (1989). We used split-complexity pruning borrowed from LeBlanc Crowley (1993) and use test sample for determining the right tree size. 4.1.1 The splitting statistic We consider n independent subjects but each subject to have K potential types or number of failures. If there are an unequal number of failures within the subjects, then K is the maximum. We let Tik = min(Yik,Cik ) where Yik = time of the failure in the ith subject for the kth type of failure and Cik = potential censoring time of the ith subject for the kth type of failure with i = 1,†¦,n and k = 1,†¦,K. Then dik = I (Yik ≠¤ Cik) is the indicator for failure and the vector of covariates is denoted Zik = (Z1ik,†¦, Zpik)T. To partition the data, we consider the hazard model for the ith unit for the kth type of failure, using the distinguishable baseline hazard as described by Wei et al. (1989), namely where the indicator function I(Zik Parameter b is estimated by maximizing the partial likelihood. If the observations within the same unit are independent, the partial likelihood functions for b for the distinguishable baseline model (10) would be, (11) Since the observations within the same unit are not independent for multivariate failure time, we refer to the above functions as the pseudo-partial likelihood. The estimator can be obtained by maximizing the likelihood by solving . Wei et al. (1989) showed that is normally distributed with mean 0. However the usual estimate, a-1(b), for the variance of , where (12) is not valid. We refer to a-1(b) as the naà ¯ve estimator. Wei et al. (1989) showed that the correct estimated (robust) variance estimator of is (13) where b(b) is weight and d(b) is often referred to as the robust or sandwich variance estimator. Hence, the robust Wald statistic corresponding to the null hypothesis H0 : b = 0 is (14) 4.1.2 Tree growing To grow a tree, the robust Wald statistic is evaluated for every possible binary split of the predictor space Z. The split, s, could be of several forms: splits on a single covariate, splits on linear combinations of predictors, and boolean combination of splits. The simplest form of split relates to only one covariate, where the split depends on the type of covariate whether it is ordered or nominal covariate. The â€Å"best split† is defined to be the one corresponding to the maximum robust Wald statistic. Subsequently the data are divided into two groups according to the best split. Apply this splitting scheme recursively to the learning sample until the predictor space is partitioned into many regions. There will be no further partition to a node when any of the following occurs: The node contains less than, say 10 or 20, subjects, if the overall sample size is large enough to permit this. We suggest using a larger minimum node size than used in CART where the default value is 5; All the observed times in the subset are censored, which results in unavailability of the robust Wald statistic for any split; All the subjects have identical covariate vectors. Or the node has only complete observations with identical survival times. In these situations, the node is considered as pure. The whole procedure results in a large tree, which could be used for the purpose of data structure exploration. 4.1.3 Tree pruning Let T denote either a particular tree or the set of all its nodes. Let S and denote the set of internal nodes and terminal nodes of T, respectively. Therefore, . Also let |Ãâ€"| denote the number of nodes. Let G(h) represent the maximum robust Wald statistic on a particular (internal) node h. In order to measure the performance of a tree, a split-complexity measure Ga(T) is introduced as in LeBlanc and Crowley (1993). That is, (15) where the number of internal nodes, |S|, measures complexity; G(T) measures goodness of split in T; and the complexity parameter a acts as a penalty for each additional split. Start with the large tree T0 obtained from the splitting procedure. For any internal node h of T0, i.e. h ÃŽ S0, a function g(h) is defined as (16) where Th denotes the branch with h as its root and Sh is the set of all internal nodes of Th. Then the weakest link in T0 is the node such that   < Decision Tree for Prognostic Classification Decision Tree for Prognostic Classification Decision Tree for Prognostic Classification of Multivariate Survival Data and Competing Risks 1. Introduction Decision tree (DT) is one way to represent rules underlying data. It is the most popular tool for exploring complex data structures. Besides that it has become one of the most flexible, intuitive and powerful data analytic tools for determining distinct prognostic subgroups with similar outcome within each subgroup but different outcomes between the subgroups (i.e., prognostic grouping of patients). It is hierarchical, sequential classification structures that recursively partition the set of observations. Prognostic groups are important in assessing disease heterogeneity and for design and stratification of future clinical trials. Because patterns of medical treatment are changing so rapidly, it is important that the results of the present analysis be applicable to contemporary patients. Due to their mathematical simplicity, linear regression for continuous data, logistic regression for binary data, proportional hazard regression for censored survival data, marginal and frailty regression for multivariate survival data, and proportional subdistribution hazard regression for competing risks data are among the most commonly used statistical methods. These parametric and semiparametric regression methods, however, may not lead to faithful data descriptions when the underlying assumptions are not satisfied. Sometimes, model interpretation can be problematic in the presence of high-order interactions among predictors. DT has evolved to relax or remove the restrictive assumptions. In many cases, DT is used to explore data structures and to derive parsimonious models. DT is selected to analyze the data rather than the traditional regression analysis for several reasons. Discovery of interactions is difficult using traditional regression, because the interactions must be specified a priori. In contrast, DT automatically detects important interactions. Furthermore, unlike traditional regression analysis, DT is useful in uncovering variables that may be largely operative within a specific patient subgroup but may have minimal effect or none in other patient subgroups. Also, DT provides a superior means for prognostic classification. Rather than fitting a model to the data, DT sequentially divides the patient group into two subgroups based on prognostic factor values (e.g., tumor size The landmark work of DT in statistical community is the Classification and Regression Trees (CART) methodology of Breiman et al. (1984). A different approach was C4.5 proposed by Quinlan (1992). Original DT method was used in classification and regression for categorical and continuous response variable, respectively. In a clinical setting, however, the outcome of primary interest is often duration of survival, time to event, or some other incomplete (that is, censored) outcome. Therefore, several authors have developed extensions of original DT in the setting of censored survival data (Banerjee Noone, 2008). In science and technology, interest often lies in studying processes which generate events repeatedly over time. Such processes are referred to as recurrent event processes and the data they provide are called recurrent event data which includes in multivariate survival data. Such data arise frequently in medical studies, where information is often available on many individuals, each of whom may experience transient clinical events repeatedly over a period of observation. Examples include the occurrence of asthma attacks in respirology trials, epileptic seizures in neurology studies, and fractures in osteoporosis studies. In business, examples include the filing of warranty claims on automobiles, or insurance claims for policy holders. Since multivariate survival times frequently arise when individuals under observation are naturally clustered or when each individual might experience multiple events, then further extensions of DT are developed for such kind of data. In some studies, patients may be simultaneously exposed to several events, each competing for their mortality or morbidity. For example, suppose that a group of patients diagnosed with heart disease is followed in order to observe a myocardial infarction (MI). If by the end of the study each patient was either observed to have MI or was alive and well, then the usual survival techniques can be applied. In real life, however, some patients may die from other causes before experiencing an MI. This is a competing risks situation because death from other causes prohibits the occurrence of MI. MI is considered the event of interest, while death from other causes is considered a competing risk. The group of patients dead of other causes cannot be considered censored, since their observations are not incomplete. The extension of DT can also be employed for competing risks survival time data. These extensions can make one apply the technique to clinical trial data to aid in the development of prognostic classifications for chronic diseases. This chapter will cover DT for multivariate and competing risks survival time data as well as their application in the development of medical prognosis. Two kinds of multivariate survival time regression model, i.e. marginal and frailty regression model, have their own DT extensions. Whereas, the extension of DT for competing risks has two types of tree. First, the â€Å"single event† DT is developed based on splitting function using one event only. Second, the â€Å"composite events† tree which use all the events jointly. 2. Decision Tree A DT is a tree-like structure used for classification, decision theory, clustering, and prediction functions. It depicts rules for dividing data into groups based on the regularities in the data. A DT can be used for categorical and continuous response variables. When the response variables are continuous, the DT is often referred to as a regression tree. If the response variables are categorical, it is called a classification tree. However, the same concepts apply to both types of trees. DTs are widely used in computer science for data structures, in medical sciences for diagnosis, in botany for classification, in psychology for decision theory, and in economic analysis for evaluating investment alternatives. DTs learn from data and generate models containing explicit rule-like relationships among the variables. DT algorithms begin with the entire set of data, split the data into two or more subsets by testing the value of a predictor variable, and then repeatedly split each subset into finer subsets until the split size reaches an appropriate level. The entire modeling process can be illustrated in a tree-like structure. A DT model consists of two parts: creating the tree and applying the tree to the data. To achieve this, DTs use several different algorithms. The most popular algorithm in the statistical community is Classification and Regression Trees (CART) (Breiman et al., 1984). This algorithm helps DTs gain credibility and acceptance in the statistics community. It creates binary splits on nominal or interval predictor variables for a nominal, ordinal, or interval response. The most widely-used algorithms by computer scientists are ID3, C4.5, and C5.0 (Quinlan, 1993). The first version of C4.5 and C5.0 were limited to categorical predictors; however, the most recent versions are similar to CART. Other algorithms include Chi-Square Automatic Interaction Detection (CHAID) for categorical response (Kass, 1980), CLS, AID, TREEDISC, Angoss KnowledgeSEEKER, CRUISE, GUIDE and QUEST (Loh, 2008). These algorithms use different approaches for splitting variables. CART, CRUISE, GUIDE and QUEST use the sta tistical approach, while CLS, ID3, and C4.5 use an approach in which the number of branches off an internal node is equal to the number of possible categories. Another common approach, used by AID, CHAID, and TREEDISC, is the one in which the number of nodes on an internal node varies from two to the maximum number of possible categories. Angoss KnowledgeSEEKER uses a combination of these approaches. Each algorithm employs different mathematical processes to determine how to group and rank variables. Let us illustrate the DT method in a simplified example of credit evaluation. Suppose a credit card issuer wants to develop a model that can be used for evaluating potential candidates based on its historical customer data. The companys main concern is the default of payment by a cardholder. Therefore, the model should be able to help the company classify a candidate as a possible defaulter or not. The database may contain millions of records and hundreds of fields. A fragment of such a database is shown in Table 1. The input variables include income, age, education, occupation, and many others, determined by some quantitative or qualitative methods. The model building process is illustrated in the tree structure in 1. The DT algorithm first selects a variable, income, to split the dataset into two subsets. This variable, and also the splitting value of $31,000, is selected by a splitting criterion of the algorithm. There exist many splitting criteria (Mingers, 1989). The basic principle of these criteria is that they all attempt to divide the data into clusters such that variations within each cluster are minimized and variations between the clusters are maximized. The follow- Name Age Income Education Occupation Default Andrew 42 45600 College Manager No Allison 26 29000 High School Self Owned Yes Sabrina 58 36800 High School Clerk No Andy 35 37300 College Engineer No †¦ Table 1. Partial records and fields of a database table for credit evaluation up splits are similar to the first one. The process continues until an appropriate tree size is reached. 1 shows a segment of the DT. Based on this tree model, a candidate with income at least $31,000 and at least college degree is unlikely to default the payment; but a self-employed candidate whose income is less than $31,000 and age is less than 28 is more likely to default. We begin with a discussion of the general structure of a popular DT algorithm in statistical community, i.e. CART model. A CART model describes the conditional distribution of y given X, where y is the response variable and X is a set of predictor variables (X = (X1,X2,†¦,Xp)). This model has two main components: a tree T with b terminal nodes, and a parameter Q = (q1,q2,†¦, qb) ÃÅ' Rk which associates the parameter values qm, with the mth terminal node. Thus a tree model is fully specified by the pair (T, Q). If X lies in the region corresponding to the mth terminal node then y|X has the distribution f(y|qm), where we use f to represent a conditional distribution indexed by qm. The model is called a regression tree or a classification tree according to whether the response y is quantitative or qualitative, respectively. 2.1 Splitting a tree The DT T subdivides the predictor variable space as follows. Each internal node has an associated splitting rule which uses a predictor to assign observations to either its left or right child node. The internal nodes are thus partitioned into two subsequent nodes using the splitting rule. For quantitative predictors, the splitting rule is based on a split rule c, and assigns observations for which {xi For a regression tree, conventional algorithm models the response in each region Rm as a constant qm. Thus the overall tree model can be expressed as (Hastie et al., 2001): (1) where Rm, m = 1, 2,†¦,b consist of a partition of the predictors space, and therefore representing the space of b terminal nodes. If we adopt the method of minimizing the sum of squares as our criterion to characterize the best split, it is easy to see that the best , is just the average of yi in region Rm: (2) where Nm is the number of observations falling in node m. The residual sum of squares is (3) which will serve as an impurity measure for regression trees. If the response is a factor taking outcomes 1,2, K, the impurity measure Qm(T), defined in (3) is not suitable. Instead, we represent a region Rm with Nm observations with (4) which is the proportion of class k(k ÃŽ {1, 2,†¦,K}) observations in node m. We classify the observations in node m to a class , the majority class in node m. Different measures Qm(T) of node impurity include the following (Hastie et al., 2001): Misclassification error: Gini index: Cross-entropy or deviance: (5) For binary outcomes, if p is the proportion of the second class, these three measures are 1 max(p, 1 p), 2p(1 p) and -p log p (1 p) log(1 p), respectively. All three definitions of impurity are concave, having minimums at p = 0 and p = 1 and a maximum at p = 0.5. Entropy and the Gini index are the most common, and generally give very similar results except when there are two response categories. 2.2 Pruning a tree To be consistent with conventional notations, lets define the impurity of a node h as I(h) ((3) for a regression tree, and any one in (5) for a classification tree). We then choose the split with maximal impurity reduction (6) where hL and hR are the left and right children nodes of h and p(h) is proportion of sample fall in node h. How large should we grow the tree then? Clearly a very large tree might overfit the data, while a small tree may not be able to capture the important structure. Tree size is a tuning parameter governing the models complexity, and the optimal tree size should be adaptively chosen from the data. One approach would be to continue the splitting procedures until the decrease on impurity due to the split exceeds some threshold. This strategy is too short-sighted, however, since a seeming worthless split might lead to a very good split below it. The preferred strategy is to grow a large tree T0, stopping the splitting process when some minimum number of observations in a terminal node (say 10) is reached. Then this large tree is pruned using pruning algorithm, such as cost-complexity or split complexity pruning algorithm. To prune large tree T0 by using cost-complexity algorithm, we define a subtree T T0 to be any tree that can be obtained by pruning T0, and define to be the set of terminal nodes of T. That is, collapsing any number of its terminal nodes. As before, we index terminal nodes by m, with node m representing region Rm. Let denotes the number of terminal nodes in T (= b). We use instead of b following the conventional notation and define the risk of trees and define cost of tree as Regression tree: , Classification tree: , (7) where r(h) measures the impurity of node h in a classification tree (can be any one in (5)). We define the cost complexity criterion (Breiman et al., 1984) (8) where a(> 0) is the complexity parameter. The idea is, for each a, find the subtree Ta T0 to minimize Ra(T). The tuning parameter a > 0 governs the tradeoff between tree size and its goodness of fit to the data (Hastie et al., 2001). Large values of a result in smaller tree Ta and conversely for smaller values of a. As the notation suggests, with a = 0 the solution is the full tree T0. To find Ta we use weakest link pruning: we successively collapse the internal node that produces the smallest per-node increase in R(T), and continue until we produce the single-node (root) tree. This gives a (finite) sequence of subtrees, and one can show this sequence must contains Ta. See Brieman et al. (1984) and Ripley (1996) for details. Estimation of a () is achieved by five- or ten-fold cross-validation. Our final tree is then denoted as . It follows that, in CART and related algorithms, classification and regression trees are produced from data in two stages. In the first stage, a large initial tree is produced by splitting one node at a time in an iterative, greedy fashion. In the second stage, a small subtree of the initial tree is selected, using the same data set. Whereas the splitting procedure proceeds in a top-down fashion, the second stage, known as pruning, proceeds from the bottom-up by successively removing nodes from the initial tree. Theorem 1 (Brieman et al., 1984, Section 3.3) For any value of the complexity parameter a, there is a unique smallest subtree of T0 that minimizes the cost-complexity. Theorem 2 (Zhang Singer, 1999, Section 4.2) If a2 > al, the optimal sub-tree corresponding to a2 is a subtree of the optimal subtree corresponding to al. More general, suppose we end up with m thresholds, 0 (9) where means that is a subtree of . These are called nested optimal subtrees. 3. Decision Tree for Censored Survival Data Survival analysis is the phrase used to describe the analysis of data that correspond to the time from a well-defined time origin until the occurrence of some particular events or end-points. It is important to state what the event is and when the period of observation starts and finish. In medical research, the time origin will often correspond to the recruitment of an individual into an experimental study, and the end-point is the death of the patient or the occurrence of some adverse events. Survival data are rarely normally distributed, but are skewed and comprise typically of many early events and relatively few late ones. It is these features of the data that necessitate the special method survival analysis. The specific difficulties relating to survival analysis arise largely from the fact that only some individuals have experienced the event and, subsequently, survival times will be unknown for a subset of the study group. This phenomenon is called censoring and it may arise in the following ways: (a) a patient has not (yet) experienced the relevant outcome, such as relapse or death, by the time the study has to end; (b) a patient is lost to follow-up during the study period; (c) a patient experiences a different event that makes further follow-up impossible. Generally, censoring times may vary from individual to individual. Such censored survival time underestimated the true (but unknown) time to event. Visualising the survival process of an individual as a time-line, the event (assuming it is to occur) is beyond the end of the follow-up period. This situation is often called right censoring. Most survival data include right censored observation. In many biomedical and reliability studies, interest focuses on relating the time to event to a set of covariates. Cox proportional hazard model (Cox, 1972) has been established as the major framework for analysis of such survival data over the past three decades. But, often in practices, one primary goal of survival analysis is to extract meaningful subgroups of patients determined by the prognostic factors such as patient characteristics that are related to the level of disease. Although proportional hazard model and its extensions are powerful in studying the association between covariates and survival times, usually they are problematic in prognostic classification. One approach for classification is to compute a risk score based on the estimated coefficients from regression methods (Machin et al., 2006). This approach, however, may be problematic for several reasons. First, the definition of risk groups is arbitrary. Secondly, the risk score depends on the correct specification of the model. It is difficult to check whether the model is correct when many covariates are involved. Thirdly, when there are many interaction terms and the model becomes complicated, the result becomes difficult to interpret for the purpose of prognostic classification. Finally, a more serious problem is that an invalid prognostic group may be produced if no patient is included in a covariate profile. In contrast, DT methods do not suffer from these problems. Owing to the development of fast computers, computer-intensive methods such as DT methods have become popular. Since these investigate the significance of all potential risk factors automatically and provide interpretable models, they offer distinct advantages to analysts. Recently a large amount of DT methods have been developed for the analysis of survival data, where the basic concepts for growing and pruning trees remain unchanged, but the choice of the splitting criterion has been modified to incorporate the censored survival data. The application of DT methods for survival data are described by a number of authors (Gordon Olshen, 1985; Ciampi et al., 1986; Segal, 1988; Davis Anderson, 1989; Therneau et al., 1990; LeBlanc Crowley, 1992; LeBlanc Crowley, 1993; Ahn Loh, 1994; Bacchetti Segal, 1995; Huang et al., 1998; KeleÃ…Å ¸ Segal, 2002; Jin et al., 2004; Cappelli Zhang, 2007; Cho Hong, 2008), including the text by Zhang Singer (1999). 4. Decision Tree for Multivariate Censored Survival Data Multivariate survival data frequently arise when we faced the complexity of studies involving multiple treatment centres, family members and measurements repeatedly made on the same individual. For example, in multi-centre clinical trials, the outcomes for groups of patients at several centres are examined. In some instances, patients in a centre might exhibit similar responses due to uniformity of surroundings and procedures within a centre. This would result in correlated outcomes at the level of the treatment centre. For the situation of studies of family members or litters, correlation in outcome is likely for genetic reasons. In this case, the outcomes would be correlated at the family or litter level. Finally, when one person or animal is measured repeatedly over time, correlation will most definitely exist in those responses. Within the context of correlated data, the observations which are correlated for a group of individuals (within a treatment centre or a family) or for on e individual (because of repeated sampling) are referred to as a cluster, so that from this point on, the responses within a cluster will be assumed to be correlated. Analysis of multivariate survival data is complex due to the presence of dependence among survival times and unknown marginal distributions. Multivariate survival times frequently arise when individuals under observation are naturally clustered or when each individual might experience multiple events. A successful treatment of correlated failure times was made by Clayton and Cuzik (1985) who modelled the dependence structure with a frailty term. Another approach is based on a proportional hazard formulation of the marginal hazard function, which has been studied by Wei et al. (1989) and Liang et al. (1993). Noticeably, Prentice et al. (1981) and Andersen Gill (1982) also suggested two alternative approaches to analyze multiple event times. Extension of tree techniques to multivariate censored data is motivated by the classification issue associated with multivariate survival data. For example, clinical investigators design studies to form prognostic rules. Credit risk analysts collect account information to build up credit scoring criteria. Frequently, in such studies the outcomes of ultimate interest are correlated times to event, such as relapses, late payments, or bankruptcies. Since DT methods recursively partition the predictor space, they are an alternative to conventional regression tools. This section is concerned with the generalization of DT models to multivariate survival data. In attempt to facilitate an extension of DT methods to multivariate survival data, more difficulties need to be circumvented. 4.1 Decision tree for multivariate survival data based on marginal model DT methods for multivariate survival data are not many. Almost all the multivariate DT methods have been based on between-node heterogeneity, with the exception of Molinaro et al. (2004) who proposed a general within-node homogeneity approach for both univariate and multivariate data. The multivariate methods proposed by Su Fan (2001, 2004) and Gao et al. (2004, 2006) concentrated on between-node heterogeneity and used the results of regression models. Specifically, for recurrent event data and clustered event data, Su Fan (2004) used likelihood-ratio tests while Gao et al. (2004) used robust Wald tests from a gamma frailty model to maximize the between-node heterogeneity. Su Fan (2001) and Fan et al. (2006) used a robust log-rank statistic while Gao et al. (2006) used a robust Wald test from the marginal failure-time model of Wei et al. (1989). The generalization of DT for multivariate survival data is developed by using goodness of split approach. DT by goodness of split is grown by maximizing a measure of between-node difference. Therefore, only internal nodes have associated two-sample statistics. The tree structure is different from CART because, for trees grown by minimizing within-node error, each node, either terminal or internal, has an associated impurity measure. This is why the CART pruning procedure is not directly applicable to such types of trees. However, the split-complexity pruning algorithm of LeBlanc Crowley (1993) has resulted in trees by goodness of split that has become well-developed tools. This modified tree technique not only provides a convenient way of handling survival data, but also enlarges the applied scope of DT methods in a more general sense. Especially for those situations where defining prediction error terms is relatively difficult, growing trees by a two-sample statistic, together with the split-complexity pruning, offers a feasible way of performing tree analysis. The DT procedure consists of three parts: a method to partition the data recursively into a large tree, a method to prune the large tree into a subtree sequence, and a method to determine the optimal tree size. In the multivariate survival trees, the between-node difference is measured by a robust Wald statistic, which is derived from a marginal approach to multivariate survival data that was developed by Wei et al. (1989). We used split-complexity pruning borrowed from LeBlanc Crowley (1993) and use test sample for determining the right tree size. 4.1.1 The splitting statistic We consider n independent subjects but each subject to have K potential types or number of failures. If there are an unequal number of failures within the subjects, then K is the maximum. We let Tik = min(Yik,Cik ) where Yik = time of the failure in the ith subject for the kth type of failure and Cik = potential censoring time of the ith subject for the kth type of failure with i = 1,†¦,n and k = 1,†¦,K. Then dik = I (Yik ≠¤ Cik) is the indicator for failure and the vector of covariates is denoted Zik = (Z1ik,†¦, Zpik)T. To partition the data, we consider the hazard model for the ith unit for the kth type of failure, using the distinguishable baseline hazard as described by Wei et al. (1989), namely where the indicator function I(Zik Parameter b is estimated by maximizing the partial likelihood. If the observations within the same unit are independent, the partial likelihood functions for b for the distinguishable baseline model (10) would be, (11) Since the observations within the same unit are not independent for multivariate failure time, we refer to the above functions as the pseudo-partial likelihood. The estimator can be obtained by maximizing the likelihood by solving . Wei et al. (1989) showed that is normally distributed with mean 0. However the usual estimate, a-1(b), for the variance of , where (12) is not valid. We refer to a-1(b) as the naà ¯ve estimator. Wei et al. (1989) showed that the correct estimated (robust) variance estimator of is (13) where b(b) is weight and d(b) is often referred to as the robust or sandwich variance estimator. Hence, the robust Wald statistic corresponding to the null hypothesis H0 : b = 0 is (14) 4.1.2 Tree growing To grow a tree, the robust Wald statistic is evaluated for every possible binary split of the predictor space Z. The split, s, could be of several forms: splits on a single covariate, splits on linear combinations of predictors, and boolean combination of splits. The simplest form of split relates to only one covariate, where the split depends on the type of covariate whether it is ordered or nominal covariate. The â€Å"best split† is defined to be the one corresponding to the maximum robust Wald statistic. Subsequently the data are divided into two groups according to the best split. Apply this splitting scheme recursively to the learning sample until the predictor space is partitioned into many regions. There will be no further partition to a node when any of the following occurs: The node contains less than, say 10 or 20, subjects, if the overall sample size is large enough to permit this. We suggest using a larger minimum node size than used in CART where the default value is 5; All the observed times in the subset are censored, which results in unavailability of the robust Wald statistic for any split; All the subjects have identical covariate vectors. Or the node has only complete observations with identical survival times. In these situations, the node is considered as pure. The whole procedure results in a large tree, which could be used for the purpose of data structure exploration. 4.1.3 Tree pruning Let T denote either a particular tree or the set of all its nodes. Let S and denote the set of internal nodes and terminal nodes of T, respectively. Therefore, . Also let |Ãâ€"| denote the number of nodes. Let G(h) represent the maximum robust Wald statistic on a particular (internal) node h. In order to measure the performance of a tree, a split-complexity measure Ga(T) is introduced as in LeBlanc and Crowley (1993). That is, (15) where the number of internal nodes, |S|, measures complexity; G(T) measures goodness of split in T; and the complexity parameter a acts as a penalty for each additional split. Start with the large tree T0 obtained from the splitting procedure. For any internal node h of T0, i.e. h ÃŽ S0, a function g(h) is defined as (16) where Th denotes the branch with h as its root and Sh is the set of all internal nodes of Th. Then the weakest link in T0 is the node such that   <