IT Security Essay

With the advent of the new technological age, businesses and individuals find it more and more difficult to cope with the growing amount of information. The more technological businesses become, the more information they are compelled to process and store, thus creating a whole set of challenges and controversies in the IT field. The problem is that managing business information is impossible without developing and implementing effective data storage systems. Very often, backing up business data to a remote location becomes the only possible means to guarantee effectiveness of all information processes within organization. In this context, online backup services could potentially resolve the most complicated IT issues in business. Really, in business, organizations gather large amounts of information about their products, market reputation, customers, and competitors. They work to determine the major weaknesses and strengths of their sales strategies and use this information in the process of achieving strategic organizational objectives. Information improves organizations’ competitive positions, and â€Å"the company losing information may have its competitive edge dulled. Losing a competitive edge can be a significant cost to any business, but even losing competitive edge is not as dangerous as losing and revealing information about possible business vulnerabilities and gaps to potential and current competitors† (Halibozek, Jones & Kovacich, 2007). The fact is that the loss of data may take different forms and patterns; the reasons of losing information are also many and numerous. Regardless of whether the loss of data is caused by a virus or an external attack, customer files, emails, financial and accounting information – all these may become a serious threat to the stability of businesses. Statistical research suggests that one half of businesses that lose critical information file for bankruptcy (Jacobi, 2005); as such, online backup mechanisms seem to be a viable solution to the discussed problems. The problem of losing information is well-known to businesses, but here it is more than important to investigate the relevance of online backup services. The problem of losing information in business is significant from the IT security perspective for numerous reasons: these include the risks of losing competitiveness, the risks of bankruptcy, and the risks of competitive vulnerability, as discussed in the previous paragraph. Investigating the relevance of online backup services is needed to evaluate its effectiveness, cost-effectiveness, and the principles of use. Losing information seems a difficult and hardly resolvable problem, but with the current speed of technological advancement, even the most controversial and difficult technological issues can be successfully resolved. The issue of losing data is not an exception, and TechSoup meta-site provides brief but comprehensible information with regard to using online backup services. Upon visiting the website, the first impression is that information is well-structured, is divided into several subcategories, and is written in an easy understandable language – the features that even inexperienced IT users can use to grasp the meaning of online backup services. Furthermore, it is objectivity of provided data and the lack of clear or hidden advertising that makes the website fully informative and not imposing. That the authors discuss both pros and cons of using online backup services makes it possible for the reader to make a relevant and justified choice; and where online backup services display serious technological limitations, the meta-site provides a set of recommendations for overcoming these limitations in practice (Lasa, 2006). For example, when it comes to using online backup services, â€Å"speed and amount of data backup is limited by the speed of your Internet connection. Online backup over dial-up connection will be slow and is generally only suitable for small amounts of data† (Lasa, 2006). Here, it also means that the speed of data management and its effectiveness largely depends on the particular choice of Internet providers. Bearing in mind the variety and number of Internet companies in the market, choosing the right one with the best and the most appropriate speed of connection will help companies resolve these issues at hand. Also, the meta-site suggests that companies that limit their choice of data storage mechanisms to online backup services actually trust all important information to a single person (and provider), and in case the data is lost, the given provider will hardly be able to restore it. To mitigate these risks, the authors also recommend using CDs or DVDs to archive backed-up data (Lasa, 2006). These are the most feasible solutions to the issues, with which online backup services can be associated. In general, the website provides detailed and unbiased information about online backup services. Unfortunately, the information regarding the seriousness of data storage issues is absent. As such, IT users may not understand the seriousness of the issue and may not be willing to seek immediate and effective solutions. Even when the need to investigate the problem arises, IT professionals will need to search the net for possible statistical or descriptive information with regard to the issue of losing information and its impact on businesses. Nevertheless, the provided information is structured in a way that makes it easier to understand HOW to cope with the growing information management tensions. The website does not simply describe how online backup services work, but evaluates their benefits and drawbacks, and provides a set of recommendations for choosing a provider. The structure of information is extremely convenient and is designed to cover broad audiences. Conclusion Certainly, the mere fact that IT users can access information about backup services does not mean that the issue of data management and storage is no longer relevant. On the contrary, the more meta-sites devote time and effort to describing such services, the more concerned they become about possible implications of losing information in business. Objectively, technology works to provide IT users and professionals with a whole set of effective instruments for storing and managing data; and it is obvious that online backup services can significantly reduce the risks of losing important and sensible data. Simultaneously, even when using online backup services, there is still much room for technological improvement, and whether businesses and individuals are offered relevant technological solutions depends on the speed and the quality of the current technological progress.

Curriculum packages,proposals or prescriptions? Advantages and Disadvantages Essay

This exposition will explore some of the major benefits of an adaptive approach to curriculum implementation in Zimbabwe, as a pose to an adoptive approach, namely increased professional autonomy and creative freedom for teachers, relevance to learner demographics and a wholesome learning experience. Considerations will also be made of the constraints of such an approach, chiefly the issue of resource intensity, accountability and control. It will also outline the applicability of an adoptive approach, in Zimbabwe’s examination oriented educational system, where homogeneity of delivery at the peripheral level is of essence. A curriculum provides the framework for how and when to teach what. McKimm (2007) suggests, the curriculum defines learning outcomes, timetables, content, appropriate teaching methods and assessment instruments. Materials such as teacher’s guides, recommended text books and syllabi for each subject all form part of the curriculum package. In the Zimbabwean context, the curriculum package is arranged by the centre, called the Central Curriculum Development Unit (CDU). The CDU prepares and distributes the curriculum package to the various provinces via the district office to the schools. Taking the curriculum as a proposal is like using it as a prop on the stage, it’s a mere accessory, and it accentuates the core theme of the story. It gives the setting while the actual script is in the hands of the director and cast who are the teacher and the learners respectively. In this case, modifications can be made to suit the geographical and social location of the learners. While a prescriptive approach implies the curriculum package is a script which is to be aped word for word and gesture by gesture, mimicking the demands of the examination. A prescription enforces rules about how a subject should be taught as such the teacher is like a drill sergeant implementing objectives in finite timeframes. To begin with, Ndawi and Maravanyika (2011), â€Å"argue that education and human experiences are too wide and too complex to be reduced down to specifiable and measurable objectives.† From this tenet, one can contend that when a curriculum package is used as a recommendation rather than dogma the teacher can regard every exchange as an opportunity for learning to occur, even when tacitly expressed in the curriculum package. Using this approach, the teacher is limited neither by explicit goals nor by resources, which are sometimes in short supply in resettlement schools, but rather empowered to incorporate innovative tactics, rich creativity and a wholesome range of experiences into his instruction. The product is a well-rounded and adaptable member of the wider society. By contrast having a prescribed curriculum, with exacted and measurable goals, unambiguous methods, specified teaching aids and finite timeframes, is a motivating factor for teachers in the Zimbabwean context where incentives inspire those whose pupils attain a certain level of academic prowess, measured strictly through structured examinations. Thus, it can be said that the system rewards homogeneity more than heterogeneity. What Lawton (1980) terms ‘†¦teacher’s legitimate desire for professional autonomy†¦Ã¢â‚¬â„¢ has been motivated by the pronouncement by the Zimbabwean ministry of education to develop the standard of the teaching fraternity by awarding degreed teachers with job security and a disparate pay scale from that of their diploma holder counterparts. This trend of empowerment and upward mobility can sustain a proposal based approach, which requires highly trained and resourceful teachers. To this end, it is advantageous to approach the curriculum package as a suggested plan of action or recommendation, as it fulfills the teacher’s need to express his ingenuity and self actualise. On the contrary, this adaptive approach can be resource intensive. It takes expertise to enforce variations in curriculum delivery, and training this highly skilled manpower may not be financially feasible for the ministry of education. Where teachers are minimally trained or untrained as in the case of temporary teachers in Zimbabwe, the prescriptive slant tends to be enormously helpful as it defines exactly what to teach, when to teach it and how it should be taught. Textbooks and teacher’s guide explicitly state procedure. The Indian National Council of Educational Research and Training (2006) asserts, â€Å"†¦diversity of languages, social customs, manners, mores and uneven economic development, the needs and demands of individuals and society will have differential pulls on the school curriculum, varying from one region to the other.† Similarly, in Zimbabwe an adaptive approach can cater for the range of abilities, tribal nuances and economic strata found in any school community or classroom. In this light, the teacher is given room to improvise using locally available material, from the community’s culture and landscape, to suit learner demographics, thus the learning experience becomes socially relevant, meaningful and learners gain a sense of ownership of their education. Adversely, Lawton (1980), in this statement, â€Å"†¦secondary-modern-school curricula, often lacked structure and purpose†, alludes to the unconstructiveness, that can be generated by a laissez-faire approach to curriculum interpretation, where teachers have extensive flexibility to manipulate their instruction to suit the demographics of their community rather than the universal values which may be tested at Grade 7, O’ Level and A’ Level examinations. The prescriptive approach to curriculum implementation satisfies theâ€Å"†¦political need for some kind of system of accountability†¦Ã¢â‚¬  Lawton (1980), as in the Zimbabwean case where there are considerably more state funded rural day schools than there are independent ones. When the prescriptive approach is unequivocally applied, teachers can account for their time and the resources the state has invested in the system by way of mid and end of term and final examinations, whereas, hybrid varieties of curriculum are more complex to control, monitor and assess. Delivery problems can be easily diagnosed and corrected. Again, variations may tend to be too localized, producing a breed of learners with limited regional or international marketability in this era of globalization and the information boom. In a subject like science and mathematics there is not much scope for local variations and the adoption of common textbooks in all parts of the country is feasible. Eunitah et al (2013) imply that, in developing socialist educational contexts like Zimbabwe, it is premature to do away with centrally prescribed curricula in order to accomplish uniformity in the provision of education. This uniformity means, all students in Zimbabwe use standardized learning material and receive a standard educational experience. When a student transfers from a rural to an urban school, as is the trend in developing countries, he has the assurance of continuity. Thus, the prescriptive approach to curriculum implementation achieves meritocracy and functionality. Moreover, the Zimbabwean curriculum pays more attention to acquired skills that can be measured; it is largely objectives oriented, in that learning outcomes are evaluated through summative examinations, from time to time. To this end, a prescriptive approach is more effective, as it provides exact standards and expectations of the learner while limiting deviations which may otherwise be of no relevance to the learner, come examination time. Lawton (1980) points out the love-hate relationship teachers may have with the examination system, though meritocratic and fair it can extend so far into the classroom that it stifles independent thinking, self-discovery, curiosity and creativity, which form part of wholesome learning. It can be concluded that while taking the curriculum package as a proposal, encourages a broader range of experiences and an expansive exercise of potentialities in learners due to its adaptability to various geographical and economic circumstances as is found in Zimbabwe. The prescriptive approach is equally beneficial and perhaps more applicable to Zimbabwe because of the nature of the education system which is examination oriented.

The Zen of Listening

Douglas, Susan. (2004). The Zen of Listening, in Listening in  : Radio and the American Imagination (22-39). Minneapolis, University of Minnesota Press. Abstract Radio is examined here as a shaper of generational identities, as a uniting force for the creation of' †imagined communities† or nations, and as a nostalgic device with associational links in our past. In addition, it is portrayed as a powerful aural gadget that stimulates us cognitively not only through our imagination; our creation of images or ideas based on listening, but also through music, which engages us emotionally.Further discussed is a comprehensive history of radio in America and its contrasting relationship with newspapers and literacy, and television and its visual component. This contrast, and the existence of the radio and the ways we listen have important temporally bound characteristics that are important in understanding times, the medium itself and our relationship with it as it becomes engr ained or interwoven into our everyday lives.The text examines the social implications and reasons for being of radio and refers to various scholars who have examined the form and its effects of this revolutionary device which unites listeners through simultaneity of listening and the physical responses listening engenders. Through the physiological, social, cultural, and technological spheres of this medium, it is obvious that it is much more complex than commonly believed, and the text brings to light the ramifications of its introduction into a literary, visual culture, creating a hybrid America  : a conservative, literate society entwined with a traditional, preliterate. ral culture. Word Count  : 230 Keywords  : nostalgia, radio, imagined community, modes of listening, music, ritual Response †With radio, the interior †I† began oscillating with the voices of those never met, never even seen (31). † The permeating qualities of the †voices of rad io† in the minds of listeners is an issue, in my opinion, that clearly implicates radio as a persuasion tool, which is an element of the medium that appears to be neglected in the text.This neglect to fully examine the implications of the medium and the various elements that are quintessential to the formation of a complete and comprehensive understanding of the workings and complexities of radio presents a rudimentary portrait of the form which should definately be corrected. I argue that Susan Douglas presents an incomplete account of the rise of radio in her idealization of the medium and that, like the listener who is †inclined to remember [radio] at its best†, she fails to examine the intention of radio messages and focuses more on the experience of listening to the radio (Douglas, 2004, p. 5). Firstly, with a basis on the above sentence, she idealizes the form and effects of radio by overlooking or barely touching on the idea of the commercial hand that plays a rather large role in the medium, and affects the intentions and motives of the speakers and the content they disclose. Furthermore, the pervasiveness of these voices is cause for concern for listeners as they are prey to subtle influence from these †familiar voices† who infiltrate themselves into the very thoughts of individuals.Susan Douglas' article addresses many ideas that revolve around radio, but does not seem to pay much attention to the commercialization of the medium despite her mentionning that †by the 1930's, with the highly commercialized network system in place, a great majority of these voices—which sought to sound familiar, intimate, and even folksy—represented a centralized consumer-culture (Douglas, 2004, p. 31). ‘ Beyond the idealized concept of the †imagined community† and the positive unity it creates among the listeners, the commercial hand in the medium of radio implies a certain intention in the scale of the medium; one that seeks numbers. Douglas does mention that in an effort to maximize profits, the network and advertisers aimed for the largest possible audience, promoting the medium of radio as a †nation-building technology (Douglas, 2004, p. 24). ‘ This emphasis, however, on the maximization of profits casts doubt on the integrity and the intention of radio. The oscillating voices of †those never met, never even seen† which interact with the inner voice of the listener are tainted by an underlying struggle between social consolidation and betterment, and commercialism. This leads to the need to examine content and intention in radio, and to the need for a critical assessment of this revolutionary device.Secondly, these voices which penetrated our minds, spoken by unknown radio personalities, did more than allow us to free our imagination. In effect, these voices which now interacted with the inner voice of the individual could become subtle influences of ou r ideas, and beliefs without our even knowing. This danger, which I greatly believe is applicable in this mass medium, especially when taking into consideration the novelty of the device in the 1930's, could leave listeners unguarded against potential manipulation or influence.The idea that the voices of the radio speakers have a certain familiar or intimate quality illustrates this desire to identify with the listener, which leaves that latter to fend for himself in the identification of the veracity of messages, and in the intention of the speaker who is trained to please an audience. The various personalities that would speak to the nation through radio—the †politically powerful and the rich, [†¦ ministers, educators, [†¦] comedians, singers and actors†Ã¢â‚¬â€could have various intentions in their speeches; they could seek to sway auditors to favor certain ideologies, to act in certain ways, or could misdirect or misinform listeners (Douglas, 2004, p 31). Furthermore, the ability for radio to adjust to various circumstances of listening makes it even more alarming as it becomes the background music of our daily lives, making these voices that much more likely to become a part of our interior dialogue (Douglas, 2004).In conclusion, as mass media of various sorts—newspapers, television and radio—become national, and all-encompassing, the need for critical analysis of every aspect of each medium becomes necessary to understand the limitations of each, and their intentions. Since there are many underlying motives to every medium, especially commercial or political ones, and since mass media have developed into such huge social entities with powerful nfluence, it is important to think by ourselves, without the implication of unknown others in our reasoning; to question why we believe certain things, and how we came to so as to remain individuals in the mass, and to be able to ward off unwanted influences which may find their way into our subconscious. Word Count  : 782

Players view on the NBA Lockout 2011 Research Paper

Players view on the NBA Lockout 2011 - Research Paper Example he players since the partnership loses a lot of money and has given proposition to reduce the player’s salaries by 40% as well as set up a fixed payment for each team (Croslis). The proposition has generated many outcries from the players who have aired out different views on the matter. The players view the lockout as a result of failure of communication between them, and the league officials since most of them were not provided with the copy of the proposal that was regarded as final (Stein). Most players have insisted to vote out the final plan if they had the opportunity to give their opinion on the matter. The players also insisted that the executive director would have prevented the lockout from happening if he had learnt something from the last lockout that occurred between 1998 and 1999 (Stein). The players view the leaders especially Stern as dictators since they have been enforcing certain rules and regulation without consulting the players. Therefore, the lockout comes because of the officials being ignorant of the role that players hold in the league. The players take the lockout as a great obstacle to a new sporting year which most of the diehard fans have anticipated for long since the end of the last sporting year. The players view the lockout as a fa ilure by the officials to come into terms, and most have moved out to join other teams outside the country in an effort to continue earning, but still in waiting for the deadlock to stop. The players feel that they have been exploited in the fact that their salaries will be reduced by about 40% while the league continues to thrive on their success (Croslis). The players still think that the lockout should continue since they are not willing to accept any person to dictate their career, which happens to, be their life and source of livelihood. Their view is that their patterns have turned out to be their enemies, and they cannot surrender to their terms (Stein). They feel that they are not the cause

The God Father Movie Review Example | Topics and Well Written Essays - 250 words

The God Father - Movie Review Example The film has been accused of promoting the view that Italian immigrants brought into the country their vices such as organised crime and corrupted the American social fabric. On the other hand, the trilogy has been credited with telling the story of a family uprooted from its ancestral home in Sicily, immigration to and adaptation in America, and the succession. The Corleone family depicts the Italian immigrants struggle to settle in a strange country, retain their culture and deal with past problems, familial ties, bad choices and, above all, a will to survive any problems (Sciannameo, 2010). The trilogy neither condemns nor excuses organised crime, but rather brings out into the open the hitherto secret operations of the Mafia imported from Sicily. It shows the original purpose of the organisation; which was the protection from oppression, and subsequent corruption into organised crime. Overriding this theme is the determination of a family to stay afloat, presented without judgement of the means by which they choose to achieve their

Individual Report Essay Example | Topics and Well Written Essays - 3000 words

Individual Report - Essay Example †¦..8 4.2 PEST Analysis†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..8 Political Factors†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦8 Economic Factors†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.9 Social Factors†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦9 Technological Factors†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢ € ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..9 5. Solutions and Recommendations†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦9 6. Forecasts and Outcomes†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦10 7. Reference List†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦12 8. Glossary†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.13 1. ... More questioning of authority and challenging of the organization system, whether public or private, have been observed. The work force is becoming outspoken, articulate and less willing to be dictated to and driven without their involvement and control. The aim of the essay is to proffer management issues in the Philippines, as representative of an Asian culture, and compare it with other prominent management practices in the West. The discourse would be presented with reference to culture theories such as those of Hofstede’s cultural dimensions to solve management problems for a client. 2. Terms of Reference As a group of professionals with diverse cultural orientations, the task given is to prepare a briefing paper to a client in solving management problems in an organization in the Philippines. Our group is composed of one man from Kuwait, one lady from Nigeria, two men from India, and one man from Pakistan. The client is a British national tasked in managing a global orga nization in the Philippines. He is particularly interested in determining management practices in the Philippines, as well as cultural orientation (values, preferences, religion) that influences the way people work in an organization. The cultural orientation of a nation significantly reflects the intricate interaction of attitudes, values, behavior and perceptions manifested by the local population. Using Hofstede’s cultural dimensions, the client is requiring an assessment of each cultural dimension as it pertains to management practices in the Philippines, as compared to other management practices in organizations in the West. The information gathered would be used to assist the client in applying the appropriate management and leadership style needed to solicit the

Counceling (w3) Essay Example | Topics and Well Written Essays - 500 words

Counceling (w3) - Essay Example Therefore, psychologists and psychiatrist nowadays pay a great attention in solving family problems. Psychologists have been adopting a method in their counseling therapy called "Family Systems Theory". "[It] works with families and couples to nurture change and development," (Wikipedia1). This theory perceives the family as an independent and interdependent system. Therefore, this theory focuses on fixing any present damages between the parts of the family. In other words, the Family Systems Theory aims at repairing the relationships between the family members in order to end any stressful situations and solve any existing problems. There are several techniques which the therapist uses in order to reach his prime target. However, the main and most principle step is family meetings. "This offers the opportunity to discuss specific, practical issues and provides a safe space to talk about feelings that surround [the family] and long-term planning," (CareSupportofAmerica1). The therapi st meets with the family together trying to listen to their individual points of view. This step is considered to be extremely beneficial because the psychologist gets a fair chance of viewing the way each member of the family interacts with the other. Moreover, everyone gains an opportunity of knowing the other persons point of view, which can absolutely be a successful way of resolving a lot of current misunderstandings (Wikipedia1). The counselor within his sessions tries to point out and explain to the whole family different methods of dealing with problems and certain situations than the ones they have been adopting or using (Wikipedia1). In other words, the psychotherapist trains the family members how to alter their responses towards each other in certain situations in order to change their behaviors and thus prevent future conflicts. The family systems theory is used by psychologists all over the world.

MPH502 - Introduction to Public Health Module 3 - Case Essay

MPH502 - Introduction to Public Health Module 3 - Case - Essay Example The constitutional design reveals a plain objective in government to protect community health and safety. Government has great responsibilities towards public health sector; health is not only indispensible to finance but also to individuals. Public health is a collective action not only government can save the community’s health. On this point, I completely agree with the author, as if individuals work alone, they cannot save the minimum level of health. Government support is always needed for this great cause. According to the author, it is quiet difficult to separate government responsibility and individual’s effort. Public health also takes in account the individuals that stake a claim to health protection. A strong relationship exists between individual’s health and the health of community at large. I completely agree with author that public health efforts need collective actions for better results because it’s nearly impossible to improve health sector without governments help. Public health law states the advantages and burdens by government on individuals and private health sectors on legally protected interest. Government acts for health sector, it may de-motivate individuals to invest in health sector. The law address that how government act on the growth of health sector both individuals and a large population. Author point is valid up to some extent as both public and private sector has own responsibilities. Government has primary responsibility to promote both mental and physical health and prevent injury and disability. Government responsibility is to inform, educate individuals and invest heavy amount on health. Public health law focuses on governmental responsibilities to the community and individuals health. Government can do much for public health as it owns thousands of resources and power. Government is authorized

Business M2 Essay Example | Topics and Well Written Essays - 250 words

Business M2 - Essay Example Features that can be added to the website are such as virtual help desks, whereby a customer can access real time customer care services. In this case, this requires embedment of a chat widget, where they can initiate a chat with an online operator. Businesses have derived substantial benefits from their websites, whereby they are able to promote their services and products. Other uses their websites to conduct online transactions that contribute to overall sales for the company (Smith, 2012). On the other hand, they can communicate to their customers through the website and this leads to increased efficiency. Customers are provided with a platform through the website where they can communicate effectively and send their complaints, facilitate processing of orders, following up and seeking other services (Smith, 2012). Moreover, customers are able to gather information concerning the business that can be used for making relevant decisions such as selection of vendors. Smith, D. (2012). IT and Business Working Together for Better Compliance. In Defense of Data. Retrived from:

Role of leadership when merging companies Essay Example | Topics and Well Written Essays - 500 words

Role of leadership when merging companies - Essay Example This teamwork between companies is essential to enhance the potential success of the merging. Basically, every organization has a culture, an interconnected value system, shared by the majority of the organization’s members. Organizational culture also involves and is influenced by the trend of effective internal reactions to adjust to external problems and threats (Keyton, 2005). Since the culture is an outcome of previous achievements, it will oppose change such as that brought about by merger or acquisition. Hence, the role of leadership is to facilitate the transition of organizational culture during the process of merging (Hunt, 2009). The auto industry has been historically known for its horizontal formations (Badrtalei & Bates, 2007). The future merging of American automaker Chrysler and Italian automaker Fiat will be discussed in this essay. The possible success or failure of this merging will be discussed in terms of the management perspective and organizational cultu re differences between the two totally distinct automakers. Organizational Challenges to the Chrysler-Fiat Merge It is obvious that American and Italian cultures are starkly dissimilar. The collective bargaining process of Chrysler and Fiat is different.

PepsiCo Team-Board of Governance Essay Example | Topics and Well Written Essays - 250 words

PepsiCo Team-Board of Governance - Essay Example The board of directors is tasked with the responsibility of overseeing the activities of a company. The activities of the board of directors are only delegated powers that are outside the organization itself, which have authority given to it by the bylaws of the organization (Malline 82). The board often faces challenges, and at this team company’s board, the most crucial governance issue is the compliance of public policy issues. There are countless issues that are put across that try and restrict the movement and actions of the board, which tries as much as possible to comply with these policies. In this firm’s case, by bringing in public persons, there is a chance for the organization to find a clear-cut channel to address the compliance of certain policies. It also creates transparency that the firm really needs. Conscious capitalism is what may be used to refer to the philanthropic activities that a firm is willing to undertake (Malline 87). This is in order to help the surrounding external environment benefit and also assist the firm benefit. The firm often participates in different sports activities for some of the different organizations that exist in the area. This is often done as a means to have donations for the groups involved, and also build awareness for the group in question. The skills and capabilities that the firm boasts of make it possible to have different activities in different areas, which also help in fostering exceptional relations between the firm and the people in the external environment.

Explain the theory of Virtue Ethics Essay Example for Free

Explain the theory of Virtue Ethics Essay Aristotle originally introduced virtue Ethics to society in ancient Greek times. Virtue Ethics tells us that we should look at the character of the person instead of the actions or duties a person performs. Instead of concentrating on what is the right thing to do, virtue ethics asks how you can be a better person. Aristotle claims that leading a virtuous life is easy, and those who do, do so to be happy. Happiness is the ultimate goal for everyone in life. To become a better person, you must practice virtuous acts regularly. After a while, these acts will become routine and so the virtuous acts will be nothing more than everyday life and the person a virtuous person. Aristotle said that although virtues should become a habit we must never forget that we behave in such a way because it is right. For example, if a singer practices singing everyday, they will become better at it and used to doing it. This is the same as people who practice their virtues and soon automatically act in the right way, by practicing our skills we improve them, becoming happier. Virtues should not be an effort, but simply a part of everyones personality. Aristotle says that virtue is something that we acquire and are not just born with, people are not inherently good or bad, but become good or bad according to the habits they develop. Aristotle said that a virtue was a Golden Mean in between to vices. These Vices are two extremes of a scale at opposite ends, one of excess and one of deficiency. For example the vices would be shamelessness and shyness, and the virtue modesty. Another example of this would be rudeness and a sense of humour as the two vices and the virtue as wittiness. Such virtues must be cultivated, we must learn when to use certain virtues and to what extent, for example we must not ever use humour in excess to act like a fool, but at the same time we must also not pass into rudeness. Two philosophers, Anscombe and MacIntyre say that there has been a mistake in how virtues have been portrayed. The majority of people look at the actions a person does to judge whether they are virtuous or not. The way in which we behave provides an opportunity for others to judge our virtues and vices. This however is not right. People should look at the character within and look at what the person believes is right and how they think they should help people instead of what they do to help. A famous example of a virtuous person is Mother Theresa. She helped millions of suffering people across the world and for this became well known as a virtuous person. There are hundreds of other virtuous people who would have liked to have helped but were unable to do so in such a huge way who are not considered as virtuous, but these people are just as virtuous but not recognised for it. Aristotle tells us that we are most likely to learn virtuous behaviour from watching others. If we experience others being kind to us and see the happiness it creates we are more likely to practice it then if we were just told to do it. For example, if we were told to be courageous we may occasionally stand up for small things that we disagree with, but if we see someone telling others off for not doing the right thing then we are more likely to not allow bad behaviour towards ourselves. Aristotle said that the best way of becoming virtuous was to follow in the footsteps of a virtuous person, e.g. Mother Theresa and do what they do. Virtue Ethics is relative; Aristotle recognised that virtues in one country may not be the same as virtues in another. He believed that there was no absolute platonic good beyond our world. As virtues have evolved through habits of society it is probable that different societies would deem different actions good or bad. However there is no difference between the virtues of a community and individuals within that community, the supreme happiness that Aristotle talks about is one for the community, and not just and individual. MacIntyre suggests that philosophy is too far removed from ordinary life and said that it is not good enough that philosophers spend their time debating the nature of ethical language or forming reasoned theories of morality in a way that is far removed from real people and real life. All actions are done in order to reach an aim. A successive series of actions are also for an aim, for example getting up in to morning to go to work, is to make money, is to feed our families is to go on nice holidays is to but them nice things etc. all ultimate aims is to make people happy, everything is subordinate to the supreme good, which is happiness. Everyone has different ideas of what happiness is and different things all make different people happy, and Aristotle called this feeling of all round well being eudemonia. Therefore, Virtue Ethics concentrates on what a person is then what a person does. Its aim is to achieve something, which people genuinely want rather then being based on arguably incoherent ideas about the after-life. It is a system, which can be easily applied and understood by all. It fits into a variety of philosophies, and religions, which both do and dont include God. However, there are a few problems with Virtue Ethics. Ones of these which has been pointed out by MacIntyre is that although a virtue is the golden mean between two vices it cannot be applied to all virtues. Virtues such as promise keeping, loyalty, and compassion do not fall between any two vices and so Aristotles theory of this does not really work. Another problem with this theory is that it is of little help to people faced with a moral dilemma. It does not help them make a decision like other theories such a natural law or utilitarianism.

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   <