JULIE Its my fathers fault that I cant trust men Essays

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

womens lib essays

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

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

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

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

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

Integrated Marketing Communication To Build Brands Essay

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

Decision Tree for Prognostic Classification

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

Fireworks :: essays research papers

Every year, America celebrates many holidays with fireworks. One of the most popular selections is a Roman Candle. If you want to try to make this at home, common pyrotechnics stores have all the supplies you would need. Just think of the â€Å"oohhs† and â€Å"ahhhhs† when you light off your homemade fireworks at home.   Ã‚  Ã‚  Ã‚  Ã‚  First of all, you need a sturdy, good tube. The tube should be cylindrical and should be at least 3/32 of an inch thick. The opening at the top of your tube should have a 5/8 inch opening. Then take a 1/16 inch fuse, make sure it covers the whole tube and sticks out a little bit, just like any other firework and keep the tube in place by using tape. Next, 1.25 grams of 3F BP should be poured into the tube. Then, gently put a one-half inch star down the tube. This is what will go up into the air and is responsible for the shots. Then, put some sawdust through the tube. Make sure the sawdust is evenly spread and turn the tube over. All contents should not fall out if this is done correctly. Make sure you use some sort of mechanism to push down upon the sawdust. Keep repeating these instructions. The tube should consist of bp, star, sawdust, bp, star, and sawdust for as many shots as you want. Good Luck with your newly made Roman Candle and have a safe experience. Next, we will examine how to make a salute go up in the air. Salutes are generally products that make a Kaboom sound when launched.   Ã‚  Ã‚  Ã‚  Ã‚   The lifting cup is made when you glue kraft paper that overhangs the salute. Next, you add some lift usually gunpowder to propel it. The inner paper should be glued with a small device or a glue gun. Meanwhile, while the glue is wet fold the paper into quarters. Place a cut in the newly formed pouch and add a piece of quick match. Now, we will learn how to make salute inserts. First off, buy some top- notch 3 inch tubes. Take all of your tubes and set them on a piece of tin foil. Secondly, you need to fill a tube to the top with hot glue and as the glue is about to dry put it into the freezer for 5 minutes. After 5 minutes is up pull the tin foil off of the tubes and put toilet paper down the open end of the tube.

Drayton 61 Structure Essay

There are many different ways to approach the structure of a poem, a piece of fiction, a play. In what follows I’m going to make some suggestions about the structure of Michael Drayton’s poem beginning â€Å"Since there’s no help, come let us kiss and part,† a sonnet from his collection titled Idea, first published in 1593. It’s important for you to understand that there are many valuable and illuminating ways to talk about this poem’s structure, not any one, single, right way. That’s why I’m writing suggestions, not prescriptions. When I say â€Å"the structure† of Drayton’s poem, I mean not only how it’s put together but also the way it works. Learning how something is put together shows us what the parts are. Learning how those â€Å"put-together† parts work shows us the thing in action. And a short lyric poem like Drayton’s (any work of literature that we’re reading, for that matter) is a thing in action, a dynamic process. Here is Drayton’s poem. Since there’s no help, come let us kiss and part; Nay, I have done, you get no more of me, And I am glad, yea glad with all my heart That thus so cleanly I myself can free;4 Shake hands forever, cancel all our vows, And when we meet at any time again, Be it not seen in either of our brows That we one jot of love retain. 8 Now at the last gasp of love’s latest breath, When, his pulse failing, passion speechless lies, When faith is kneeling by his bed of death, And innocence is closing up his eyes, 12 Now if thou wouldst, when all have given him over, From death to life thou mightst him yet recover. Well, what are the parts of this poem? Words in lines. Specifically, words in lines which usually add up to ten syllables each. Words put together so that they make a rhythm as we say them, a sort of di-da di-da di-da di-da di-da rhythm, with emphasis usually on the â€Å"da† syllable, like this: And I am glad, yea glad with all my heart or this: And when we meet at any time again. And the poem is made up of lines whose end words rhyme (that is, chime together) in a certain pattern throughout the poem, like this: part / me / heart / free(abab)lines 1-4 vows /again / brows / retain (cdcd)lines 5-8 breath / lies / death / eyes (efef)lines 9-12 over / recover(gg)lines 13-14 This pattern creates groups of lines (they have technical English-teacher terms), which go together because their end-word rhymes link them together: lines 1-4=first quatrain lines 5-8=second quatrain  lines 9-12=third quatrain lines 13-14=final couplet The words in this poem are also organized grammatically, in several ways: sentences–the first (a cumulative sentence—check out the term in a handbook or do a Google search) consisting of the poem’s first and second quatrains and the second (a periodic sentence) consisting of the third quatrain and the final couplet; clauses–a bunc h; notice, for example, the first line of the poem– Since there’s no help, come let us kiss and part— a subordinate clause followed by a main clause in a combination showing a cause-and-effect relationship;  verbs—significant mood shifts within the poem (another technical English-teacher term—verbs come in â€Å"moods,† namely the indicative, subjunctive, or imperative, which, if you can’t recognize, you’d better get a grammar/composition handbook), with the imperative and indicative dominating the first eight lines and the indicative and subjunctive the last six (note especially â€Å"wouldst† and â€Å"mightst† in ll. 13-14); subjects—all personal pronouns in the first eight lines (â€Å"us,† â€Å"I,† â€Å"you,† â€Å"we†), nouns in the next four (â€Å"passion,† â€Å"faith,† â€Å"innocence†), and a return to pronouns in the final couplet (â€Å"thou ,† â€Å"all†); adverbs expressing time—â€Å"when† X 4, â€Å"Now† X 2, â€Å"again,† and â€Å"yet†; adjectives—there are very few: why Well, despite the fact that GRAMMAR IS REALITY, we probably should get off the grammar wagon for the time being. There are other ways to look at how words in a poem are organized. Consider the way they get sounded when you read them. Listen carefully as you say the first two quatrains of the poem: Since there’s no help, come let us kiss and part; Nay, I have done, you get no more of me, And I am glad, yea glad with all my heart That thus so cleanly I myself can free;4 Shake hands forever, cancel all our vows, And when we meet at any time again, Be it not seen in either of our brows That we one jot of love retain. 8 I’m hearing a lot of one-syllable words. The first three lines consist entirely of one-syllable words, and there are only seven two-syllable words in all of the eight lines. I’m also hearing a kind of clipped, short way of speaking in these lines. Partly this is due to (ALERT-ALERT: another technical term) alliteration, as in the hard â€Å"c† sounds—come, kiss, cleanly, can, Shake, cancel—and â€Å"t† sounds—let, part, get, heart, That, meet, time, it, not, That, jot, retain. Now listen to the way you’re sounding the words in the third quatrain: Now at the last gasp of love’s latest breath, When, his pulse failing, passion speechless lies, When faith is kneeling by his bed of death, And innocence is closing up his eyes 12 I’m hearing a lot more two- and even a three-syllable word now, especially in ll. 10-12. Also, I’m more aware of a kind of â€Å"breathiness† than I was when saying the first eight lines. Partly this is due to the fact that I’m saying words here that require more breath than one-syllable words. There’s another reason for the â€Å"breathiness,† and, yup, there’s a technical term for this, too, but let’s skip over it and listen to what’s causing this â€Å"breathiness. † What do you notice when you say these words: gasp, breath, pulse, failing, passion, faith, bed, death? Feel a little puff of breath coming out of your mouth, a kind of â€Å"uh,† after you say the initial consonant of the word? That’s what I’m getting. I think there’s another reason I’m feeling this â€Å"breathiness,† a reason not related to the sounds of words but to what they’re saying. The speaker in this poem is painting a picture in the third quatrain by using images. LOOK OUT (another technical term): â€Å"imagery† or â€Å"images† can refer to literal, descriptive pictures in a piece of writing, as well as to figurative language like (technical alert) similes, metaphors, personifications, etc. , or to both. In the present case, the speaker’s imagery is both literal and figurative. S/he’s creating a deathbed scene: there’s a â€Å"last gasp of . . . breath,† a â€Å"pulse failing,† a â€Å"bed of death,† even the â€Å"closing up† of the dying person’s eyes by an attendant. All this is vivid, literal imagery. But who’s dying? Someone named â€Å"love. † Who else is present in the scene? Persons named â€Å"passion,† â€Å"faith,† and â€Å"innocence† (in some printed versions of the poem these names are capitalized). These â€Å"persons† are abstract nouns that are being given the characteristics of humans—hence the term personification. So I’m getting both literal and figurative images, a double-whammy deathbed scene that strongly conveys the idea of the dying person’s final expiration. How does the imagery of the end of the poem compare with imagery at the beginning of the poem? I can’t see any figurative language at all in the first two quatrains, except for â€Å"you get no more of me† in l. 2, which suggests the idea of possession in a love relationship, and â€Å"Be it not seen in either of our brows† in l. 7, a (you got it) metonymy or figure of speech in which a part is substituted for the whole (brow for face). But for these exceptions, I can take more or less literally everything the speaker is saying. S/he and her/his partner are going to kiss and separate—that’s all that can be done. The speaker is finished with the partner, and s/he’s glad that s/he can make this separation so neatly. It’s simply a case of shaking hands goodbye, freeing each other of any obligation created by what the lovers might have said in the past (â€Å"I swear I’ll love you forever,† â€Å"There’ll never be another person in my life,† â€Å"You’re the center of my world,† etc. ), and making sure that, whenever they meet in the future, no bystander will be able to detect the slightest trace of their former love. I think it’s time to start asking how these put-together parts work in action, that is, to see what dynamic process is operating in the poem. If the structure of this poem is a dynamic process, then you ought to be able to see changes, differences, shifts, as you move through the poem. In fact, if you compare the beginning of the poem with the end, you can see major shifts. I’ve already noted some—for example, the change in verb moods from imperative and indicative in the first eight lines to indicative and subjunctive in the last six. Then there’s the difference in the sounds the words make and the style of speaking you can hear, from the direct, concise, controlled tone of ll. 1-8 to the breathy, drawn out speech of the last part of the poem, where the speaker creates a vivid picture of Love at the point of death. How do these grammatical and tonal differences work together to reinforce the changes you can hear as the speaker confronts his/her soon-to-be-ex partner? In the first part of the poem the speaker is giving orders to his/her partner, using imperative verbs (â€Å"come let us kiss and part,† â€Å"Shake hands,† â€Å"cancel,† â€Å"be it not seen†) and making statements s/he intends the partner to take as true and literal, using indicative verbs (â€Å"there’s no help,† â€Å"I have done,† â€Å"you get,† â€Å"I am glad,† â€Å"I .  can free†). Then there’s the alliteration of hard â€Å"c† and â€Å"t† sounds and the dominance of one-syllable words, creating a sense of directness. It’s almost as if the speaker is trying to maintain emotional contr ol of the situation, as if s/he needed to suppress feelings of regret over the breakup. You can even see this in the use of â€Å"you† in l. 2, a formal style of address in early modern English. (In a similar situation, why would you formally address your soon-to-be-ex? ) There is also an effort at matter-of-factness here, evident in the avoidance of figurative language. All this is accomplished in a cumulative sentence, where you get the main message at the beginning (we know we’re breaking up, so let’s get on with it). In the last part of the poem the speaker is painting a vivid picture of Love at the point of death, surrounded by mourning figures (those personifications) attending at the bedside, and maybe, if s/he were willing, the speaker’s partner. Note that indicative verbs are used in ll. 10-12 (in the subordinate â€Å"when† clauses), then subjunctive verbs in the final couplet (â€Å"if thou wouldst† and â€Å"mightst .. recover†). The important thing to know about the subjunctive mood here is that it expresses an action that might take place, not one that does take place. Note also that in this final couplet the speaker addresses his/her partner by using the informal, intimate form â€Å"thou† instead of the formal â€Å"you. † In addition to the figurative language and significant gr ammatical differences between the beginning of the poem and this part, you now get longer words and the breathiness I noted. It’s as if the speaker is encouraging his/her partner to imagine, to see, to feel what the death of their love is going to be like, complete with mourners and last gasps. This invitation to participate is clearly intended to have an emotional impact on the partner. The speaker is also feeling some emotion, I think. You can see this in something I haven’t spoken of before. It’s the shift from a regular di-da di-da rhythm in the first part of the poem to some pretty strong, off-beat rhythms in the last six lines. Look, for instance, at the beats in ll. 9-10 or l. 13. Something different is going on here, not the regular di-da di-da amble you’ve gotten used to. Why this shift? I think it may have to do with the emotion the speaker is starting to feel as s/he describes the deathbed scene. S/he is getting near the end of the poem, and if anything is going to happen other than shaking hands and saying goodbye, it had better happen soon. I’m sensing that emotions are getting much more noticeable. S/he even makes his/her partner the central figure, on whom love’s life or death depends: Now if thou wouldst, when all have given him over, From death to life thou mightst him yet recover. All this happens in a periodic sentence, where you get the main message at the end, here in the final couplet (it’s up to you dear, if you want to bring love back . . . ) Well, I could go on, but I won’t—not for much longer, anyway. I’ve been trying to show you that the closer you look at a piece of literature, the more things happen. Drayton’s poem—any good poem—is super dynamic. However, you can’t capture this dynamic quality just by taking a photograph or making a list of the poem’s parts. You’ve got to experience the dynamic quality of the poem in order to know its structure.

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