Machine Learning for Survival Analysis: A Survey <s> Survival Trees <s> The survival experience of 982 non-Hodgkin's lymphoma patients registered at Princess Margaret Hospital, Toronto, between 1967 and 1975, was studied. Prognostic groups were obtained by means of a classification procedure based on standard statistical techniques; the variables utilized in the classification were ones of known reproducibility which could be measured with little inconvenience to the patient. The results show that these prognostic groups give better information than the Ann Arbor staging classification in the sense that the survival curves are clearly separated and "good prognosis" and "poor prognosis" groups are clearly identified. Implications for therapy planning are briefly discussed. <s> BIB001 </s> Machine Learning for Survival Analysis: A Survey <s> Survival Trees <s> In this note, tree-structured recursive partitioning schemes for classification, probability class estimation, and regression are adapted to cover censored survival analysis. The only assumptions required are those which guarantee identifiability of conditional distributions of lifetime given covariates. Thus, the techniques are applicable to more general situations than are those of the famous semi-parametric model of Cox. <s> BIB002 </s> Machine Learning for Survival Analysis: A Survey <s> Survival Trees <s> Abstract The problem of defining prognostic groups on the basis of censored survival times and covariates is central in medical biostatistics. Several methods have been proposed, but little is known about their relative advantages. Here three methods are discussed: Stepwise Regression, Correspondence Analysis and Recursive Partition. The approach is empirical in that the focus is on the performance on real data sets. Our example is discussed at length. We find that Stepwise Regression has the advantage of flexibility and economy of description, but is limited in discovering interactions and other complex features of the data. Correspondence Analysis is equally flexible, though less economical, and is very powerful in revealing unexpected features of the data: it is recommended as an exploratory tool. Recursive Partition is efficient in discovering interactions within large data sets and has the advantage of being the only method that produces clear descriptions in direct clinical terms; its flexibility, however, is limited, especially when the number of covariates is large relative to the number of individuals. Since no method is universally preferable, their joint use is recommended. A variety of criteria for ranking stratifications are proposed when a choice to be made. <s> BIB003 </s> Machine Learning for Survival Analysis: A Survey <s> Survival Trees <s> In clinical and epidemiological studies, interactions among covariates are of primary importance. In the absence of clearly stated a priori hypotheses, it is usual to build predictive models by means of stepwise logistic or Cox regression, a practice that tends to emphasize main effects and overlook possible interactions. <s> BIB004 </s> Machine Learning for Survival Analysis: A Survey <s> Survival Trees <s> This paper concerns a recursive partitioning algorithm for incomplete survival data. The splitting criterion employed is exponential log-likelihood loss. The method has been integrated into a computer program similar in structure to the commercial package CART. Special features incorporated into the program include a modification to prevent zero hazard estimates during the cross-validation procedure and a method based on the chi-square distribution for final tree selection. Simulation results demonstrate the program's capability to identify the underlying hazard structure in survival data. An example utilizing data from patients with diffuse large cell lymphoma is presented. <s> BIB005 </s> Machine Learning for Survival Analysis: A Survey <s> Survival Trees <s> A method is developed for obtaining tree-structured relative risk estimates for censored survival data. The first step of a full likelihood estimation procedure is used in a recursive partitioning algorithm that adopts most aspects of the widely used Classification and Regression Tree (CART) algorithm of Breiman et al. (1984, Classification and Regression Trees, Belmont, California: Wadsworth). The performance of the technique is investigated through stimulation and compared to the tree-structured survival methods proposed by Davis and Anderson (1989, Statistics in Medicine 8, 947-961) and Therneau, Grambsch, and Fleming (1990, Biometrika 77, 147-160). <s> BIB006
Survival trees are classification and regression trees that are specifically tailored to handle censored data. The basic intuition behind tree models is that data are recursively partitioned based on a particular splitting criterion, and objects that are similar to each other based on the event of interest will be placed in the same node. Although the earliest attempt to use a tree structure for survival data was reported in BIB001 , BIB002 was the first paper to explicitly discuss the creation of survival trees. The primary difference between a survival tree and the standard decision tree is in the choice of splitting criterion. The decision tree method performs recursive partitioning on the data by setting a threshold for each feature, but it can neither consider the interactions between the features nor the censored information in the model (Safavian and Landgrebe 1991). The splitting criteria used for survival trees can be grouped into two categories; namely, those that minimize within-node homogeneity and those that maximize between-node heterogeneity. The first of these approaches minimizes the loss function using the within-node homogeneity criterion. For example, BIB002 measured the homogeneity and Hellinger distances between the estimated distribution functions using the Wasserstein metric, while an exponential log-likelihood function was employed in BIB005 for recursive partitioning based on the sum of residuals from the Cox model and BIB006 measured the node deviance based on the first step of a full likelihood estimation procedure. For the second type of splitting criteria, Ciampi et al. BIB003 employed log-rank test statistics for betweennode heterogeneity measures. The same group BIB004 then went on to propose the use of a likelihood ratio statistic to measure the dissimilarity between two nodes. Based on the Tarone-Ware class of two-sample statistics, Segal Segal (1988) introduced a procedure to measure the between-node dissimilarity. The main advantage a survival tree has over a standard decision tree is its ability to handle censored data using the tree structure. Another important aspect of building a survival tree is the selection of the final tree. Procedures such as backward or forward selection can be followed for choosing the optimal tree structure  ). However, an ensemble of trees (described in Section 4.5) can avoid the problem of final tree selection and provide a better performance than is possible with a single tree.