Machine Learning for Survival Analysis: A Survey <s> Competing Risks. <s> Modern survival analysis and more general event history analysis may be effectively handled in the mathematical framework of counting processes, stochastic integration, martingale central limit theory and product integration. This book presents this theory, which has been the subject of an intense research activity during the past one-and-a-half decades. The exposition of the theory is integrated with the careful presentation of many practical examples, based almost exlusively on the authors' experience, with detailed numerical and graphical illustrations. "Statistical Models Based on Counting Processes" may be viewed as a research monograph for mathematical statisticians and biostatisticians, although almost all methods are given in sufficient detail to be used in practice by other mathematically oriented researchers studying event histories (demographers, econometricians, epidemiologists, actuariala mathematicians, reliability engineers, biologists). Much of the material has so far only been available in the journal literature (if at all), and a wide variety of researchers will find this an invlauable survey of the subject. <s> BIB001 </s> Machine Learning for Survival Analysis: A Survey <s> Competing Risks. <s> TheCoxregressionmodel,whichiswidelyusedfortheanalysisoftreatmentandprognosticefiectswithcensoredsurvivaldata,makestheassumptionofconstanthazardratio. Intheviolationofthisassumption, difierent methods should be used to deal with non-proportionality of hazards. Inthisstudy,thestratifledCoxregressionmodelandextended Coxregressionmodel,whichusestimedependentcovariatetermswith flxed functions of time are discussed. The results are illustrated by an analysis of lung cancer data in order to compare these methods with respect to Cox regression model in the presence of nonproportional hazards. <s> BIB002
In a survival problem, if several different types of events are considered, but only one of them can occur for each instance over the follow-up period, then the competing risks will be defined as the probabilities of different events. In other words, competing risks can only exist in survival problems with more than one possible event of interest, but only one event will occur at any given time. For example, in the healthcare domain, a patient may have both a heart attack and lung cancer before his death, but the cause of death can only be either lung cancer or a heart attack, not both. In this case, competing risks are events that prevent an event of interest from occurring, which is different from censoring. Note that, in the case of censoring, the event of interest still occurs at a later time, while the event of interest is impeded. 6.3.2 Recurrent Events. In many application domains, the event of interest in a survival problems may occur several times during the observation time period. This is significantly different from a single event, such as the death of a patient in the healthcare domain, which can occur only once. Here, the outcome event can occur for each instance more than once during the observation time period. In survival analysis, we refer to events that can occur more than once as recurrent events, which contrasts with the case of competing risks just discussed. Typically, if all the recurring events for each instance are of the same type, the Counting Process (CP) algorithm BIB001 can be used to tackle this problem. However, if there are different types of events or determining the order of the events is the main goal, other methods using stratified Cox (SC) approaches are more appropriate BIB002 . These methods include the stratified CP, Gap Time, and Marginal approaches. These differ not only in the way they determine the risk set, but also in the data format required. The reader can refer to the supplementary material of this article for more details regarding both competing risks and recurrent events problems.