Machine Learning for Survival Analysis: A Survey <s> INTRODUCTION <s> This paper is a survey of statistical methods used to analyze the length of time until a specified event occurs. These models have often been used to analyze the survival times (i.e., time until death) of medical patients, and so the term survival analysis is natural. In criminology, the main application of these models has been to analyze the time until recidivism, but many other applications are possible. The paper summarizes the statistical literature on survival analysis, and describes its applications in criminology. The methods are illustrated by an application to the prediction of time until recidivism for a sample of North Carolina prison releasees. <s> BIB001 </s> Machine Learning for Survival Analysis: A Survey <s> INTRODUCTION <s> Biomedical and social science researchers who want to analyze survival data with SAS will find just what they need with this easy-to-read and comprehensive guide. Written for the reader with a modest statistical background and minimal knowledge of SAS software, this book teaches many aspects of data input and manipulation. Numerous examples of SAS code and output make this an eminently practical resource, ensuring that even the uninitiated becomes a sophisticated user of survival analysis. The main topics presented include censoring, survival curves, Kaplan-Meier estimation, accelerated failure time models, Cox regression models, and discrete-time analysis. Also included are topics not usually covered, such as time-dependent covariates, competing risks, and repeated events. <s> BIB002 </s> Machine Learning for Survival Analysis: A Survey <s> INTRODUCTION <s> Introduction to Survival Analysis.- Kaplan-Meier Survival Curves and the Log-Rank Test.- The Cox Proportional Hazards Model and Its Characteristics.- Evaluating the Proportional Hazards Assumption.- The Stratified Cox Procedure.- Extension of the Cox Proportional Hazards Model for Time-Dependent Variables.- Parametric Survival Models.- Recurrent Events Survival Analysis.- Competing Risks Survival Analysis. <s> BIB003 </s> Machine Learning for Survival Analysis: A Survey <s> INTRODUCTION <s> Cancer has been characterized as a heterogeneous disease consisting of many different subtypes. The early diagnosis and prognosis of a cancer type have become a necessity in cancer research, as it can facilitate the subsequent clinical management of patients. The importance of classifying cancer patients into high or low risk groups has led many research teams, from the biomedical and the bioinformatics field, to study the application of machine learning (ML) methods. Therefore, these techniques have been utilized as an aim to model the progression and treatment of cancerous conditions. In addition, the ability of ML tools to detect key features from complex datasets reveals their importance. A variety of these techniques, including Artificial Neural Networks (ANNs), Bayesian Networks (BNs), Support Vector Machines (SVMs) and Decision Trees (DTs) have been widely applied in cancer research for the development of predictive models, resulting in effective and accurate decision making. Even though it is evident that the use of ML methods can improve our understanding of cancer progression, an appropriate level of validation is needed in order for these methods to be considered in the everyday clinical practice. In this work, we present a review of recent ML approaches employed in the modeling of cancer progression. The predictive models discussed here are based on various supervised ML techniques as well as on different input features and data samples. Given the growing trend on the application of ML methods in cancer research, we present here the most recent publications that employ these techniques as an aim to model cancer risk or patient outcomes. <s> BIB004
Due to the development of various new data acquisition and big data technologies, the ability to collect a wide variety of data and monitor observations over long periods is now reality in many different disciplines. For most of these real-world applications, the primary objective is to obtain a better estimate of the time a particular event of interest occurs. One of the main challenges for such time-to-event data is that censored instances where the event of interest is not observed either due to time limitations or losing track during the observation period are not uncommon. It often happens that instances that have experienced an event (or are labeled as an event) occur but information about the outcome variable for the remaining instances is only available up to a specific time point. This makes it impractical to apply predictive algorithms directly using the statistical and machine learning approaches normally used to analyze the survival data. Survival analysis, which is an important subfield of statistics, provides various mechanisms to handle such censored data problems when they arise in modeling complex data. This is also referred to as time-to-event data when modeling a particular event of interest is the main objective and is very common in real-world application domains. In addition to the difficulty of handling censored data, there are other unique challenges that must be overcome when performing predictive modeling with survival data. A number of researchers have begun to work on developing new computational algorithms that are capable of handling such complex challenges. To address these practical concerns, some related works have adapted machine learning methods to solve survival analysis problems, and machine learning researchers have developed a suite of sophisticated and effective algorithms that either complement or compete with the traditional statistical methods. However, in spite of the importance of these problems and their relevance to various real-world applications, research on this topic is scattered across several different disciplines. Moreover, few surveys are available in the literature on this topic, and, to the best of our knowledge, there has not yet been a comprehensive review of survival analysis and its recent developments from a machine learning perspective. Almost all of these existing survey articles focus solely on the statistical methods utilized and either completely ignore or barely mention recent advances in machine learning in this field. One of the earliest surveys BIB001 gives an overview of the statistical survival analysis methods and describes their application in criminology for predicting the time until recidivism. Most of the existing books on survival analysis BIB003  BIB002 introduce this topic from a traditional statistical perspective rather than a machine learning standpoint. Recently, however, this has begun to change and  and BIB004 both discussed applications in cancer prediction and included a comparison of several machine learning techniques. The primary purpose of this survey article is therefore to provide a comprehensive and structured overview of various machine learning methods for survival analysis, along with a discussion of the traditional statistical methods. We demonstrate the commonly used evaluation metrics and advanced related formulations that are typically investigated in connection with this research topic. We will discuss a detailed taxonomy of all the survival analysis methods developed in traditional statistics, as well as those that have been proposed more recently by the machine learning community. We will also provide links to various implementations and source codes which will enable readers to delve more deeply into the methods discussed in this article. Finally, we will discuss various applications of survival analysis. The rest of this article is organized as follows. We will begin with a brief review of the basic concepts, notations, and definitions that are necessary to comprehend the survival analysis algorithms and provide a formal problem statement for the survival analysis problem in Section 2. A taxonomy of the existing survival analysis methods, including both statistical and machine learning methods, will also provide a holistic view of existing works in the area of survival analysis. We will then move on to review the existing well-studied representative conventional statistical methods, including nonparametric, semi-parametric, and parametric models, in Section 3. Section 4 describes several basic machine learning approaches, including survival trees, Bayesian methods, support vector machines, and neural networks that have been specifically developed for survival analysis. Different kinds of advanced machine learning algorithms such as ensemble learning, transfer learning, multitask learning, and active learning for handling survival data will also be discussed. Section 5 focuses on appropriate evaluation metrics for survival models. In addition to the survival analysis algorithms, some interesting topics related to this topic have attracted considerable attention in various fields. In Section 6, several related concepts such as early prediction and complex events will be discussed. Various data transformation techniques such as uncensoring and calibration, both of which are typically used in conjunction with existing predictive methods, will also be mentioned briefly. A discussion of relevant topics in complex event analysis, such as competing risks and recurrent events, will also be provided. In Section 7, some real-world applications of survival analysis methods will be briefly explained, and more insights into these application domains are provided. In Section 8, details regarding various implementations and software packages for survival analysis methods are discussed. Finally, Section 9 concludes our discussion.