Machine Learning for Survival Analysis: A Survey <s> Bayesian Methods <s> Abstract Although successful in medical diagnostic problems, inductive learning systems were not widely accepted in medical practice. In this paper two different approaches to machine learning in medical applications are compared: the system for inductive learning of decision trees Assistant, and the naive Bayesian classifier. Both methodologies were tested in four medical diagnostic problems: localization of primary tumor, prognostics of recurrence of breast cancer, diagnosis of thyroid diseases, and rheumatology. The accuracy of automatically acquired diagnostic knowledge from stored data records is compared, and the interpretation of the knowledge and the explanation ability of the classification process of each system is discussed. Surprisingly, the naive Bayesian classifier is superior to Assistant in classification accuracy and explanation ability, while the interpretation of the acquired knowledge seems to be equally valuable. In addition, two extensions to naive Bayesian classifier are briefly des... <s> BIB001 </s> Machine Learning for Survival Analysis: A Survey <s> Bayesian Methods <s> It is argued that P-values and the tests based upon them give unsatisfactory results, especially in large samples. It is shown that, in regression, when there are many candidate independent variables, standard variable selection procedures can give very misleading results. Also, by selecting a single model, they ignore model uncertainty and so underestimate the uncertainty about quantities of interest. The Bayesian approach to hypothesis testing, model selection, and accounting for model uncertainty is presented. Implementing this is straightforward through the use of the simple and accurate BIC approximation, and it can be done using the output from standard software. Specific results are presented for most of the types of model commonly used in sociology. It is shown that this approach overcomes the difficulties with P-values and standard model selection procedures based on them. It also allows easy comparison of nonnested models, and permits the quantification of the evidence for a null hypothesis of interest, such as a convergence theory or a hypothesis about societal norms. <s> BIB002 </s> Machine Learning for Survival Analysis: A Survey <s> Bayesian Methods <s> A Bayesian framework is introduced to carry out Automatic Relevance Determination (ARD) in feedforward neural networks to model censored data. A procedure to identify and interpret the prognostic group allocation is also described. These methodologies are applied to 1616 records routinely collected at Christie Hospital, in a monthly cohort study with 5-year follow-up. Two cohort studies are presented, for low- and high-risk patients allocated by standard clinical staging. The results of contrasting the Partial Logistic Artificial Neural Network (PLANN)-ARD model with the proportional hazards model are that the two are consistent, but the neural network may be more specific in the allocation of patients into prognostic groups. With automatic model selection, the regularised neural network is more conservative than the default stepwise forward selection procedure implemented by SPSS with the Akaike Information Criterion. <s> BIB003
The Bayes theorem is one of the most fundamental principles in probability theory and mathematical statistics. It provides a link between the posterior probability and the prior probability so users can see how probability values change before and after accounting for a certain event. There are two models, namely Naïve Bayes (NB) and Bayesian networks (BN)  , both of which provide the probability of an event of interest as their output and are commonly used for clinical prediction BIB001   . The experimental results of applying Bayesian methods to survival data show that these methods have excellent interpretability and uncertainty reasoning . NB, a well-known probabilistic method in machine learning, is one of the simplest yet most effective prediction algorithms. Its uses are legion; for example,  built a naïve Bayesian classifier to make predictions in clinical medicine by estimating various probabilities from the data, while Fard et al. (2016) effectively integrated Bayesian methods with an AFT model by extrapolating the prior event probability to perform early-stage prediction on survival data for future time points. One drawback of the NB method, however, is that it assumes independence between all the features, which may not be true for many problems in survival analysis. A BN, in which the features can be related to each other at a number of different levels, can graphically represent a theoretical distribution over a set of variables. BNs can visually represent all the relationships between the variables, making it easily interpretable for the end user. It can also acquire knowledge by estimating the network structures and parameters from a given dataset. BIB003 proposed a Bayesian neural network framework to perform model selection for survival data using an automatic relevance determination procedure MacKay (1995) . BIB002 proposed a Bayesian model averaging procedure for Cox proportional hazards models which was then used to evaluate the Bayes factors in the problem. More recently, Fard et al. (2016) proposed a novel framework that combines the power of BN representations with the AFT model by extrapolating the prior probabilities to future time points. The time complexity of these Bayesian approaches depends primarily on the types of Bayesian method used in the models.