Bayesian Survival Analysis Book - Springer Series in Statistics | Statistical Modeling for Medical Research, Clinical Trials & Reliability Engineering

The first reviewer of this book seems to be knowledgeable about the subject but in my view overly harsh. The book is not intended for researchers without background in statistics. In fact, the authors state that the text is an advanced text for graduate students requiring as a prerequisite a course in mathematical statistics and one in Bayesian statistics at the level of Box and Tiao. The authors do claim to place a balance between theory and applications. Although I do feel this is an advanced text that is heavy on theory, there claim is somewhat justified in the sense that they provide several motivating examples particularly from the area of cancer research right upfront in chapter 1 even before discussing the basics of survival analysis and Bayesian methods.An attractive feature of the text is that many topics are covered in book form for the first time. I found the coverage of cure rate models particularly interesting. Another reviewer criticized the use of piecewise models for hazard rate modelling as esoteric. However I find the exploration of these new and somewhat complicated techniques rather fascinating. The Cox proportional hazard rate model has been a mainstay in survival analysis since introduced by Cox in the 1970s. But experience has shown many applications where the proportionality assumption is not valid. Generalizations such as those in Therneau's book and the ones that Ibrahim et al. introduce here should be welcomed. The authors illustrate their applications of these techniques throughout the book. Future use will determine the degree of applicability of these techniques and issues of overparameterization needs to be addressed, but the authors should be praised for making the attempt.The text is not just an advanced book on the authors' research. It also includes a wealth of discussion and references to the growing literature on MCMC, survival analysis and specialized topics such as cure models, frailty models and methods for comparing models.The reference list is authoritative, scholarly and extensive, providing reference to the very early articles from the 1950s (e.g. Berkson and Gage) as well as the most recent from the 1990s and 2000-2001.In the first chapter the authors make a strong case for the advantages of the Bayesian approach through the use of MCMC. I would only caution that the real issue between the Bayesian and frequentist inference schools lies in the appropriateness of prior distribution in inference and whether or not subjective probability is more appropriate than objective probability. These are deeper philosophical issues and seemed to be glossed over a little by the authors. However, MCMC has allowed the use of richer classes of prior distributions and the ability to look at the sensitivity of the prior modeling assumptions. For this reason many statisticians are accepting the Bayesian approach and are doing data analysis using both paradigms.Bayesian methods are seeing growth in clinical trials particularly regarding the choice of sequential rules for stopping a trial. This has been particularly true in the medical device area where FDA statisticians have even encouraged its use in the design of trials.With the publication of this book we can only hope to see greater use of it in survival analysis.My one disappointment is that I would have liked to have seen a more systematic account of the various MCMC algorithms explaining their differences, limitations and advantages. The current literature on MCMC is suitably referenced including the fine tutorials on Gibbs Sampling and the Metropolis-Hastings algorithm. I just wish this book had been a little more self-contained from the MCMC point of view. Perhaps that will come in a second edition a few years hence.The authors do jump into advanced topics and this can be frustrating for the novice. However its intended aim is for research statisticians and graduate students in statistics and with the prerequisites in hand, the book is very valuable. It does achieve its intended goal.The theory is well covered but to make it an easier reference source, mathematical proofs are left to appendices. Other advanced topics not commonly found in text books and worthy of note are Dirichlet priors and multivariate survival models. Other recent texts that include such advanced topics as extensions to proportional hazards and multivariate surival models are respectively the text by Therneau and Grambsch and the text by Hougaard.