Preface

Survival analysis arises in many fields of study including medicine, biology, engineering, public health, epidemiology, and economics. Recent advances in computing, software development such as BUGS, and practical methods for prior elicitation have made Bayesian survival analysis of complex models feasible for both practitioners and researchers. This book provides a comprehensive treatment of Bayesian survival analysis. Several topics are addressed, including parametric and semiparametric models, proportional and nonproportional hazards models, frailty models, cure rate models, model selection and comparison, joint models for longitudinal and survival data, models with time-varying covariates, missing covariate data, design and monitoring of clinical trials, accelerated failure time models, models for multivariate survival data, and special types of hierarchical survival models. We also consider various censoring schemes, including right and interval censored data. Several additional topics related to the Bayesian paradigm are discussed, including noninformative and informative prior specifications, computing posterior quantities of interest, Bayesian hypothesis testing, variable selection, model checking techniques using Bayesian diagnostic methods, and Markov chain Monte Carlo (MCMC) algorithms for sampling from the posterior and predictive distributions.

The book will present a balance between theory and applications, and for each of the models and topics mentioned above, we present detailed examples and analyses from case studies whenever possible. Moreover, we demonstrate the use of the statistical package BUGS for several of the models and methodologies discussed in this book. Theoretical and applied problems are given in the exercises at the end of each chapter. The book is structured so that the methodology and applications are presented in the main body of each chapter and all rigorous proofs and derivations are placed in Appendices. This should enable a wide audience of readers to use the book without having to go through the technical details. Without compromising our main goal of presenting Bayesian methods for survival analysis, we have tried to acknowledge and briefly review the relevant frequentist methods. We compare the frequentist and Bayesian techniques whenever possible and discuss the advantages and disadvantages of Bayesian methods for each topic.

Several types of parametric and semiparametric models are examined. For the parametric models, we discuss the exponential, gamma, Weibull, log-normal, and extreme value regression models. For the semiparametric models, we discuss a wide variety models based on prior processes for the cumulative baseline hazard, the baseline hazard, or the cumulative baseline distribution function. Specifically, we discuss the gamma process, beta process, Dirichlet process, and correlated gamma process. We also discuss frailty survival models that allow the survival times to be correlated between subjects, as well as multiple event time models where each subject has a vector of time-to-event variables. In addition, we examine parametric and semiparametric models for univariate survival data with a cure fraction (cure rate models) as well as multivariate cure rate models. Also, we discuss accelerated failure time models and flexible classes of hierarchical survival models based on neural networks. The applications are all essentially from the health sciences, including cancer, AIDS, and the environment.

The book is intended as a graduate textbook or a reference book for a one- or two-semester course at the advanced masters or Ph.D. level. The prerequisites include one course in statistical inference and Bayesian theory at the level of CasellaCasella, G. and BergerBerger, R.L. (1990) and BoxBox, G.E.P. and TiaoTiao, G.C. (1992). The book can also be used after a course in Bayesian statistics using the books by CarlinCarlin, B. P. and LouisLouis, T. A. (1996) or GelmanGelman, A., CarlinCarlin, J. B., SternStern, H. S., and RubinRubin, D. B. (1995). This book focuses on an important subfield of application. It would be most suitable for second- or third-year graduate students in statistics or biostatistics. It would also serve as a useful reference book for applied or theoretical researchers as well as practitioners. Moreover, the book presents several open research problems that could serve as useful thesis topics.

We would like to acknowledge the following people, who gave us permission to use some of the contents from their work, including tables and figures: Elja Arjas, Brad Carlin, Paul Damien, Dipak Dey, Dario Gasbarra, Robert J. Gray, Paul Gustafson, Lynn Kuo, Sandra Lee, Bani Mallick, Nalini Ravishanker, Sujit Sahu, Daniel Sargent, Dongchu Sun, Jeremy Taylor, Bruce Turnbull, Helen Vlachos, Chris Volinsky, Steve Walker, and Marvin Zelen. Joseph Ibrahim would like to give deep and special thanks to Marvin Zelen for being his wonderful mentor and friend at Harvard, and to whom he feels greatly indebted. Ming-Hui Chen would like to give special thanks to his advisors James Berger and Bruce Schmeiser, who have served as his wonderful mentors for the last ten years. Finally, we owe deep thanks to our parents and our families for their constant love, patience, understanding, and support. It is to them that we dedicate this book.

Joseph G. Ibrahim, Ming-Hui Chen, and Debajyoti Sinha
$~$ March 2001