Proportional Hazards Regression

ISBN-13: 9780387251486 / Angielski / Twarda / 2008 / 542 str.

John O'Quigley

Opis

Proportional hazards models and their extensions (models with ti- dependent covariates, models with time dependent regression co- cients, models with random coe?cients and any mixture of these) can be used to characterize just about any applied problem to which the techniques of survival analysis are appropriate. This simple obser- tion enables us to ?nd an elegant statistical expression for all plausible practical situations arising in the analysis of survival data. We have a single unifying framework. In consequence, a solid understanding of the framework itself o?ers the statistician the ability to tackle the thorniestofquestionswhichmayarisewhendealingwithsurvivaldata. The main goal of this text is not to present or review the very s- stantial amount of research that has been carried out on proportional hazards and related models. Rather, the goal is to consider the many questions which are of interest in a regression analysis of survival data (prediction, goodness of ?t, model construction, inference and int- pretation in the presence of misspeci?ed models) from the standpoint of the proportional hazards and the non-proportional hazards models.

Recenzje

From the reviews:

"The book is clearly intended to be student-friendly. Each chapter begins with a section called Summary and a following one called motivation; each chapter ends with some exercises and class projects. ... It is very carefully written, with detailed explanation and discussion everywhere. ... I believe that the book can be thoroughly recommended to the student starting his research in the field and to the practitioner who needs to understand some of the theory." (Martin Crowder, International Statistical Review, Vol. 76 (3), 2008)

Spis treści

Background: Probability.- Background: General inference.- Background: Survival analysis.- Marginal survival.- Regression models and subject heterogeneity.- Inference: Estimating equations.- Inference: Functions of Brownian motion.- Inference: Likelihood.- Inference: Stochastic integrals.- Inference: Small samples.- Inference: Changepoint models.- Explained variation.- Explained randomness.- Survival given covariates.- Proofs of theorems, lemmas and corollaries.

Blurb

The place in survival analysis now occupied by proportional hazards models and their generalizations is so large that it is no longer conceivable to offer a course on the subject without devoting at least half of the content to this topic alone. This book focuses on the theory and applications of a very broad class of models—proportional hazards and non-proportional hazards models, the former being viewed as a special case of the latter—which underlie modern survival analysis.

Unlike other books in this area the emphasis is not on measure theoretic arguments for stochastic integrals and martingales. Instead, while inference based on counting processes and the theory of martingales is covered, much greater weight is placed on more traditional results such as the functional central limit theorem. This change in emphasis allows us in the book to devote much greater consideration to practical issues in modeling. The implications of different models, their practical interpretation, the predictive ability of any model, model construction, and model selection as well as the whole area of mis-specified models receive a great deal of attention.

The book is aimed at both those interested in theory and those interested in applications. Many examples and illustrations are provided. The required mathematical and statistical background for those relatively new to the field is carefully outlined so that the material is accessible to a broad range of levels.

John O’Quigley—Director of Research at the French Institut National de la Santé et de la Recherche Médicale and Professor of Mathematics at the University of California at San Diego—has published extensively on the subject of survival analysis, both in theoretical and applied journals. He has taught and carried out collaborative research at several of the world's leading departments of mathematics and statistics including the University of Washington, the Fred Hutchinson Cancer Research Center in Seattle, Harvard University, and Lancaster University, UK.