Modeling Survival Data: Extending the Cox Model (Statistics for Biology and Health)

Book Description

This is a book for statistical practitioners, particularly those who design and analyze studies for survival and event history data. Its goal is to extend the toolkit beyond the basic triad provided by most statistical packages: the Kaplan-Meier estimator, log-rank test, and Cox regression model. Building on recent developments motivated by counting process and martingale theory, it shows the reader how to extend the Cox model to analyse multiple/correlated event data using marginal and random effects (frailty) models. It covers the use of residuals and diagnostic plots to identify influential or outlying observations, assess proportional hazards and examine other aspects of goodness of fit. Other topics include time-dependent covariates and strata, discontinuous intervals of risk, multiple time scales, smoothing and regression splines, and the computation of expected survival curves. A knowledge of counting processes and martingales is not assumed as the early chapters provide an introduction to this area. The focus of the book is on actual data examples, the analysis and interpretation of the results, and computation. The methods are now readily available in SAS and S-Plus and this book gives a hands-on introduction, showing how to implement them in both packages, with worked examples for many data sets. The authors call on their extensive experience and give practical advice, including pitfalls to be avoided. Terry Therneau is Head of the Section of Biostatistics, Mayo Clinic, Rochester, Minnesota. He is actively involved in medical consulting, with emphasis in the areas of chronic liver disease, physical medicine, hematology, and laboratory medicine, and is an author on numerous papers in medical and statistical journals. He wrote two of the original SAS procedures for survival analysis (coxregr and survtest), as well as the majority of the S-Plus survival functions. Patricia Grambsch is Associate Professor in the Division of Biostatistics, School of Public Health, University of Minnesota. She has collaborated extensively with physicians and public health researchers in chronic liver disease, cancer prevention, hypertension clinical trials and psychiatric research. She is a fellow the American Statistical Association and the author of many papers in medical and statistical journals.

Customer Reviews:

One of the best statistics texts available today!.......2002-05-02

As a biostatistics PhD student I've had to endure many very poorly written textbooks (though there are many good one's too). Not only is this book a great text on applied survival analysis, it's a great piece of statistical writing and should be used as an example for all applied texts. The general approach of introducing the theory followed by examples with SAS/SPlus code makes learning the material easy and fun. I wish all statistics texts were even half this good!

Anderson et al for the common man.......2002-01-10

This text is one of the few to make the work of Andersen et al. (Statistical Models Based on Counting Processes, Springer, 1993) accessible to the average statistician. It has three limitations:
1) fails to mention the use of permutation tests for hypotheses regarding the Nelson-Aalen estimator,
2) fails to cite Good PI, Globally almost most powerful tests for censored data,Nonpar Statist 1992, 1:253-262.
3) fails to deal with multiple dependent events (the most common case).
The text also fails to be prescriptive; one is often left feeling that all tests are equal which simply isn't the case.

Great coverage of extensions to important models.......2000-09-08

Terry Therneau is a research statistician at the Mayo Clinic and Patricia Grambsch is a Professor of Biostatistics at the University of Minnesota. The Cox proportional hazards model has been one of the key methods for analyzing survival data with covariates for the last 25 years. Proportionality is a key assumption that limits its use. There has long been a need to find methods which diagnose when the hazard rates are not proportional and provide alternative methods in such situations. Using the theory of counting processes the authors are able to extend the Cox model to more general situations including multiple/correlated event data using either marginal models or random effects (frailty) models. Time dependent covariates are also covered. Some of the theory of martigales and counting processes is included to make the book self-contained. Generalized residuals are used to identify outlying and influential observations (analogous to ordinary regression) and also to assess the proportional hazards assumption.

Although the topics are advanced and the mathematical level is high the book is designed for practitioners, emphasizing applications and providing numerous examples, many from the authors' experience. Statistical analyses are done in SAS and SPlus. The authors tend to use SAS for data management and analysis and SPlus for diagnostics and other plots. Therneau is an expert programmer who has written much of the necessary software in both systems.

Therneau gave an excellent short course that I attended a couple of years ago at the Joint Statistical Meetings based on a draft of the text. The finished product is as good as I expected.

Book Description

This general introduction to the mathematical techniques needed to understand epidemiology begins with an historical outline of some disease statistics dating from Daniel Bernoulli's smallpox data of 1760. The authors then go on to describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (nonhomogeneous) populations. They offer a range of methods for constructing and analyzing models, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumors and macro-parasitic diseases. Questions of fitting data to models, and the use of models to understand methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text.

Customer Reviews:

A Foundation Book.......2007-05-16

This book tells what we knew about the mathematics of epidemics up until 1990. The differential equations (beginning with Bernoulli and moving forward) are presented well. That is, the variables are defined in the text and not too many steps are skipped in the derivations. The high point in this type of epidemiology came in 1927, when Kermack and McKendrick wrote the continuous-time epidemic equations. Diseases were characterized by the parameter rho, the relative removal rate. Up until the 1990s, we were just fitting our data to this model, and estimating rho.

Along came 'computational biology', or 'agent-based models' or 'numerical methods'. After 1990, these new techniques allowed us to escape from the perfect-mixing assumption that caused the Kermack and McKendrick model to depart from reality. With computation, we were able to see the impact of social networks, targeted innoculuations, and to test the value of different intervention strategies. See March 2005 Scientific American. None of those advances are discussed in this book. As a historical treatise, however, it is a superb addition to the library.

Great Service.......2007-02-02

My book arrived before estimated time and in better condition than described. I am a math dork and given the choice I would purchase from this seller.

Excellent Text.......2005-05-14

This is a broad, wonderful introduction to the mathematics of epidemic modeling. The authors have done an outstanding job at pointing out the mathematics of both deterministic and stochastic epidemic models.

Careful study of this small text will prepare one for a serious look at the current research on the subject. This material is far from ``old fashioned" as one reviewer wrote, indeed, this text is a welcome introduction to the subject!

Old-fashioned.......2004-11-04

The authors mainly give an introduction how to do the calculations by hand for several epidemic models. However, some of their tricks for doing the calculations are not very interesting anymore in times where computers are available. More imporatant, they hardly ever explain why they choose a particular model, what they want to calculate and how to interpret the results of the calculations. So reading the book does not give you much insight in epidemic modelling, only in doing some calculation. Furthermore they ignore all kind of recent approaches in epidemic modelling. (Most references are quite old (before 1990) and the few more recent references are most of the time only mentioned without going into detail.)

Cancer Modelling and Simulation (Chapman & Hall/Crc Mathematical Biology & Medicine Series)

Average customer rating:

Excellent survey of the field

Cancer Modelling and Simulation (Chapman & Hall/Crc Mathematical Biology & Medicine Series)

Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 1584883618

Book Description

Tumour evolution is a complex process involving many different phenomena. Mathematical modelling and computer simulations can help us understand these phenomena, but their development requires a multidisciplinary background-one that includes an understanding of the biological phenomena involved and knowledge of the mathematical techniques used to obtain both qualitative and quantitative results. Cancer Modelling and Simulation builds the requisite biological foundation and presents the mathematical models and methods most useful for understanding the dynamics of tumour development and growth. In chapters contributed by an interdisciplinary team of leading researchers, this book addresses the entire modelling process, from phenomenological observation to simulation and validation, through the development of mathematical models and their qualitative and quantitative study. This treatment effectively links the analytical, mathematical, and biological aspects of tumour growth modelling to provide researchers from multiple disciplines with the common language and practical knowledge they need to break down the barriers that can hamper interdisciplinary research. Cancer Modelling and Simulation is an important contribution to the field that undoubtedly will stimulate and remain a valuable reference for continued research for many years.

Customer Reviews:

Excellent survey of the field.......2004-03-16

This survey text does a great job of getting across the current research and future directions of mathematical modeling of cancer. A range of models across different scales (sub-cellular, cellular, tissue) and aspects (avascular tumor growth, angiogenesis, metastasis, immune/cancer interaction) of cancer dynamics. Also of great value are the explanations of the biology aimed at an applied mathematics audience. A must read for anyone interested in the field.

Functional Imaging and Modeling of the Heart: First International Workshop, FIMH 2001, Helsinki, Finland, November 15-16, 2001, Proceedings (Lecture Notes in Computer Science)

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Functional Imaging and Modeling of the Heart: First International Workshop, FIMH 2001, Helsinki, Finland, November 15-16, 2001, Proceedings (Lecture Notes in Computer Science)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540428615

Book Description

This book constitutes the refereed proceedings of the First International Workshop on Functional Imaging and Modeling of the Heart, FIMH 2001, held in Helsinki, Finland, in November 2001.The 17 revised full papers presented together with four invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on anatomical modeling, motion and deformation, functional imaging, and towards electromechanical modeling.

Dynamical Disease: Mathematical Analysis of Human Illness

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Dynamical Disease: Mathematical Analysis of Human Illness

Manufacturer: AIP Press
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Binding: Paperback

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Book Description

Here are 29 ground-breaking research papers presented at a 1994 workshop in Quebec that offer fresh insights into the possible etiology and treatment of disease. Each chapter reveals how mathematical methods for understanding dynamical behavior in nonlinear equations are ideally suited to the analysis of complex rhythms confronted by physicians.

Modeling and Simulation in Medicine and the Life Sciences

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Modeling and Simulation in Medicine and the Life Sciences
Frank C. Hoppensteadt , and Charles S. Peskin
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Accessories:

ASIN: 0387950729

Book Description

Mathematics in Medicine and the Life Sciences grew from lectures given by the authors at New York University, the University of Utah, and Michigan State University. The material is written for students who have had but one term of calculus, but it contains material that can be used in modeling courses in applied mathematics at all levels through early graduate courses. Numerous exercises are given as well, and solutions to selected exercises are included. Numerous illustrations depict physiological processes, population biology phenomena, models of them, and the results of computer simulations. Mathematical models and methods are becoming increasingly important in medicine and the life sciences. This book provides an introduction to a wide diversity of problems ranging from population phenomena to demographics, genetics, epidemics and dispersal; in physiological processes, including the circulation, gas exchange in the lungs, control of cell volume, the renal counter-current multiplier mechanism, and muscle mechanics; to mechanisms of neural control. Each chapter is graded in difficulty, so a reading of the first parts of each provides an elementary introduction to the processes and their models. Materials that deal with the same topics but in greater depth are included later. Finally, exercises and some solutions are given to test the reader on important parts of the material in teh text, or to lead the reader to the discovery of interesting extensions of that material.

Computational Cardiology: Modeling of Anatomy, Electrophysiology, and Mechanics (Lecture Notes in Computer Science)

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Computational Cardiology: Modeling of Anatomy, Electrophysiology, and Mechanics (Lecture Notes in Computer Science)
Frank B. Sachse
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Mathematically Modeling the Electrical Activity of the Heart: From Cell to Body Surface and Back

ASIN: 3540219072

Book Description

This book is devoted to computer-based modeling in cardiology, by taking an educational point of view, and by summarizing knowledge from several, commonly considered delimited areas of cardiac research in a consistent way.

First, the foundations and numerical techniques from mathematics are provided, with a particular focus on the finite element and finite differences methods. Then, the theory of electric fields and continuum mechanics is introduced with respect to numerical calculations in anisotropic biological media. In addition to the presentation of digital image processing techniques, the following chapters deal with particular aspects of cardiac modeling: cardiac anatomy, cardiac electro physiology, cardiac mechanics, modeling of cardiac electro mechanics.

This book was written for researchers in modeling and cardiology, for clinical cardiologists, and for advanced students.

Average customer rating:

This book sucks

Calculus for Biology and Medicine
Claudia Neuhauser
Manufacturer: Pearson Education
ProductGroup: Book
Binding: Hardcover

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ASIN: 013085137X

Book Description

This volume teaches calculus in the biology context without compromising the level of regular calculus. Each new concept is typically introduced with a biological example; the concept is then developed without the biological context; and then the concept is tied into additional biological examples. This allows readers to first see why a certain concept is important; then lets them focus on how to use the concepts without getting distracted by applications; and then, once they feel more comfortable with the concepts, it revisits the biological applications to make sure that they can apply the concepts. The book features exceptionally detailed step-by-step worked examples and a variety of problems, including an unusually large number of word problems in a biological context. Limits and Continuity. Derivatives. Integration. Integration Techniques. Differential Equations. Applications. Linear Algebra and Analytic Geometry. Multivariable Calculus. Systems of Differential Equations. For anyone in the biological sciences who needs a working knowledge of calculus.

Customer Reviews:

This book sucks.......2007-03-25

I've taken calculus in the past and have had much better books. I currently own this book because my current class requires it, but it is terrible.

Why so bad?

1) A lot of wrong answers in back of book

2) Not enough examples

3) Examples given are very brief and unhelpful

4) Uses mathematical terms that are not the standard for professors and the mathematics world. Making it difficult to transition from pre-calc

5) Teacher hates it too but got stuck with it from prior professors

Just avoid it all together and get a substitute.

Modelling Survival Data in Medical Research

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Good introduction

Modelling Survival Data in Medical Research
David Collett
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Paperback

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ASIN: 0412448904

Book Description

Data collected on the time to an event-such as the death of a patient in a medical study-is known as survival data. The methods for analyzing survival data can also be used to analyze data on the time to events such as the recurrence of a disease or relief from symptoms. Modelling Survival Data in Medical Research begins with an introduction to survival analysis and a description of four studies in which survival data was obtained. These and other data sets are then used to illustrate the techniques presented in the following chapters, including the Cox and Weibull proportional hazards models; accelerated failure time models; models with time-dependent variables; interval-censored survival data; model checking; and use of statistical packages. Designed for statisticians in the pharmaceutical industry and medical research institutes, and for numerate scientists and clinicians analyzing their own data sets, this book also meets the need for an intermediate text which emphasizes the application of the methodology to survival data arising from medical studies.

Customer Reviews:

Good introduction.......2000-03-30

A well-written introductory book. Broad range of material make it a good reference for new comers in survival analysis.

Advances in Mathematical Population Dynamics: Molecules, Cells and Man : 23-27 May 1995 (Series in Mathematical Biology and Medicine, Vol 6)

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Advances in Mathematical Population Dynamics: Molecules, Cells and Man : 23-27 May 1995 (Series in Mathematical Biology and Medicine, Vol 6)
International Conference on Mathematical Population Dynamics 1995 hou , and V. Capasso
Manufacturer: World Scientific Pub Co Inc
ProductGroup: Book
Binding: Hardcover

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