Modelling Survival Data in Medical Research: 3rd Edition (Hardback) book cover

Modelling Survival Data in Medical Research

3rd Edition

By David Collett

Chapman and Hall/CRC

548 pages | 110 B/W Illus.

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pub: 2014-12-04
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Modelling Survival Data in Medical Research describes the modelling approach to the analysis of survival data using a wide range of examples from biomedical research.

Well known for its nontechnical style, this third edition contains new chapters on frailty models and their applications, competing risks, non-proportional hazards, and dependent censoring. It also describes techniques for modelling the occurrence of multiple events and event history analysis. Earlier chapters are now expanded to include new material on a number of topics, including measures of predictive ability and flexible parametric models. Many new data sets and examples are included to illustrate how these techniques are used in modelling survival data.

Bibliographic notes and suggestions for further reading are provided at the end of each chapter. Additional data sets to obtain a fuller appreciation of the methodology, or to be used as student exercises, are provided in the appendix. All data sets used in this book are also available in electronic format online.

This book is an invaluable resource for statisticians in the pharmaceutical industry, professionals in medical research institutes, scientists and clinicians who are analyzing their own data, and students taking undergraduate or postgraduate courses in survival analysis.


"Now in its third edition, Collett’s book provides a comprehensive overview of survival analyses and extensions. The book has been expanded considerably; it has increased to 532 pages from the 395 pages in the second edition. Most notably, Collett has expanded his chapter on the Cox regression model and added more information on extensions to standard survival analyses such as frailty models, competing risks, multiple events, and event history modeling…A strength of this book is the author’s emphasis on diagnostics and model-checking and the integration of thorough references to other works so the reader can seek more background or additional information as necessary. As Collett describes it, he is aiming his writing at an intermediate level. This book is quite well written and straightforward to follow, but does require some statistics background of the reader…this book is definitely worth a look for anyone who teaches or conducts survival analyses. It is an excellent resource for applied statisticians and biostatisticians, and has strong potential as a textbook for upper-year statistics undergraduate or graduate-level courses in survival analysis."

—Bethany J. G. White, The University of Western Ontario, in The American Statistician, March 2016

"The third edition of Dave Collett’s book enhances its position as a superb introduction to the area of survival analysis for medical statisticians, academic statisticians, their students, and statistically aware medical practitioners. It is easy to read and has clear explanations and enough mathematical material to satisfy the statistician but not too much that it would deter others. The extra material added since the second edition keeps this book at the forefront."

Dr. Trevor Cox, Director of Statistics, Cancer Research UK Liverpool Cancer Trials Unit

"This is an excellent book, which should appeal to anyone involved in quantitative medical research or research training. Earlier editions have already established this remarkable book as a standard reference to one of the most important topics in medical research: survival analysis. In the latest edition, the author has widened the scope of his coverage of the subject far beyond the standard Cox analysis that still dominates the medical literature. He does this with the same lucid style and systematic harmonization of theory and practice as before. The key equations are provided, but not allowed to distract the practitioner. Examples are used both to explain all the important concepts and methodologies and to motivate the theory."

Mark Woodward, Professor of Statistics and Epidemiology, Nuffield Department of Population Health, University of Oxford

"Dr. Collett has provided an invaluable resource for all students of biostatistics and epidemiology, whether new learners or long-time professionals in the field. He covers the fundamentals of survival analysis by providing thorough treatments of the theory and underpinnings of the concepts while making the material accessible to the reader by providing numerous real-world examples that nicely illustrate the concepts. In addition, he covers many recent additions to the field ensuring that the text is up to date and relevant to today’s practicing biostatistician. Dr. Collett’s text will be an indispensable resource to all who are charged with drawing proper inference from survival data."

Jon J. Snyder, PhD, Director of Transplant Epidemiology, Minneapolis Medical Research Foundation

"As a master’s student in biostatistics, with a medical background, I missed having a good reference book for survival analysis that is interlarded with clinical examples. Albeit too late for my studies, I was glad to see the appearance of the first edition of this book. It has been a good friend since that time and the second edition—again full of examples of medical data—fulfilled all expectations. … this newest edition remains fresh as a daisy and will certainly join its older brothers in my bookcase."

Jacqueline M. Smits, MD, PhD

Praise for the Second Edition:

Collett has succeeded admirably in updating the first edition of his book … [This book] has numerous, carefully worked, real-data examples. There is enough new material in the second edition to justify its purchase by someone who already owns the first edition.

Journal of the American Statistical Association, Sept. 2004, Vol. 99, No. 467

this text is a fine example of technical writing and remains highly recommended for both students and researchers requiring an introduction to survival analysis in a medical context.

Journal of the Royal Statistical Society, Issue 167 (4)

… a well written practical guide with a demonstration of SAS software to perform survival analysis. … It can be used as a textbook in a graduate-level survival analysis course … .

Journal of Statistical Computation & Simulation, Vol. 74, No. 5, May 2004

It is thorough and authoritative, covers all essential theory and contains many practical tips.

Journal of the Royal Statistical Society, Vol. 157

Praise for the First Edition:

… a useful book that has particular merit for the applied statistician. Chapters 1-6 and 11 alone supply a wonderful introduction to survival analysis. The mathematical statistician unfamiliar with survival analysis who desires to become quickly abreast will also gain much from the book.

Journal of the American Statistical Association

Students found the presentation of the material and examples to be very helpful … an excellent book … I highly recommend this book for practising statisticians engaged in analysing univariate survival data. … This book will not only serve the statistical practitioner in the medical and pharmaceutical research areas well, but will be a convenient text for the lecturer aiming to include a useful applied component into a post-graduate statistics or operational research degree course.

Journal of the Royal Statistical Society

The book would be a popular text for courses and a well-thumbed addition to any medical statistician’s collection. It is sufficiently general to be of interest to industrial statisticians concerned with lifetime testing but the focus is clearly on survival of patients under treatment.

The Statistician

Table of Contents

Survival Analysis

Special Features of Survival Data

Some Examples

Survivor, Hazard and Cumulative Hazard Functions

Computer Software for Survival Analysis

Further Reading

Some Non-Parametric Procedures

Estimating the Survivor Function

Standard Error of the Estimated Survivor Function

Estimating the Hazard Function

Estimating the Median and Percentiles of Survival Times

Confidence Intervals for the Median and Percentiles

Comparison of Two Groups of Survival Data

Comparison of Three or More Groups of Survival Data

Stratified Tests

Log-Rank Test for Trend

Further Reading

The Cox Regression Model

Modelling the Hazard Function

The Linear Component of the Model

Fitting the Cox Regression Model

Confidence Intervals and Hypothesis Tests

Comparing Alternative Models

Strategy for Model Selection

Variable Selection Using the Lasso

Non-Linear Terms

Interpretation of Parameter Estimates

Estimating the Hazard and Survivor Functions

Risk Adjusted Survivor Function

Explained Variation in the Cox Regression Model

Proportional Hazards and the Log-Rank Test

Further Reading

Model Checking in the Cox Regression Model

Residuals for the Cox Regression Model

Assessment of Model Fit

Identification of Influential Observations

Testing the Assumption of Proportional Hazards


Further Reading

Parametric Proportional Hazards Models

Models for the Hazard Function

Assessing the Suitability of a Parametric Model

Fitting a Parametric Model to a Single Sample

Fitting Exponential and Weibull Models

A Model for the Comparison of Two Groups

The Weibull Proportional Hazards Model

Comparing Alternative Weibull Models

Explained Variation in the Weibull Model

The Gompertz Proportional Hazards Model

Model Choice

Further Reading

Accelerated Failure Time and Other Parametric Models

Probability Distributions for Survival Data

Exploratory Analyses

Accelerated Failure Model for Two Groups

The General Accelerated Failure Time Model

Parametric Accelerated Failure Time Models

Fitting and Comparing Accelerated Failure Time Models

The Proportional Odds Model

Some Other Distributions for Survival Data

Flexible Parametric Models

Modelling Cure Rates

Effect of Covariate Adjustment

Further Reading

Model Checking In Parametric Models

Residuals for Parametric Models

Residuals for Particular Parametric Models

Comparing Observed and Fitted Survivor Functions

Identification of Influential Observations

Testing Proportional Hazards in the Weibull Model

Further Reading

Time-Dependent Variables

Types of Time-Dependent Variables

A Model with Time-Dependent Variables

Model Comparison and Validation

Some Applications of Time-Dependent Variables

Three Examples

Counting Process Format

Further Reading

Interval-Censored Survival Data

Modelling Interval-Censored Survival Data

Modelling the Recurrence Probability in the Follow-Up Period

Modelling the Recurrence Probability at Different Times

Arbitrarily Interval-Censored Survival Data

Parametric Models for Interval-Censored Data


Further Reading

Frailty Models

Introduction to Frailty

Modelling Individual Frailty

The Gamma Frailty Distribution

Fitting Parametric Frailty Models

Fitting Semi-Parametric Frailty Models

Comparing Models with Frailty

The Shared Frailty Model

Some Other Aspects of Frailty Modelling

Further Reading

Non-Proportional Hazards and Institutional Comparisons

Non-Proportional Hazards

Stratified Proportional Hazards Models

Restricted Mean Survival

Institutional Comparisons

Further Reading

Competing Risks

Introduction to Competing Risks

Summarising Competing Risks Data

Hazard and Cumulative Incidence Functions

Modelling Cause-Specific Hazards

Modelling Cause-Specific Incidence

Model Checking

Further Reading

Multiple Events and Event History Modelling

Introduction to Counting Processes

Modelling Recurrent Event Data

Multiple Events

Event History Analysis

Further Reading

Dependent Censoring

Identifying Dependent Censoring

Sensitivity to Dependent Censoring

Modelling with Dependent Censoring

Further Reading

Sample Size Requirements for a Survival Study

Distinguishing between Two Treatment Groups

Calculating the Required Number of Deaths

Calculating the Required Number of Patients

Further Reading

Appendix A: Maximum Likelihood Estimation

Inference about a Single Unknown Parameter

Inference about a Vector of Unknown Parameters

Appendix B: Additional Data Sets

Chronic Active Hepatitis

Recurrence of Bladder Cancer

Survival of Black Ducks

Bone Marrow Transplantation

Chronic Granulomatous Disease


Index of Examples


About the Author

David Collett, PhD, associate director of statistics and clinical studies, NHS Blood and Transplant, Bristol and visiting professor of statistics, Southampton Statistical Sciences Research Institute, University of Southampton, UK

About the Series

Chapman & Hall/CRC Texts in Statistical Science

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General
MEDICAL / Biostatistics