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Modelling Survival Data in Medical Research, Third Edition
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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
Recommendations
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
Discussion
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

Bibliography

Index of Examples

Index

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

Reviews

"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

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