Applied Survival Analysis E-Book

David W. Hosmer

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Probability and Statistics
• Sprache: Englisch
• Veröffentlichungsjahr: 2011

Seitenzahl: 668

Beschreibung

THE MOST PRACTICAL, UP-TO-DATE GUIDE TO MODELLING AND ANALYZING TIME-TO-EVENT DATA--NOW IN A VALUABLE NEW EDITION Since publication of the first edition nearly a decade ago, analyses using time-to-event methods have increase considerably in all areas of scientific inquiry mainly as a result of model-building methods available in modern statistical software packages. However, there has been minimal coverage in the available literature to9 guide researchers, practitioners, and students who wish to apply these methods to health-related areas of study. Applied Survival Analysis, Second Edition provides a comprehensive and up-to-date introduction to regression modeling for time-to-event data in medical, epidemiological, biostatistical, and other health-related research. This book places a unique emphasis on the practical and contemporary applications of regression modeling rather than the mathematical theory. It offers a clear and accessible presentation of modern modeling techniques supplemented with real-world examples and case studies. Key topics covered include: variable selection, identification of the scale of continuous covariates, the role of interactions in the model, assessment of fit and model assumptions, regression diagnostics, recurrent event models, frailty models, additive models, competing risk models, and missing data. Features of the Second Edition include: * Expanded coverage of interactions and the covariate-adjusted survival functions * The use of the Worchester Heart Attack Study as the main modeling data set for illustrating discussed concepts and techniques * New discussion of variable selection with multivariable fractional polynomials * Further exploration of time-varying covariates, complex with examples * Additional treatment of the exponential, Weibull, and log-logistic parametric regression models * Increased emphasis on interpreting and using results as well as utilizing multiple imputation methods to analyze data with missing values * New examples and exercises at the end of each chapter Analyses throughout the text are performed using Stata® Version 9, and an accompanying FTP site contains the data sets used in the book. Applied Survival Analysis, Second Edition is an ideal book for graduate-level courses in biostatistics, statistics, and epidemiologic methods. It also serves as a valuable reference for practitioners and researchers in any health-related field or for professionals in insurance and government.

Leseprobe

Contents

Preface

1Introduction to Regression Modeling of Survival Data

1.1 Introduction,

1.2 Typical Censoring Mechanisms,

1.3 Example Data Sets,

Exercises,

2Descriptive Methods for Survival Data

2.1 Introduction,

2.2 Estimating the Survival Function,

2.3 Using the Estimated Survival Function,

2.4 Comparison of Survival Functions,

2.5 Other Functions of Survival Time and Their Estimators,

Exercises,

3. Regression Models for Survival Data

3.1 Introduction,

3.2 Semi-Parametric Regression Models,

3.3 Fitting the Proportional Hazards Regression Model,

3.4 Fitting the Proportional Hazards Model with Tied Survival Times,

3.5 Estimating the Survival Function of the Proportional Hazards Regression Model,

Exercises,

4.Interpretation of a Fitted Proportional Hazards Regression Model

4.1 Introduction,

4.2 Nominal Scale Covariate,

4.3 Continuous Scale Covariate,

4.4 Multiple-Covariate Models,

4.5 Interpreting and Using the Estimated Covariate-Adjusted Survival Function,

Exercises,

5.Model Development

5.1 Introduction,

5.2 Purposeful Selection of Co variâtes,

5.3 Stepwise, Best-Subsets and Multivariable Fractional PolynomialMethods of Selecting Covariates,

5.4 Numerical Problems,

Exercises,

6.Assessment of Model Adequacy

6.1 Introduction,

6.2 Residuals,

6.3 Assessing the Proportional Hazards Assumption,

6.4 Identification of Influential and Poorly Fit Subjects,

6.5 Assessing Overall Goodness-of-Fit,

6.6 Interpreting and Presenting Results From the Final Model,

Exercises,

7.Extensions of the Proportional Hazards Model

7.1 Introduction,

7.2 The Stratified Proportional Hazards Model,

7.3 Time-Varying Covariates,

7.4 Truncated, Left Censored and Interval Censored Data,

Exercises,

8.Parametric Regression Models

8.1 Introduction,

8.2 The Exponential Regression Model,

8.3 The Weibull Regression Model,

8.4 The Log-Logistic Regression Model,

8.5 Other Parametric Regression Models,

Exercises,

9.Other Models and Topics

9.1 Introduction,

9.2 Recurrent Event Models,

9.3 Frailty Models,

9.4 Nested Case-Control Studies,

9.5 Additive Models,

9.6 Competing Risk Models,

9.7 Sample Size and Power,

9.8 Missing Data,

Exercises,

Appendix 1 The Delta Method

Appendix 2 An Introduction to the Counting Process Approach to Survival Analysis

Appendix 3 Percentiles for Computation of the Hall and Wellner Confidence Band

References

Index

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Library of Congress Cataloging-in-Publication Data:

Hosmer, David W.paraApplied survival analysis : regression modeling of time-to-event data /David W. Hosmer, Stanley Lemeshow, Susanne May. — 2nd ed. p. cm.Includes bibliographical references and index.ISBN 978-0-471-75499-2 (cloth : alk. paper)1. Medicine—Research—Statistical methods. 2. Medicalsciences—Statistical methods—Computer programs. 3. Regressionanalysis—Data processing. 4. Prognosis—Statistical methods. 5. Logisticdistribution. I. Lemeshow, Stanley. II. May, Susanne. III. Title.[DNLM: 1. Survival Analysis. 2. Logistic Models. 3. MathematicalComputing. 4. Prognosis. 5. Regression Analysis. WA 950 H827a 2008]R853.S7H67 2008610.727—dc22

2007035523

To Trina: Wife, Mother, Athlete, and Companion in Life’s Adventures

D. W. H.

To Elaine: with respect and admiration for her compassion, generosity and appreciation of what is important in our lives and in our world

S.L.

To Bruce: Husband, Friend and Partner

S.M.

Preface to the Second Edition

Since the publication of the first edition nine years ago, analyses using time-to-event methods have increased considerably in all areas of scientific inquiry. We believe that two important reasons for the increase are: (1) the statistical methods for the analysis of time-to-event data are now taught in many intermediate level methods courses and not just advanced courses and (2) the software to perform most of the methods is now available and easy to use in all the major software packages.

The approach taken in the second edition has not changed from the first edition, where the goal was to provide a focused text on regression modeling for the time-to-event data typically encountered in health related studies. As in the first edition, we assume that the reader has had a course in linear regression at the level of Kleinbaum, Kupper, Muller and Nizam (1998) and one in logistic regression at the level of Hosmer and Lemeshow (2000). Emphasis is placed on the modeling of data and the interpretation of the results. Crucial to this is an understanding of the nature of the “incomplete” or “censored” data encountered. Understanding the censoring mechanism is important as it may influence model selection and interpretation. Yet, once understood and accounted for, censoring is often just another technical detail handled by the computer software, allowing emphasis to return to model building, assessment of model fit, and assumptions and interpretation of the results.

In the second edition, we have replaced the HMO-HÏV data as the main data set for illustrating methods with a sample of 100 observations from the Worcester Heart Attack Study. We have kept the data from the UMARU Impact Study (UIS), but only use it occasionally. The main modeling data set is a sample of 500 observations from the Worcester Heart Attack Study. Data from the German Breast Cancer Study and the ACTG320 Study are used to demonstrate various modeling and analysis techniques and methods. In short, most of the examples in the text and exercises are new or use new data.

A reading of the Table of Contents for the first four chapters will look as if nothing much has changed. However, the actual text has many changes and additions. For example, the discussions of interactions and the covariate-adjusted survival functions in Chapter Four are greatly expanded. In Chapter Five, we have added variable selection by multivariable fractional polynomials. Changes in Chapter Six follow from a new model based on data from the Worcester Heart Attack Study studied in Chapter Five. The major change to Chapter Seven is a greatly expanded discussion of time varying covariates with examples. In Chapter Eight we, again, focus on the exponential, Weibull, and log-logistic parametric regression models but have expanded the discussion of each. In Chapter Nine, we have taken advantage of the addition of the capability to fit frailty/random effects models in Stata. Examples are used to compare fitting stratified models to frailty models. The last sections of Chapter Nine contain new material on competing risk models, sample size and power, and using multiple imputation methods to analyze data with missing values.

As we noted, we believe that the increase in the use of statistical methods for time-to-event data is directly related to their incorporation into the major statistical software packages. There are some differences in the capabilities of the various software packages and, when a particular approach is available in a limited number of packages, we note this in the text. Analyses have, for the most part, been performed in Stata Version 9 [Stata Corp. (2005)]. This easy-to-use package combines good graphics and excellent analysis routines, is fast, is compatible across Macintosh, Windows, and UNIX platforms, and interacts well with Microsoft Word 2004 for Mac. Just as we were going to press, Stata Version 10 was released. Among the enhancements in this version is the ability to perform time to event analysis of survey data. Unfortunately we were not able to incorporate that capability into this text. The only other major statistical package employed at various points during the preparation of this text is SAS Version 9.1 [SAS Institute Inc. (2003)J.

This text was prepared in camera-ready format using Microsoft Word 2004 for Mac Version 11.3.5 on a PowerBook G4 using Mac OS X Version 10.4.9. Mathematical equations and symbols were built using Math Type Version 5.1 [MathType5 Mathematical Equation Editor (2004)].

All data may be obtained from the John Wiley & Sons, Inc. ftp site,

ftp://ftp.wiley.com/public/sci_tech_med/survival.

They may also be obtained from the a web site at the University of Massachusetts / Amherst by going the following link and then the section for survival analysis,

http://www.umass.edu/statdata/statdata.

As was the case with the first edition we will have a link at the John Wiley & Sons, Inc. ftp site listed above for errata and corrections.

As in any project with the scope and magnitude of this text, there are many who have contributed directly or indirectly to its content and style and we feel quite fortunate to be able to acknowledge the contributions of others. We thank Rob Goldberg for providing us with a subset of the Worcester Heart Attack Study that we used to create further subsets of 100 and 500 observations. These are used extensively in the text. We thank Fred Anderson and Gordon FitzGerald for providing a subset of data from the GRACE registry containing time-varying covari-ates. We thank former faculty colleagues Jane McCusker, Anne Stoddard, and Carol Bigelow for the use and insights into the data from the Project IMPACT Study. We thank the AIDS Clinical Trials Group for making the ACTG 320 data available. We appreciate Ohio State Provost Barbara Snyder’s agreeing to allow SL to take a special research assignment (SRA) so that he had the time necessary to work on this book. Not only did Annick Alpérovitch, Carole Dufouil and Christophe Tzourio at INSERM Unit 708 in Paris, France provide an office and an environment conducive for working on this book during the SRA, but they also facilitated obtaining data from the 3C Study Investigators that we were able to use as an exercise in Chapter 7.

We express special thanks to Patrick Royston and Willi Sauerbrei for their helpful suggestions on the text describing fractional polynomials and for comments on numerous other sections of the text. They generously shared with us data from the German Breast Cancer Study that they have analyzed extensively in their publications.

We would like to thank Janice Jones for pointing out the 5731 commas that were missing in the initial draft and for many suggestions that made the text much easier to read. We also thank Charisse Darrell-Fields for inserting Janice’s commas into the manuscript. Finally, we thank Tracy McHone for coordinating the printing and organization of the final manuscript.

Over the last nine years we have used the first edition in semester-long course offerings at the University of Massachusetts as well as numerous short courses to audiences around the world. We thank collectively the students in these courses for their comments and insights on how to make things clearer. We hope we have done so in this edition.

DAVID W. HOSMERSTANLEY LEMESHOWSUSANNE MAY

Stowe, VermontColumbus, OhioSan Diego, CaliforniaAugust, 2007