Applied Survival Analysis: Regression Modeling of Time to Event Data

by David W. Hosmer (Univ. of Massachusetts); Stanley Lemeshow (The Ohio State Univ.)

• ISBN13: 9780471154105
• ISBN10: 0471154105
• Edition: 1st
• Format: Hardcover
• Copyright: 1999-01-01
• Publisher: Wiley-Interscience

Summary

A Practical, Up-To-Date Guide To Modern Methods In The Analysis Of Time To Event Data. The rapid proliferation of powerful and affordable statistical software packages over the past decade has inspired the development of an array of valuable new methods for analyzing survival time data. Yet there continues to be a paucity of statistical modeling guides geared to the concerns of health-related researchers who study time to event data. This book helps bridge this important gap in the literature. Applied Survival Analysis is a comprehensive introduction to regression modeling for time to event data used in epidemiological, biostatistical, and other health-related research. Unlike other texts on the subject, it focuses almost exclusively on practical applications rather than mathematical theory and offers clear, accessible presentations of modern modeling techniques supplemented with real-world examples and case studies. While the authors emphasize the proportional hazards model, descriptive methods and parametric models are also considered in some detail. Key topics covered in depth include: * Variable selection. * Identification of the scale of continuous covariates. * The role of interactions in the model. * Interpretation of a fitted model. * Assessment of fit and model assumptions. * Regression diagnostics. * Recurrent event models, frailty models, and additive models. * Commercially available statistical software and getting the most out of it. Applied Survival Analysis is an ideal introduction for graduate students in biostatistics and epidemiology, as well as researchers in health-related fields.

Author Biography

DAVID W. HOSMER, Jr., PhD, is a professor of biostatistics in the Department of Biostatistics and Epidemiology of the University of Massachusetts School of Public Health and Health Sciences in Amherst, Massachusetss. <P> STANLEY LEMESHOW, PhD, is a professor of biostatistics in the Department of Statistics at The Ohio State University.

Table of Contents

Preface	ix
1 Introduction to Regression Modeling of Survival Data	1	(26)
1.1 Introduction	1	(16)
1.2 Typical Censoring Mechanisms	17	(5)
1.3 Example Data Sets	22	(3)
Exercises	25	(2)
2 Descriptive Methods for Survival Data	27	(60)
2.1 Introduction	27	(1)
2.2 Estimation of the Survivorship Function	28	(12)
2.3 Using the Estimated Survivorship Function	40	(17)
2.4 Comparison of Survivorship Functions	57	(16)
2.5 Other Functions of Survival Time and Their Estimators	73	(11)
Exercises	84	(3)
3 Regression Models for Survival Data	87	(26)
3.1 Introduction	87	(3)
3.2 Semiparametric Regression Models	90	(3)
3.3 Fitting the Proportional Hazards Regression Model	93	(13)
3.4 Fitting the Proportional Hazards Model with Tied Survival Times	106	(2)
3.5 Estimating the Survivorship Function of the Proportional Hazards Regression Model	108	(3)
Exercises	111	(2)
4 Interpretation of a Fitted Proportional Hazards Regression Model	113	(45)
4.1 Introduction	113	(2)
4.2 Nominal Scale Covariate	115	(12)
4.3 Continuous Scale Covariate	127	(2)
4.4 Multiple-Covariate Models	129	(8)
4.5 Interpretation and Use of the Covariate-Adjusted Survivorship Function	137	(15)
4.6 Confidence Interval Estimation of the Covariate-Adjusted Survivorship Function	152	(4)
Exercises	156	(2)
5 Model Development	158	(38)
5.1 Introduction	158	(1)
5.2 Purposeful Selection of Covariates	159	(21)
5.3 Stepwise Selection of Covariates	180	(7)
5.4 Best Subsets Selection of Covariates	187	(6)
5.5 Numerical Problems	193	(2)
Exercises	195	(1)
6 Assessment of Model Adequacy	196	(45)
6.1 Introduction	196	(1)
6.2 Residuals	197	(8)
6.3 Methods for Assessing the Proportional Hazards Assumption	205	(11)
6.4 Identification of Influential and Poorly Fit Subjects	216	(9)
6.5 Overall Goodness-of-Fit Tests and Measures	225	(5)
6.6 Interpretation and Presentation of the Final Model	230	(9)
Exercises	239	(2)
7 Extensions of the Proportional Hazards Model	241	(30)
7.1 Introduction	241	(2)
7.2 The Stratified Proportional Hazards Model	243	(5)
7.3 Time-Varying Covariates	248	(5)
7.4 Truncated, Left Censored, and Interval Censored Data	253	(16)
Exercises	269	(2)
8 Parametric Regression Models	271	(36)
8.1 Introduction	271	(2)
8.2 The Exponential Regression Model	273	(16)
8.3 The Weibull Regression Model	289	(10)
8.4 The Log-Logistic Regression Model	299	(5)
8.5 Other Parametric Regression Model	304	(1)
Exercises	305	(2)
9 Other Models and Topics	307	(47)
9.1 Introduction	307	(1)
9.2 Recurrent Event Models	308	(9)
9.3 Frailty Models	317	(9)
9.4 Nested Case-Control Studies	326	(7)
9.5 Additive Models	333	(17)
Exercises	350	(4)
Appendix 1 The Delta Method	354	(4)
Appendix 2 An Introduction to the Counting Process Approach to Survival Analysis	358	(6)
Appendix 3 Percentiles for Computation of the Hall and Wellner Confidence Band	364	(1)
References	365	(14)
Index	379