Statistical Methods for the Analysis of Repeated Measurements,9780387953700

Statistical Methods for the Analysis of Repeated Measurements

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ISBN13: 9780387953700
ISBN10: 0387953701
Format: Hardcover
Pub. Date: 2002-03-01
Publisher(s): Springer Verlag
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Summary

This book provides a comprehensive summary of a wide variety of statistical methods for the analysis of repeated measurements. It is designed to be both a useful reference for practitioners and a textbook for a graduate-level course focused on methods for the analysis of repeated measurements. This book will be of interest to * Statisticians in academics, industry, and research organizations* Scientists who design and analyze studies in which repeated measurements are obtained from each experimental unit* Graduate students in statistics and biostatistics.The prerequisites are knowledge of mathematical statistics at the level of Hogg and Craig (1995) and a course in linear regression and ANOVA at the level of Neter et. al. (1985).The important features of this book include a comprehensive coverage of classical and recent methods for continuous and categorical outcome variables; numerous homework problems at the end of each chapter; and the extensive use of real data sets in examples and homework problems.The 80 data sets used in the examples and homework problems can be downloaded from www.springer-ny.com at the list of author websites. Since many of the data sets can be used to demonstrate multiple methods of analysis, instructors can easily develop additional homework problems and exam questions based on the data sets provided. In addition, overhead transparencies produced using TeX and solutions to homework problems are available to course instructors. The overheads also include programming statements and computer output for the examples, prepared primarily using the SAS System.Charles S. Davis is Senior Director of Biostatistics at Elan Pharmaceuticals, San Diego, California. He previously was professor in the Department of Biostatistics at the University of Iowa. He is author or co-author of more than 75 peer-reviewed papers in statistical and medical journals and one book (Categorical Data Analysis using the SAS System with Maura Stokes and Gary Koch). His research and teaching interests include categorical data analysis, methods for the analysis of repeated measurements, and clinical trials. Dr. Davis has consulted with numerous companies and has taught short courses on categorical data analysis, methods for the analysis of repeated measurements, and clinical trials methodology for industrial, government, and academic organizations. He received an "Excellence in Continuing Education" award from the American Statistical Association in 2001 and has served as associate editor of the journals Controlled Clinical Trials and The American Statistician and as chair of the Biometrics Section of the ASA.

Table of Contents

Preface v
List of Tables
xv
List of Figures
xxiii
Introduction
1(14)
Repeated Measurements
1(1)
Advantages and Disadvantages of Repeated Measurements Designs
2(1)
Notation for Repeated Measurements
3(1)
Missing Data
4(4)
Sample Size Estimation
8(1)
Outline of Topics
9(3)
Choosing the ``Best'' Method of Analysis
12(3)
Univariate Methods
15(30)
Introduction
15(1)
One Sample
16(5)
Multiple Samples
21(5)
Comments
26(2)
Problems
28(17)
Normal-Theory Methods: Unstructured Multivariate Approach
45(28)
Introduction
45(1)
Multivariate Normal Distribution Theory
46(3)
The Multivariate Normal Distribution
46(1)
The Wishart Distribution
46(1)
Wishart Matrices
47(1)
Hotelling's T2 Statistic
47(1)
Hypothesis Tests
48(1)
One-Sample Repeated Measurements
49(6)
Methodology
49(1)
Examples
50(4)
Comments
54(1)
Two-Sample Repeated Measurements
55(6)
Methodology
55(2)
Example
57(3)
Comments
60(1)
Problems
61(12)
Normal-Theory Methods: Multivariate Analysis of Variance
73(30)
Introduction
73(1)
The Multivariate General Linear Model
74(4)
Notation and Assumptions
74(1)
Parameter Estimation
75(1)
Hypothesis Testing
76(1)
Comparisons of Test Statistics
77(1)
Profile Analysis
78(5)
Methodology
78(3)
Example
81(2)
Growth Curve Analysis
83(11)
Introduction
83(1)
The Growth Curve Model
83(4)
Examples
87(7)
Problems
94(9)
Normal-Theory Methods: Repeated Measures ANOVA
103(22)
Introduction
103(1)
The Fundamental Model
104(2)
One Sample
106(6)
Repeated Measures ANOVA Model
106(3)
Sphericity Condition
109(2)
Example
111(1)
Multiple Samples
112(4)
Repeated Measures ANOVA Model
112(3)
Example
115(1)
Problems
116(9)
Normal-Theory Methods: Linear Mixed Models
125(44)
Introduction
125(1)
The Linear Mixed Model
126(4)
The Usual Linear Model
126(1)
The Mixed Model
126(1)
Parameter Estimation
127(1)
Background on REML Estimation
128(2)
Application to Repeated Measurements
130(4)
Examples
134(15)
Two Groups, Four Time Points, No Missing Data
134(5)
Three Groups, 24 Time Points, No Missing Data
139(6)
Four Groups, Unequally Spaced Repeated Measurements, Time-Dependent Covariate
145(4)
Comments
149(7)
Use of the Random Intercept and Slope Model
149(2)
Effects of Choice of Covariance Structure on Estimates and Tests
151(4)
Performance of Linear Mixed Model Test Statistics and Estimators
155(1)
Problems
156(13)
Weighted Least Squares Analysis of Repeated Categorical Outcomes
169(70)
Introduction
169(1)
Background
170(14)
The Multinomial Distribution
170(1)
Linear Models Using Weighted Least Squares
171(4)
Analysis of Categorical Data Using Weighted Least Squares
175(3)
Taylor Series Variance Approximations for Nonlinear Response Functions
178(6)
Application to Repeated Measurements
184(20)
Overview
184(1)
One Population, Dichotomous Response, Repeated Measurements Factor Is Unordered
184(3)
One Population, Dichotomous Response, Repeated Measurements Factor Is Ordered
187(4)
One Population, Polytomous Response
191(5)
Multiple Populationss Dichotomous Response
196(8)
Accommodation of Missing Data
204(16)
Overview
204(1)
Ratio Estimation for Proportions
204(1)
One Population, Dichotomous Response
205(4)
Multiple Populations, Dichotomous Response
209(5)
Assessing the Missing-Data Mechanism
214(6)
Problems
220(19)
Randomization Model Methods for One-Sample Repeated Measurements
239(34)
Introduction
239(1)
The Hypergeometric Distribution and Large-Sample Tests of Randomness for 2 x 2 Tables
240(4)
The Hypergeometric Distribution
240(1)
Test of Randomness for a 2 x 2 Contingency Table
241(1)
Test of Randomness for s 2 x 2 Contingency Tables
242(2)
Application to Repeated Measurements: Binary Response, Two Time Points
244(2)
The Multiple Hypergeometric Distribution and Large-Sample Tests of Randomness for r x c Tables
246(7)
The Multiple Hypergeometric Distribution
247(1)
Test of Randomness for an r x c Contingency Table
248(1)
Test of Randomness for s r x c Tables
249(2)
Cochran-Mantel-Haenszel Mean Score Statistic
251(2)
Cochran-Mantel-Haenszel Correlation Statistic
253(1)
Application to Repeated Measurements: Polytomous Response, Multiple Time Points
253(5)
Introduction
253(2)
The General Association Statistic QG
255(1)
The Mean Score Statistic QM and the Correlation Statistic QC
255(3)
Accommodation of Missing Data
258(5)
General Association Statistic QG
258(2)
Mean Score Statistic QM
260(2)
Correlation Statistic QC
262(1)
Use of Mean Score and Correlation Statistics for Continuous Data
263(1)
Problems
264(9)
Methods Based on Extensions of Generalized Linear Models
273(74)
Introduction
273(1)
Univariate Generalized Linear Models
274(12)
Introduction
274(1)
Random Component
275(4)
Systematic Component
279(1)
Link Function
279(1)
Canonical Links
279(2)
Parameter Estimation
281(5)
Quasilikelihood
286(5)
Introduction
286(1)
Construction of a Quasilikelihood Function
287(2)
Quasilikelihood Estimating Equations
289(2)
Comparison Between Quasilikelihood and Generalized Linear Models
291(1)
Overview of Methods for the Analysis of Repeated Measurements
291(4)
Introduction
291(1)
Marginal Models
292(1)
Random-Effects Models
293(1)
Transition Models
293(1)
Comparisons of the Three Approaches
294(1)
The GEE Method
295(19)
Introduction
295(1)
Methodology
296(5)
Example
301(7)
Hypothesis Tests Using Wald Statistics
308(1)
Assessing Model Adequacy
309(1)
Sample Size Estimation
310(1)
Studies of the Properties of GEE
311(1)
Computer Software
312(1)
Cautions Concerning the Use of GEE
313(1)
Subsequent Developments
314(4)
Alternative Procedures for Estimation of GEE Association Parameters
314(2)
Other Developments and Extensions
316(1)
GEE1 and GEE2
316(1)
Extended Generalized Estimating Equations (EGEE)
317(1)
Likelihood-Based Approaches
318(1)
Random-Effects Models
318(2)
Methods for the Analysis of Ordered Categorical Repeated Measurements
320(12)
Introduction
320(1)
Univariate Cumulative Logit Models for Ordered Categorical Outcomes
321(1)
The Univariate Proportional-Odds Model
322(2)
The Stram-Wei-Ware Methodology for the Analysis of Ordered Categorical Repeated Measurements
324(7)
Extension of GEE to Ordered Categorical Outcomes
331(1)
Problems
332(15)
Nonparametric Methods
347(26)
Introduction
347(1)
Overview
348(2)
Multivariate One-Sample and Multisample Tests for Complete Data
350(5)
One Sample
350(1)
Multiple Samples
350(5)
Two-Sample Tests for Incomplete Data
355(9)
Introduction
355(1)
The Wei-Lachin Method
355(1)
The Wei-Johnson Method
356(6)
Examples
362(2)
Problems
364(9)
Bibliography 373(32)
Author Index 405(7)
Subject Index 412

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