Statistical Methods for the Analysis of Repeated Measurements

by Davis, Charles S.

• ISBN13: 9780387953700
• ISBN10: 0387953701
• Format: Hardcover
• Copyright: 2002-03-01
• Publisher: Springer Verlag

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