Statistical Methods for the Analysis of Repeated Measurements

Transcription

1 Charles S. Davis Statistical Methods for the Analysis of Repeated Measurements With 20 Illustrations #j Springer

2 Contents Preface List of Tables List of Figures v xv xxiii 1 Introduction Repeated Measurements Advantages and Disadvantages of Repeated Measurements Designs Notation for Repeated Measurements Missing Data Sample Size Estimation Outline of Topics Choosing the "Best" Method of Analysis 12 2 Univariate Methods Introduction One Sample Multiple Samples Comments Problems 28

3 x Contents 3 Normal-Theory Methods: Unstructured Multivariate Approach Introduction Multivariate Normal Distribution Theory The Multivariate Normal Distribution The Wishart Distribution Wishart Matrices Hotelling's T 2 Statistic Hypothesis Tests One-Sample Repeated Measurements Methodology Examples Comments Two-Sample Repeated Measurements Methodology Example Comments Problems 61 4 Normal-Theory Methods: Multivariate Analysis of Variance Introduction The Multivariate General Linear Model Notation and Assumptions Parameter Estimation Hypothesis Testing Comparisons of Test Statistics Profile Analysis Methodology Example Growth Curve Analysis Introduction The Growth Curve Model Examples Problems 94 5 Normal-Theory Methods: Repeated Measures ANOVA Introduction The Fundamental Model One Sample Repeated Measures ANOVA Model Sphericity Condition Example Multiple Samples Repeated Measures ANOVA Model 112

4 Contents xi Example Problems Normal-Theory Methods: Linear Mixed Models Introduction The Linear Mixed Model The Usual Linear Model The Mixed Model Parameter Estimation Background on REML Estimation..' Application to Repeated Measurements Examples Two Groups, Four Time Points, No Missing Data Three Groups, 24 Time Points, No Missing Data Four Groups, Unequally Spaced Repeated Measurements, Time-Dependent Covariate Comments Use of the Random Intercept and Slope Model Effects of Choice of Covariance Structure on Estimates and Tests Performance of Linear Mixed Model Test Statistics and Estimators Problems Weighted Least Squares Analysis of Repeated Categorical Outcomes Introduction Background The Multinomial Distribution Linear Models Using Weighted Least Squares Analysis of Categorical Data Using Weighted Least Squares Taylor Series Variance Approximations for Nonlinear Response Functions Application to Repeated Measurements Overview One Population, Dichotomous Response, Repeated Measurements Factor Is Unordered One Population, Dichotomous Response, Repeated Measurements Factor Is Ordered One Population, Polytomous Response Multiple Populations, Dichotomous Response Accommodation of Missing Data Overview Ratio Estimation for Proportions 204

5 xii Contents One Population, Dichotomous Response Multiple Populations, Dichotomous Response Assessing the Missing-Data Mechanism Problems Randomization Model Methods for One-Sample Repeated Measurements Introduction The Hypergeometric Distribution and Large-Sample Tests of Randomness for 2 x 2 Tables The Hypergeometric Distribution Test of Randomness for a 2 x 2 Contingency Table Test of Randomness for s 2 x 2 Contingency Tables Application to Repeated Measurements: Binary Response, Two Time Points The Multiple Hypergeometric Distribution and Large- Sample Tests of Randomness for r x c Tables The Multiple Hypergeometric Distribution Test of Randomness for an r x c Contingency Table Test of Randomness for s r x c Tables Cochran-Mantel-Haenszel Mean Score Statistic Cochran-Mantel-Haenszel Correlation Statistic Application to Repeated Measurements: Polytomous Response, Multiple Time Points Introduction The General Association Statistic QG The Mean Score Statistic QM and the Correlation Statistic Qc Accommodation of Missing Data General Association Statistic QG Mean Score Statistic Q M Correlation Statistic Qc Use of Mean Score and Correlation Statistics for Continuous Data Problems Methods Based on Extensions of Generalized Linear Models Introduction Univariate Generalized Linear Models Introduction Random Component Systematic Component Link Function Canonical Links 279

6 Contents xiii Parameter Estimation Quasilikelihood Introduction Construction of a Quasilikelihood Function Quasilikelihood Estimating Equations Comparison Between Quasilikelihood and Generalized Linear Models Overview of Methods for the Analysis of Repeated Measurements Introduction Marginal Models Random-Effects Models Transition Models Comparisons of the Three Approaches The GEE Method Introduction Methodology Example Hypothesis Tests Using Wald Statistics Assessing Model Adequacy Sample Size Estimation Studies of the Properties of GEE Computer Software Cautions Concerning the Use of GEE Subsequent Developments Alternative Procedures for Estimation of GEE Association Parameters Other Developments and Extensions GEE1 and GEE Extended Generalized Estimating Equations (EGEE) Likelihood-Based Approaches Random-Effects Models Methods for the Analysis of Ordered Categorical Repeated Measurements Introduction., Univariate Cumulative Logit Models for Ordered Categorical Outcomes The Univariate Proportional-Odds Model The Stram-Wei-Ware Methodology for the Analysis of Ordered Categorical Repeated Measurements Extension of GEE to Ordered Categorical Outcomes Problems Nonparametric Methods Introduction 347

7 xiv Contents 10.2 Overview Multivariate One-Sample and Multisample Tests for Complete Data One Sample Multiple Samples Two-Sample Tests for Incomplete Data Introduction The Wei-Lachin Method The Wei-Johnson Method Examples Problems 364 Bibliography 373 Author Index 405 Subject Index 412