Linear Mixed Models in Practice: A Sas-Oriented Approach

ISBN-13: 9780387982229 / Angielski / Miękka / 1997 / 306 str.

Geert Verbeke; Geert Verbeke; Geert Molenberghs

Opis

The dissemination of the MIXED procedure in SAS has provided a whole class of statistical models for routine use. We believe that both the ideas be- hind the techniques and their implementation in SAS are not at all straight- forward and users from various applied backgrounds, including the phar- maceutical industry, have experienced difficulties in using the procedure effectively. Courses and consultancy on PROC MIXED have been in great demand in recent years, illustrating the clear need for resource material to aid the user. This book is intended as a contribution to bridging this gap. We hope the book will be of value to a wide audience, including applied statisticians and many biomedical researchers, particularly in the pharma- ceutical industry, medical and public health research organizations, con- tract research organizations, and academic departments. This implies that our book is explanatory rather than research oriented and that it empha- sizes practice rather than mathematical rigor. In this respect, clear guidance and advice on practical issues are the main focus of the text. Nevertheless, this does not imply that more advanced topics have been avoided. Sections containing material of a deeper level have been sign posted by means of an asterisk.

Spis treści

1 Introduction.- 2 An Example-Based Tour in Linear Mixed Models.- 2.1 Fixed Effects and Random Effects in Mixed Models.- 2.2 General Linear Mixed Models.- 2.3 Variance Components Estimation and Best Linear Unbiased Prediction.- 2.3.1 Variance Components Estimation.- 2.3.2 Best Linear Unbiased Prediction (BLUP).- 2.3.3 Examples and the SAS Procedure MIXED.- 2.4 Fixed Effects: Estimation and Hypotheses Testing.- 2.4.1 General Considerations.- 2.4.2 Examples and the SAS Procedure MIXED.- 2.5 Case Studies.- 2.5.1 Cell Proliferation.- 2.5.2 A Cross-Over Experiment.- 2.5.3 A Multicenter Trial.- 3 Linear Mixed Models for Longitudinal Data.- 3.1 Introduction.- 3.2 The Study of Natural History of Prostate Disease.- 3.3 A Two-Stage Analysis.- 3.4 The General Linear Mixed-Effects Model.- 3.4.1 The Model.- 3.4.2 Maximum Likelihood Estimation.- 3.4.3 Restricted Maximum Likelihood Estimation.- 3.4.4 Comparison between ML and REML Estimation.- 3.4.5 Model-Fitting Procedures.- 3.5 Example.- 3.5.1 The SAS Program.- 3.5.2 The SAS Output.- 3.5.3 Estimation Problems due to Small Variance Components.- 3.6 The RANDOM and REPEATED Statements.- 3.7 Testing and Estimating Contrasts of Fixed Effects.- 3.7.1 The CONTRAST Statement.- 3.7.2 Model Reduction.- 3.7.3 The ESTIMATE Statement.- 3.8 PROC MIXED versus PROC GLM.- 3.9 Tests for the Need of Random Effects.- 3.9.1 The Likelihood Ratio Test.- 3.9.2 Applied to the Prostate Data.- 3.10 Comparing Non-Nested Covariance Structures.- 3.11 Estimating the Random Effects.- 3.12 General Guidelines for Model Construction.- 3.12.1 Selection of a Preliminary Mean Structure.- 3.12.2 Selection of Random-Effects.- 3.12.3 Selection of Residual Covariance Structure.- 3.12.4 Model Reduction.- 3.13 Model Checks and Diagnostic Tools ?.- 3.13.1 Normality Assumption for the Random Effects ?.- 3.13.2 The Detection of Influential Subjects ?.- 3.13.3 Checking the Covariance Structure ?.- 4 Case Studies.- 4.1 Example 1: Variceal Pressures.- 4.2 Example 2: Growth Curves.- 4.3 Example 3: Blood Pressures.- 4.4 Example 4: Growth Data.- 4.4.1 Model 1.- 4.4.2 Model 2.- 4.4.3 Model 3.- 4.4.4 Graphical Exploration.- 4.4.5 Model 4.- 4.4.6 Model 5.- 4.4.7 Model 6.- 4.4.8 Model 7.- 4.4.9 Model 8.- 5 Linear Mixed Models and Missing Data.- 5.1 Introduction.- 5.2 Missing Data.- 5.2.1 Missing Data Patterns.- 5.2.2 Missing Data Mechanisms.- 5.2.3 Ignorability.- 5.3 Approaches to Incomplete Data.- 5.4 Complete Case Analysis.- 5.4.1 Growth Data.- 5.5 Simple Forms of Imputation.- 5.5.1 Last Observation Carried Forward.- 5.5.2 Imputing Unconditional Means.- 5.5.3 Buck’s Method: Conditional Mean Imputation.- 5.5.4 Discussion of Imputation Techniques.- 5.6 Available Case Methods.- 5.6.1 Growth Data.- 5.7 Likelihood-Based Ignorable Analysis and PROC MIXED.- 5.7.1 Growth Data.- 5.7.2 Summary.- 5.8 How Ignorable Is Missing At Random ? ?.- 5.8.1 Information and Sampling Distributions ?.- 5.8.2 Illustration ?.- 5.8.3 Example ?.- 5.8.4 Implications for PROC MIXED.- 5.9 The Expectation-Maximization Algorithm ?.- 5.10 Multiple Imputation ?.- 5.10.1 General Theory ?.- 5.10.2 Illustration: Growth Data ?.- 5.11 Exploring the Missing Data Process.- 5.11.1 Growth Data.- 5.11.2 Informative Non-Response.- 5.11.3 OSWALD for Informative Non-Response.- A Inference for Fixed Effects.- A.1 Estimation.- A.2 Hypothesis Testing.- A.3 Determination of Degrees of Freedom.- A.4 Satterthwaite’s Procedure.- B Variance Components and Standard Errors.- C Details on Table 2.10: Expected Mean Squares.- D Example 2.8: Cell Proliferation.- References.