Applied Mixed Models in Medicine

Helen Brown, Robin Prescott

• Publisher: Wiley
• Year: 2014
• ISBN:
  9781118778241
• Edition: 3
• Topic: Medicine
• Subtopic: Biostatistics

A fully updated edition of this key text on mixed models, focusing on applications in medical research

The application of mixed models is an increasingly popular way of analysing medical data, particularly in the pharmaceutical industry. A mixed model allows the incorporation of both fixed and random variables within a statistical analysis, enabling efficient inferences and more information to be gained from the data. There have been many recent advances in mixed modelling, particularly regarding the software and applications. This third edition of Brown and Prescott's groundbreaking text provides an update on the latest developments, and includes guidance on the use of current SAS techniques across a wide range of applications.

• Presents an overview of the theory and applications of mixed models in medical research, including the latest developments and new sections on incomplete block designs and the analysis of bilateral data.
• Easily accessible to practitioners in any area where mixed models are used, including medical statisticians and economists.
• Includes numerous examples using real data from medical and health research, and epidemiology, illustrated with SAS code and output.
• Features the new version of SAS, including new graphics for model diagnostics and the procedure PROC MCMC.
• Supported by a website featuring computer code, data sets, and further material.

This third edition will appeal to applied statisticians working in medical research and the pharmaceutical industry, as well as teachers and students of statistics courses in mixed models. The book will also be of great value to a broad range of scientists, particularly those working in the medical and pharmaceutical areas.

Chapter 1
Introduction

At the start of each chapter, we will ‘set the scene’ by outlining its content. In this introductory chapter, we start Section 1.1 by describing some situations where a mixed models analysis will be particularly helpful. In Section 1.2, we describe a simplified example and use it to illustrate the idea of a statistical model. We then introduce and compare fixed effects and random effects models. In the next section, we consider a more complex ‘real-life’ multi-centre trial and look at some of the variety of models that could be fitted (Section 1.3). This example will be used for several illustrative examples throughout the book. In Section 1.4, the use of mixed models to analyse a series of observations (repeated measures) is considered. Section 1.5 broadens the discussion on mixed models and looks at mixed models with a historical perspective of their use. In Section 1.6, we introduce some technical concepts: containment, balance and error strata.

We will assume in our presentation that the reader is already familiar with some of the basic statistical concepts as found in elementary statistical textbooks.

1.1 The use of mixed models

In the course of this book, we will encounter many situations in which a mixed models approach has advantages over the conventional type of analysis, which would be accessible via introductory texts on statistical analysis. Some of them are introduced in outline in this chapter and will be dealt in detail later on.

1. Example 1: Utilisation of incomplete information in a cross-over trial Cross-over trials are often utilised to assess treatment efficacy in chronic conditions, such as asthma. In such conditions, an individual patient can be tested for response to a succession of two or more treatments, giving the benefit of a ‘within-patient’ comparison. In the most commonly used cross-over design, just two treatments are compared. If, for generality, we call these treatments A and B, then patients will be assessed either on their response to treatment A, followed by their response to treatment B, or vice versa. If all patients complete the trial, and both treatments are assessed, then the analysis is fairly straightforward. However, commonly, patients drop out during the trial and may have a valid observation from only the first treatment period. These incomplete observations cannot be utilised in a conventional analysis. In contrast, the use of a mixed model will allow all of the observations to be analysed, resulting in more accurate comparisons of the efficacy of treatment. This benefit, of more efficient use of the data, applies to all types of cross-over trial where there are missing data.
2. Example 2: Cross-over trials with fewer treatment periods than treatments In cross-over trials, for logistical reasons, it may be impractical to ask a patient to evaluate more than two treatments (e.g. if the treatment has to be given for several weeks). Nevertheless, there may be the need to evaluate three or more treatments. Special types of cross-over design can be used in this situation, but a simple analysis will be very inefficient. Mixed models provide a straightforward method of analysis, which fully uses the data, resulting again in more precise estimates of the effect of the treatments.
3. Example 3: A surgical audit A surgical audit is to be carried out to investigate how different hospitals compare in their rates of postoperative complications following a particular operation. As some hospitals carry out the operation commonly, while other hospitals perform the operation rarely, the accuracy with which the complication rates are estimated will va...