Measuring Agreement

CHAPTER 1 INTRODUCTION

1.1 PREVIEW

This chapter focuses on method comparison studies involving two methods of measurement of a quantitative variable. It introduces the companion problems of evaluation of similarity and evaluation of agreement between the methods, reviews the related concepts, critically examines the currently popular statistical tools, and describes a model-based approach for data analysis. It also points out the inadequacy of the widely used paired measurements design for data collection for the purpose of measuring agreement. To keep the flow of the text smooth, specific references are provided in the bibliographic note section at the end of the chapter. This practice is followed throughout the book.

1.2 NOTATIONAL CONVENTIONS

We generally use uppercase roman letters for random quantities whose values can be observed, for example, measurements made by medical devices. Lowercase roman letters are generally used for random quantities whose values cannot be observed (e.g., measurement errors) and for observed values of observable random quantities. Vectors and matrices are denoted by boldface letters. Their dimensions are clear from the context. By default, a vector is a column vector, and its transpose is denoted by attaching the superscript T to its symbol. For example, x is a column vector, x^T is the transpose of x, and X is a matrix. We also use I for an identity matrix, 1 for vectors and matrices of ones, and 0 for vectors and matrices of zeros. We often attach ...