Measuring Agreement

CHAPTER 2 COMMON APPROACHES FOR MEASURING AGREEMENT

2.1 PREVIEW

The notion of agreement between two methods of measurement of a continuous response variable was introduced in Section 1.5. This chapter describes some common measures of agreement and discusses approaches for agreement evaluation based on those measures. The specific ones considered include concordance correlation coefficient, total deviation index, and limits of agreement. These are used throughout the book.

2.2 INTRODUCTION

As in Chapter 1, we use (Y₁, Y₂) to denote a pair of measurements by the two methods on a randomly selected subject from a population of interest. The pair follows a continuous bivariate distribution with mean (µ₁, µ₂), variance , covariance σ₁₂, and correlation ρ. Let D = Y₁ − Y₂ denote the difference in measurements. It follows a continuous distribution with mean ξ = µ₁ − µ₂ and variance . The distributions of Y₁, Y₂, and D need not be normal, although we often make such an assumption for inference purposes.

From Section 1.5, when the methods have perfect agreement, that is, P (Y₁ = Y₂) = 1, the bivariate distribution of Y₁ and Y₂ is concentrated on the 45^◦ line. The deviation from this ideal are quantified by agreement measures, which are functions of parameters of the bivariate distribution. ...