Measuring Agreement

CHAPTER 7 DATA FROM MULTIPLE METHODS

7.1 PREVIEW

So far we have focussed on method comparison studies involving two measurement methods. Quite often, more than two methods are compared in the same study. It is of interest here to perform multiple comparisons of method pairs to evaluate the extent of similarity and agreement. This chapter generalizes the data models in Chapters 4 and 5 to accommodate multiple methods where we assume these methods are fixed rather than randomly chosen ones. It considers simultaneous inference on pairwise measures of similarity and agreement that adjusts for multiplicity. The measurements may or may not be repeated and the design may not be balanced. But it is assumed that the data are homoscedastic and the measurement methods have the same scale. Two case studies are used for illustration.

7.2 INTRODUCTION

Suppose there are J ( ≥ 2) measurement methods under comparison. Here J is considered fixed and known. Two data designs are of interest. One is where the data are unreplicated , that is, there is only one measurement from each method on every subject. These data consist of Y_ij , j = 1 ,..., J , i = 1,...,n , with Y_ij representing the measurement from the jth method on the ith subject. There are a total of N = Jn observations and they form an extension of the paired measurements data considered in Chapter 4.

The other design is where the measurements are repeated. These data are denoted as Y_ijk, k = 1,...,m_ij, j = 1 ...,J , i = 1 ,...,n, with ...