Measuring Agreement

CHAPTER 4 PAIRED MEASUREMENTS DATA

4.1 PREVIEW

Even though the paired measurements design is not a good choice for method comparison studies, it remains by far the most commonly used design in practice. This chapter coalesces ideas from previous chapters to present a methodology for analysis of paired measurements data. The methodology follows the steps outlined in Section 1.16. Modeling of data via either a mixed-effects model or a bivariate normal model is considered. Evaluation of similarity and agreement under the assumed model is taken up next. Three case studies are used to illustrate the methodology.

4.2 MODELING OF DATA

4.2.1 Mixed-Effects Model

The data consist of paired measurements (Y_i1, Y_i2), i = 1,...,n, by two measurement methods on n randomly selected subjects from a population. In principle, there are two choices for modeling these data (Section 1.12). The preferred one is the mixed-effects model (1.19), which is written as

(4.1)

where

• the true values b_i follow independent N₁(µ_b, ) distributions,
• the random errors e_ij follow independent distributions, j = 1, 2, and
• the true values and the random errors are mutually independent.

This model implicitly assumes that the ...