Measuring Agreement

CHAPTER 10 A NONPARAMETRIC APPROACH

10.1 PREVIEW

Here we present a nonparametric approach for analysis of continuous method comparison data. Attention is restricted to the evaluation of similarity and agreement. The methodology makes no assumption about either the shape of the data distribution or how the observed measurements are related to the underlying true values. It is an alternative to the normality-based parametric approaches of previous chapters, and is especially attractive for data with marked deviations from normality. It works for unreplicated as well as unlinked repeated measurements data. It takes a statistical functional approach that treats the population quantities, including the measures of similarity and agreement, as features of a population distribution and estimates them using the same features of an empirical distribution. Under certain assumptions, the resulting estimators are approximately normal for large samples. This result is used to develop nonparametric analogs of the procedures in Chapter 7 involving multiple methods. Its application is illustrated using two case studies.

10.2 INTRODUCTION

Consider the setup of Chapter 7. We have measurements from J ( ≥ 2) methods on n subjects. It is assumed that n is large. The measurements may be unreplicated or repeated. The latter are assumed to be unlinked. The unreplicated measurements are denoted by Y_ij, j = 1,..., J, i = 1,...,n. The repeated measurements are denoted by Y_ijk, k = 1,..., m_ij, j = 1 ..., ...