Unscaled Indices for Assessing Agreement of Functional Data

A decision to adopt a new medical device requires a rigorous assessment of the reliability and reproducibility of its clinical measurements. In this paper, with the goal of establishing the validity and acceptability of modern high-tech medical devices that generate functional data, we focus on the problem of assessing agreement of multiple functional data that are measured on the same subjects by different methods/technologies/raters. Specifically, we introduce a series of unscaled indices, total deviation index (TDI) and coverage probability (CP), that themselves are functions of time and can delineate the trends of intramethod, intermethod, and total (intra+inter) agreement of functional data across time in terms of the original measurement scale. We also develop scalar-valued TDI and CP indices that summarize the degree of agreement over the entire domain based on the weighted average idea. We advocate an experimental design under which each of the two methods generates replicated functional data measurements for each subject, and express each index using a mean function and variance components of a bivariate multilevel functional linear mixed effects model. Such a formulation allows us to smoothly estimate the indices based on our bivariate multilevel functional principal component analysis approach that only requires eigenanalyses of univariate covariance functions for better efficiency and scalability. Comprehensive simulation studies are conducted to examine the finite-sample properties of the estimators. The proposed method is applied to assess the reliability and reproducibility of renogram curves generated by diuresis renography, a high-tech medical imaging device widely used to detect kidney obstruction.