Assessing alignment between functional markers and ordinal outcomes based on broad sense agreement.

Functional markers and their quantitative features (eg, maximum value, time to maximum, area under the curve [AUC], etc) are increasingly being used in clinical studies to diagnose diseases. It is thus of interest to assess the diagnostic utility of functional markers by assessing alignment between their quantitative features and an ordinal gold standard test that reflects the severity of disease. The concept of broad sense agreement (BSA) has recently been introduced for studying the relationship between continuous and ordinal measurements, and provides a promising tool to address such a question. Our strategy is to adopt a general class of summary functionals (SFs), each of which flexibly captures a different quantitative feature of a functional marker, and study its alignment according to an ordinal outcome via BSA. We further illustrate the proposed framework using three special classes of SFs (AUC-type, magnitude-specific, and time-specific) that are widely used in clinical settings. The proposed BSA estimator is proven to be consistent and asymptotically normal given a consistent estimator for the SF. We further provide an inferential framework for comparing a pair of candidate SFs in terms of their importance on the ordinal outcome. Our simulation results demonstrate satisfactory finite-sample performance of the proposed framework. We demonstrate the application of our methods using a renal study.