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The dynamicity of functional (curve) markers from modern clinical studies offers deeper insights into complex disease physiology. A frequent clinical practice is to examine various ‘pharmacokinetic features’ of functional markers (definite integral, maximum value, time to maximum, etc.) that reflect important physiological underpinnings. For instance, the current diagnostic procedure for kidney obstruction is to examine several pharmacokinetic features of renogram curves characterizing renal function. Motivated by such clinical practices, we develop a statistical framework for evaluating diagnostic accuracy of pharmacokinetic features using area under the receiver operating characteristic curve (AUC). The major challenge is that functional markers are observed at discrete time points with measurement error. To address this challenge, we develop a two-stage non-parametric AUC estimator based on summary functionals providing unified representation of various pharmacokinetic features and study its asymptotic properties. We also propose a sensible adaptation of a semiparametric regression model that can describe heterogeneity of AUC across different subpopulations, while appropriately handling discreteness and noise in observed functional markers. Here, a novel data-driven approach that balances between bias and efficiency of the regression coefficient estimates is introduced. Finally, the framework is applied to rigorously evaluate pharmacokinetic features of renogram curves potentially useful for detecting kidney obstruction.

Diagnostic evaluation of pharmacokinetic features of functional markers