Extracting Scalar Measures from Functional Data withMissingness
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It is increasingly common in practice to observe functional data(including longitudinal data) consisting of curves. It is oftennecessary to extract a scalar summary from functional data. Forexample, a scalar summary may be needed to compare treatments with nonlinear longitudinal outcomes. In precisionmedicine, scalar summaries of functional data are useful fordefining optimal treatment decision rules. In practice, scalarsummaries of functional data that are commonly used areinefficient because they ignore the functional information orlead to biased results (e.g., change scores or the slope of afitted line). These inefficiencies are usually compounded in thepresence of missing data. In this talk, we introduce a scalarmeasure from a functional observation based on a weightedaverage tangent slope (WATS). Since the tangent sloperepresents an instantaneous rate of improvement ordeterioration, an appropriately weighted average tangentslope can produce a useful summary from a functionalobservation that incorporates the shape of the trajectory. Inthis talk, we illustrate the WATS and demonstrate thatestimators of the WATS provide superior summaries offunctional data.