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Extracting Scalar Measures from Functional Data with Missingness (309902)

Keywords: Functional data, ordering curves, weighted average tangent slope.

It is increasingly common in practice to observe functional data (including longitudinal data) consisting of curves. It is often necessary to extract a scalar summary from functional data. For example, scalar summaries of functional data are useful for optimal treatment decision rules. In practice, commonly used scalar summaries of functional data are inefficient because they ignore the functional information or lead to biased results (e.g., change scores or the slope of a fitted line). These inefficiencies are usually compounded in the presence of missing data. In this talk, we introduce a scalar measure from a functional observation based on a weighted average tangent slope (WATS). Since the tangent slope represents an instantaneous rate of improvement or deterioration, an appropriately weighted average tangent slope can produce a useful summary from a functional observation that incorporates the shape of the trajectory. We demonstrate that estimators of the WATS provide superior summaries of functional data compared to other common approaches, especially in the presence of missing data and dropout. Simulations and a depression trial are used to illustrate the results.