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Abstract:
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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, a scalar summary may be needed to compare treatments with nonlinear longitudinal outcomes. In precision medicine, scalar summaries of functional data are useful for defining optimal treatment decision rules. In practice, scalar summaries of functional data that are commonly used 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. In this talk, we illustrate the WATS and demonstrate that estimators of the WATS provide superior summaries of functional data.
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