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Abstract:
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Mediation analysis assesses whether a treatment, X, affects an outcome, Y, through a mediator, M. Often, each of X, M, and Y are measured at a single time point; however, there is recent interest in extending this to more intensive longitudinal or functional data, such as ecological momentary assessment data. We present a new method for estimating and testing the indirect effect of a randomized X on a distal Y as mediated by the nonparametric trajectory of a longitudinally measured M. This method combines ideas from scalar-on-function functional regression and function-on-function regression (time-varying effects modeling) but provides a simple scalar summary measure of the indirect effect. We demonstrate the performance of the method using simulations and an empirical data example to assess the effect of a randomized pharmacological intervention on abstinence from smoking at 1 month, via withdrawal symptoms, which are assessed three times per day every day for weeks 1 and 2 and every other day for weeks 3 and 4 post-quit. Finally, we discuss issues of interpretation and testing, and similarities and differences from the functional mediation approach of Lindquist (2012).
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