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Activity Number: 346 - New Methods with Applications in Mental Health Statistics
Type: Contributed
Date/Time: Tuesday, July 30, 2019 : 10:30 AM to 12:20 PM
Sponsor: Mental Health Statistics Section
Abstract #304099
Title: A Functional Additive Model for Estimating Interactions Between a Treatment and a Large Number of Functional Regressors
Author(s): Hyung Park* and Eva Petkova and Thaddeus Tarpey and Todd Ogden
Companies: New York University and New York University and New York University and Columbia University
Keywords: Functional additive models; Individualized treatment decision rules; Projection-pursuit regression
Abstract:

We propose a functional additive model, uniquely modified and constrained to model nonlinear interactions between a treatment indicator and a potentially large number of functional/scalar regressors. We extend the functional additive regression of Fan et al. (2015), by incorporating treatment-specific link functions. A structural constraint is imposed on the treatment-specific components of the model, to give a class of orthogonal main and interaction effect additive models. Then the main effect components and the interaction effect components are estimated separately. If our interest is in interactions, we can estimate the interaction effects only, without having to model the main effect functionals, which side-steps the issue of potential misspecification of the main effects. Imposing a concave penalty in estimation, the method simultaneously selects functional/scalar treatment effect modifiers that exhibit possibly nonlinear interactions with the treatment indicator. We present theoretical properties of the proposed method. A set of simulation experiments and an application to a dataset from a depression clinical trial are presented to demonstrate this approach.


Authors who are presenting talks have a * after their name.

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