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A novel functional additive model is proposed which is uniquely modified andconstrained to model nonlinear interactions between a treatment indicator and apotentially large number of functional and/or scalar pretreatment covariates.The primary motivation for this approach is to optimize individualizedtreatment rules based on data from a randomized clinical trial. We generalizefunctional additive regression models by incorporating treatment-specificcomponents into additive effect components. A structural constraint is imposedon the treatment-specific components in order to provide a class of additivemodels with main effects and interaction effects that are orthogonal to eachother. If primary interest is in the interaction between treatment and thecovariates, as is generally the case when optimizing individualized treatmentrules, we can thereby circumvent the need to estimate the main effects of thecovariates, obviating the need to specify their form and thus avoiding theissue of model misspecification. The methods are illustrated with data from adepression clinical trial with electroencephalogram functional data aspatients' pretreatment covariates.

Functional additive models for optimizing individualized treatment rules