Functional additive models for optimizing individualized treatment rules

TL;DR

This paper introduces a functional additive model tailored for optimizing individualized treatment rules, effectively capturing nonlinear treatment-covariate interactions without needing to specify main effects, demonstrated on clinical trial data.

Contribution

The paper develops a novel constrained functional additive model that isolates treatment-covariate interactions, improving personalized treatment decision-making in clinical trials.

Findings

Successfully applied to depression trial data with EEG covariates.

Effectively models nonlinear treatment interactions.

Avoids model misspecification by excluding main effects.

Abstract

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