A major focus of personalized medicine is on the development of individualized treatment rules. Good decision rules have the potential to significantly advance patient care and reduce the burden of a host of diseases. Statistical methods for developing such rules are progressing rapidly, but few methods have considered the use of pre-treatment functional data to guide in decision-making. Furthermore, those methods that do allow for the incorporation of functional pre-treatment covariates typically make strong assumptions about the relationships between the functional covariates and the response of interest. We propose two approaches for using functional data to select an optimal treatment that address some of the shortcomings of previously developed methods. Specifically, we combine the flexibility of functional additive regression models with Q-learning or A-learning in order to obtain treatment decision rules. Properties of the corresponding estimators are discussed. Our approaches are evaluated in several realistic settings using synthetic data and are applied to real data arising from a clinical trial comparing two treatments for major depressive disorder in which baseline imaging data are available for subjects who are subsequently treated.
Keywords: A-learning; Additive models; Functional data; Q-learning; Treatment regime; imaging data.