Functional additive models for optimizing individualized treatment rules

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 treatmentspecific 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.

An Innovative Non-Linear Prediction Model for Clinical Benefit in Women with Newly Diagnosed Breast Cancer Using Baseline FDG-PET/CT and Clinical Data

“…Subsequently, a logistic generalized additive model (GAM) was chosen as the statistical approach to assess the impact of all listed variables on the CB of treatment. This modeling choice was made because of its efficacy in capturing complex, non-linear relationships inherent in the data [36][37][38]. The determination of model parameters was conducted through a meticulous stratified bootstrap procedure, ensuring that the statistical properties of the stratified subsets aligned harmoniously with those of the original dataset.…”

“…A logistic generalized additive model was chosen as an innovative statistical approach to assess the impact of all listed variables on CB of treatment in our cohort. This modeling choice was rooted in its multidisciplinary approach (with regards to the data incorporated into the model) but above all, its efficacy in capturing complex, non-linear relationships inherent in the data [37,38]. Consequently, we developed a multivariate prediction model incorporating age, BMI, T, M, PT TLG, and PT volume as predictive biomarkers, with CB as the primary endpoint.…”

A single index model for longitudinal outcomes to optimize individual treatment decision rules

“…Future work will focus on developing efficient and faster algorithms for implementing the LS‐KLD TDR with variable selection. Extensions will also investigate the use of more flexible nonparametric link functions, that is, consider a smooth function of the biosignature in (1), as is done in the SIMML model (Park et al, 2020) and incorporating functional predictors into the TDR (e.g., Ciarleglio et al, 2015, Park et al, 2021). Further investigations into the impact of missing data under different missing data mechanisms (e.g., missing not a random) are currently being studied.…”