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Maximin Learning of Individualized Treatment Effect on Multi-Domain Outcomes

Yuying Lu, Wenbo Fei, Yuanjia Wang, Molei Liu

Abstract

Precision mental health requires treatment decisions that account for heterogeneous symptoms reflecting multiple clinical domains. However, existing methods for estimating individualized treatment effects (ITE) rely on a single summary outcome or a specific set of observed symptoms or measures, which are sensitive to symptom selection and limit generalizability to unmeasured yet clinically relevant domains. We propose DRIFT, a new maximin framework for estimating robust ITEs from high-dimensional item-level data by leveraging latent factor representations and adversarial learning. DRIFT learns latent constructs via generalized factor analysis, then constructs an anchored on-target uncertainty set that extrapolates beyond the observed measures to approximate the broader hyper-population of potential outcomes. By optimizing worst-case performance over this uncertainty set, DRIFT yields ITEs that are robust to underrepresented or unmeasured domains. We further show that DRIFT is invariant to admissible reparameterizations of the latent factors and admits a closed-form maximin solution, with theoretical guarantees for identification and convergence. In analyses of a randomized controlled trial for major depressive disorder (EMBARC), DRIFT demonstrates superior performance and improved generalizability to external multi-domain outcomes, including side effects and self-reported symptoms not used during training.

Maximin Learning of Individualized Treatment Effect on Multi-Domain Outcomes

Abstract

Precision mental health requires treatment decisions that account for heterogeneous symptoms reflecting multiple clinical domains. However, existing methods for estimating individualized treatment effects (ITE) rely on a single summary outcome or a specific set of observed symptoms or measures, which are sensitive to symptom selection and limit generalizability to unmeasured yet clinically relevant domains. We propose DRIFT, a new maximin framework for estimating robust ITEs from high-dimensional item-level data by leveraging latent factor representations and adversarial learning. DRIFT learns latent constructs via generalized factor analysis, then constructs an anchored on-target uncertainty set that extrapolates beyond the observed measures to approximate the broader hyper-population of potential outcomes. By optimizing worst-case performance over this uncertainty set, DRIFT yields ITEs that are robust to underrepresented or unmeasured domains. We further show that DRIFT is invariant to admissible reparameterizations of the latent factors and admits a closed-form maximin solution, with theoretical guarantees for identification and convergence. In analyses of a randomized controlled trial for major depressive disorder (EMBARC), DRIFT demonstrates superior performance and improved generalizability to external multi-domain outcomes, including side effects and self-reported symptoms not used during training.

Paper Structure

This paper contains 28 sections, 5 theorems, 20 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Related Literature
  4. Our Contribution
  5. Outline of the Paper
  6. Conceptual Framework
  7. Problem formulation
  8. Factorized outcomes and ITE
  9. On-target set of factorized outcomes
  10. Maximin framework
  11. Geometric interpretation of GEO-anchored extrapolation
  12. Estimation Method
  13. Generalized factor analysis
  14. Constructing the on-target set
  15. Maximin estimation
  16. ...and 13 more sections

Key Result

Theorem 1

Suppose the function class $\mathcal{F}$ is convex with $\tau_k\in \mathcal{F}$ for $k\in[K]$, then $\tau^*$ defined in (eq:DRIFT) is identified as: where $\Xi_{k,l}=\mathbb{E}[\tau_k(\mathbf{X})\tau_l(\mathbf{X})]$ for $k,l\in [K]$.

Figures (4)

  • Figure 1: Illustration of the DRIFT Framework and Concepts.
  • Figure 2: Boxplots of $\mathrm{ACC}_{\min}$ (left) and $\mathrm{Cor}_{\min}$ (right) for the predicted individual treatment effects (ITEs) over 100 replications. In each replication, $J=30$ observed responses and $T=1000$ external responses are sampled from the loading hyper-population with fixed concentration $\sigma_v=1$, while the deviation magnitude varies as $r\in\{0.6,1,1.5\}$. The subject sample size is fixed at $N=300$.
  • Figure 3: Boxplots of $\mathrm{ACC}_{\min}$ (left) and $\mathrm{Cor}_{\min}$ (right) for predicted ITEs over 100 replications. We fix sample size $N=300$ and scalar $r=0.6$. The $J=30$ observed-response loadings are generated with concentration at $\sigma_v\in\{2,4,8\}$, while $T=1000$ external responses are sampled from the hyper-population with $\sigma_v=1$.
  • Figure 4: Loading Analysis: Latent Domain Interpretation and Geometric Decomposition

Theorems & Definitions (6)

  • Theorem 1: Identification
  • Remark 1
  • Proposition 1
  • Proposition 2: Invariance of DRIFT to Latent Reparameterization
  • Lemma 1
  • Theorem 2