Maximin Learning of Individualized Treatment Effect on Multi-Domain Outcomes
Authors: Yuying Lu, Wenbo Fei, Yuanjia Wang, Molei Liu
Organizations: Department of Biostatistics, Columbia Mailman School of Public Health. · Department of Biostatistics, Peking University Health Science Center. · Beijing International Center for Mathematical Research, Peking University.
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.
Figures & tables
Figure 1: Illustration of the DRIFT Framework and Concepts.
Figure 2: Boxplots of ACCmin (left) and Cormin (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 σv=1 , while the deviation magnitude varies as r∈{0.6,1,1.5} . The subject sample size is fixed at N=300 .
Figure 3: Boxplots of ACCmin (left) and Cormin (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 σv∈{2,4,8} , while T=1000 external responses are sampled from the hyper-population with σv=1 .
CAST self-reported symptoms
FIBSER self-rated side effects
Method
1st
2nd
3rd
4th
Frequency
Intensity
Interference
Original
0.066
0.108
0.367
0.482
0.060
0.120
0.000
Factorized GEO
0.102
0.145
0.392
0.494
0.084
0.133
0.036
Obs Maximin
0.271
0.277
0.488
0.494
0.241
0.265
0.217
DRIFT
0.343
0.361
0.476
0.482
0.319
0.307
0.307
Table 1: Prediction accuracy (ACC) on external outcomes across items. For CAST, we list the four lowest-ranked items out of 17 ( 1 st to 4 th): CAST 7,2,17,8 for Original GEO and Factorized GEO , CAST 7,2,17,6 for Obs Maximin and CAST 2,7,6,15 for DRIFT . Notably, CAST 7,2,17,8 are mania-related, while CAST 6,15 are anxiety-related items. For FIBSER, we report the ACC for each of the three items (Frequency, Intensity, and Interference). The best ACC and any comparable results within a 0.02 margin are highlighted in bold for each column.
Figure 4: Loading Analysis: Latent Domain Interpretation and Geometric Decomposition
Predicting the effect of interventions with many possible variations, e.g., therapeutic content that affects mental health outcomes or an earnings call transcript that drives movement in share price, is useful across several domains. However, classical causal estimators tend to assume that all possible interventions are observed, which is infeasible when interventions vary widely, for instance, in the space of all text strings. We adapt a well-known approach of recasting causal inference as a learning problem, to address high-dimensional treatment spaces. Specifically, under standard assumptions like no unobserved confounding, we show that causal error decomposes into a series of moment-balancing errors of increasing order, and design objectives that directly improve causal estimation. We also show how to project the effect of a high-dimensional treatment onto lower-dimensional treatment attributes, which allows a single model to answer several causal questions without additional attribute-specific training. We empirically evaluate our estimators in settings with high-dimensional continuous, discrete, and text treatments, the last of which used a semi-synthetic dataset of Amazon Reviews. Our experiments demonstrate the benefit of higher-order balance error optimization and competitive performance of projected causal estimates with attribute-specific estimators.
Nikita Dhawan, Arnav Paruthi, Andrew Kim +3
University of Toronto, Vector Institute · University of Toronto · Vanguard
Integrative analysis of multiple datasets for estimating optimal individualized treatment rules (ITRs) can enhance decision efficiency. A central challenge is posterior shift, wherein the conditional distribution of potential outcomes given covariates differs between source and target populations. We propose a prior information-based distributionally robust ITR (PDRO-ITR) that maximizes the worst-case policy value over a covariate-dependent distributional uncertainty set, ensuring robust performance under posterior shift. The uncertainty set is constructed as an individualized combination of source distributions, with weights combining prior source-membership probabilities and deviation terms constrained to the probability simplex to accommodate posterior shift. We derive a closed-form solution for the PDRO-ITR and develop an adaptive procedure to tune the uncertainty level. We establish risk bounds for the PDRO-ITR estimator, which guarantees robust performance under the worst case. Extensive simulations and two real-data applications demonstrate that the proposed method achieves superior performance compared to existing approaches.
Wenhai Cui, Wen Su, Xingqiu Zhao
Department of Applied Mathematics, The Hong Kong Polytechnic University · Department of Biostatistics, City University of Hong Kong
Estimating individualized treatment effects from longitudinal observational data is central to data-driven medicine, yet existing methods face a fundamental limitation: reducing confounding bias often suppresses clinically informative heterogeneity, degrading patient-specific predictions. Here, we identify this tension as a bias-precision paradox in causal representation learning and introduce sampling-based maximum mean discrepancy (sMMD), a stochastic alignment strategy that replaces global adversarial balancing with subset-level matching. We instantiate this approach in a framework for counterfactual outcome prediction with attribution-grounded interpretability. Across two large-scale ICU cohorts (n = 27,783), our framework improves accuracy under distribution shift, reducing error by up to 11.5% and substantially increasing recall in high-risk tasks. Mechanistic analyses show that sMMD selectively preserves clinically decisive variables. In human-AI evaluation, our method outperforms clinicians-in-training and large language models, and improves clinician accuracy by 14.7% while reducing decision time, enabling interpretable, real-time clinical decision support.
Peisong Zhang, Manqiang Peng, Yuxuan Wu +21
School of Medicine, NUS, . · College of Design and Engineering, NUS, . · Aier Academy of Ophthalmology, Central South University. +14