From Unsupervised Subgroups to Hypothetical State-Intervention Policies: An Evaluation of Selected Subgrouping Methods in Observational Health Data
Authors: Vasundhara Acharya, Bulent Yener
Organizations: Rensselaer Polytechnic Institute, Troy, USA
Abstract
Conventional subgroup analyses can yield unstable and difficult-to-interpret conclusions, especially in observational biomedical data where each individual is observed under only one exposure state, true individual treatment effects are unavailable, and causal structure is uncertain. We investigate whether subgroups constructed from pretreatment characteristics, without using exposure, outcome, or estimated treatment-effect information, can serve as interpretable units for budget-constrained policy prioritization. We propose a framework combining causal-discovery-informed covariate selection, discovery-evaluation sample splitting, inductive unsupervised clustering, uncertainty-aware subgroup selection, and held-out doubly robust policy evaluation. We compare K-means, hard, membership-weighted, and stochastic Fuzzy C-means, Bayesian Gaussian mixture models, and a supervised causal-forest-derived CATE-tree comparator. Policies are evaluated under a 70% budget for hypothetical obesity-to-non-obesity and elevated-to-lower-glucose state shifts in the PIMA Indians Diabetes dataset and for a lifetime-smoking-history contrast in NHANES. The highest estimated ungated utilities were 0.799 for the BMI policy using Bayesian GMM, 0.735 for the glucose policy using hard or membership-weighted FCM, and 0.775 for the smoking-history policy using K-means. All paired 95% confidence intervals for policy-risk differences included zero, and no comparison remained statistically significant after Holm adjustment. Bayesian pooling generally preserved ungated allocations, whereas Empirical Bernstein gating was more conservative. Policies with similar estimated utility could nevertheless prioritize different individuals. The findings should be interpreted as assumption-dependent decision-support evidence for hypothetical state contrasts rather than proof of intervention benefit.
We study the problem of understanding where two populations differ within a feature space, which we formalize in the concept of a differential subgroup: a subset of individuals from both populations who, despite sharing similar characteristics, exhibit exceptional differences in a target outcome. Differential subgroups reveal the regions of the feature space where population-level gaps are most pronounced and can help practitioners identify the covariate combinations that are structurally responsible for these differences, e.g.~in clinical analysis, model diagnostics, or treatment-effect studies. We introduce a general optimization objective for discovering differential subgroups and establish conditions under which the resulting subgroups admit a causal interpretation of population differences. We propose DiffSub, a gradient-based approach that discovers interpretable differential subgroups in tabular data. Across synthetic benchmarks, medical case studies, model-error analyses, and treatment-effect settings, DiffSub identifies informative subgroups that reveal where population differences arise and why.
We propose \textbf{CaSPECT}, a causal spectral clustering framework for discovering causally homogeneous subgroups from observational data. Rather than clustering in covariate space, CaSPECT defines similarity through the topology of a learned directed acyclic graph (DAG); a bootstrap-stabilised PC algorithm recovers the causal skeleton; a novel \emph{Orientation Validation Score} (OVS) combines PC bootstrap evidence with DirectLiNGAM to orient edges robustly; directed edges are weighted by backdoor-identified average treatment effects estimated via OLS or double machine learning. Chung's directed Laplacian provides a spectral embedding in which individuals close together share the same causal propagation pathways. We establish almost-sure consistency of the full pipeline and validate the method through a controlled simulation study and on LaLonde CPS1, IHDP, and 401(k) datasets, where CaSPECT recovers a positive and statistically significant treatment effect within the causally comparable subpopulation and corrects for severe confounding without requiring a pre-specified propensity score model.
Arghya Pratihar, Shinjon Chakraborty, Swagatam Das
Policy learning methods are increasingly used to inform treatment allocation under budget constraints. Most proposed methods assume complete treatment data, yet applications frequently suffer from missingness that can bias estimates and lead to suboptimal policies. We address this gap by extending efficient estimators for average treatment effect (ATE) estimation to policy value and conditional average treatment effect (CATE) estimation under missing at random (MAR) and missing completely conditionally at random (MCCAR) treatment data. Through asymptotic efficiency analysis, we prove that the MAR estimator, which leverages partially-observed units, is both valid and more efficient than the MCCAR estimator when MCCAR assumptions hold. This result provides formal justification for preferring MAR-based estimation in policy learning under both missing data settings. Our comprehensive experiments using synthetic and semi-synthetic datasets confirm that correctly specifying the missingness mechanism is crucial: misspecified estimators remain biased regardless of sample size, while our estimators achieve near-oracle performance when assumptions are satisfied. Our work provides practitioners with theoretically grounded, empirically validated tools for robust policy learning in the presence of missing treatment data.