Heterogeneous Treatment Effects

Synthetic tabular data are often evaluated by distributional similarity, privacy distance, or train-on-synthetic-test-on-real predictive performance, but these criteria do not ensure validity for causal inference. We show that fully generative tabular synthesizers, including GAN- and LLM-based models, can preserve predictive utility while distorting average treatment effect (ATE) estimates. The failure is structural: ATE preservation requires both a realistic covariate law and an accurate treatment-effect contrast, whereas prediction loss penalizes treatment-effect error only through an overlap-weighted term. Thus, under imbalance or limited overlap, a generator may reproduce dominant observed outcomes while underlearning intervention-relevant contrasts. We formalize this mismatch through sensitivity and loss-decomposition results. Motivated by this causal analysis and intuition, we propose a hybrid synthetic-data framework for causal inference that generates covariates while modeling treatment and outcome mechanisms separately. We evaluate the framework in three settings: ATE preservation under fully generative versus hybrid synthesis, augmentation for practical positivity problems, and diagnostic simulation engines for comparing OR, IPW, AIPW, and TMLE before real-data analysis. We also stress-test the hybrid construction across settings that vary overlap, covariate dimension, seed sample size, and treatment-effect complexity, including a logistic outcome-model misspecification check. Across controlled simulation experiments, hybrid synthesis improves causal fidelity relative to fully generative baselines; the ACTG application shows improved predictive fidelity and potential for finite-sample estimator benchmarking. LLM-based hybrid synthesis is often more faithful than CTGAN in settings where causal fidelity can be assessed.

Single-arm trials accelerate study timelines by reducing the number of patients that must be recruited for a concurrent control group. However, these designs require an alternative comparator to estimate treatment effects. One approach is to construct a virtual control arm using a machine learning (ML) model trained on external control data to predict the counterfactual outcomes of the treatment arm. Our aim in this study was to leverage virtual controls by developing and evaluating ML-based counterfactual outcome models trained on IFX-treated patients to predict 1-year steroid-free clinical remission (SFCR ) and a composite of C-reactive protein remission plus steroid-free clinical remission (CRP-SFCR) for ADA-treated pediatric Crohn's disease patients, and to compare the resulting IFX-versus-ADA treatment effect estimates with those obtained using propensity score matching to external controls. Five ML models were used to train counterfactual models on the observed IFX cohort data. The resulting models were used to predict the counterfactual outcomes for the ADA arm patients. LGBM yields the best OR closest to the propensity score matched reference, and all 95% CI results align with the conclusion from the reference study that no statistical difference in the primary and secondary outcomes has been observed between the patients treated with ADA or IFX. Our study supports virtual controls as a viable and effective substitute for expensive, lengthy or unethical patient recruitment in an inflammatory bowel disease (IBD) trial. The developed gradient boosted prediction model can be used as a pretrained model to generate IFX counterfactual predictions in future studies, pending external validation and assessment of transportability.

In streaming platforms churn is extremely costly, yet A/B tests are typically evaluated using outcomes observed within a limited experimental horizon. Even when both short- and predicted long-term engagement metrics are considered, they may fail to capture how a treatment affects users' retention. Consequently, an intervention may appear beneficial in the short term and neutral in the long term while still generating lower total value than the control due to users churn. To address this limitation, we introduce a method that estimates long-term treatment effects (LTE) and residual lifetime value change ($ΔERLV$) in short multi-cohort A/B tests under user learning. To estimate time-varying treatment effects efficiently, we introduce an inverse-variance weighted estimator that combines multiple cohorts estimates, reducing variance relative to standard approaches in the literature. The estimated treatment trajectory is then modeled as a parametric decay to recover both the asymptotic treatment effect and the cumulative value generated over time. Our framework enables simultaneous evaluation of steady-state impact and residual user value within a single experiment. Empirical results show improved precision in estimating LTE and $ΔERLV$ and identify scenarios in which relying on either short-term or long-term metrics alone would lead to incorrect product decisions.

Randomized controlled trials (RCTs) are the gold standard for estimating treatment effects, yet they are often underpowered for detecting effect heterogeneity. Large observational studies (OS) can supplement RCTs for conditional average treatment effect (CATE) estimation, but a key barrier is covariate mismatch: the two sources measure different, only partially overlapping, covariates. We propose CALM (Calibrated ALignment under covariate Mismatch), which learns embeddings that map each source's features into a common representation space. OS outcome models are transferred to the RCT embedding space and calibrated using trial data, preserving causal identification from randomization. Finite-sample risk bounds decompose into alignment error, outcome-model complexity, and calibration complexity terms, making explicit when the learned embedding is accurate enough to reduce variance. We instantiate CALM in two forms: a closed-form linear version, CALM-Lin, and a neural representation-learning version, CALM-NN. Across 51 simulation settings, calibration-based linear methods are effectively tied in linear-CATE regimes, while CALM-NN wins all 22 nonlinear-CATE settings by wide margins. Moreover, on two real-data studies CALM-NN delivers the largest gains over the trial-only baseline.

Beyond conditional average treatment effects, treatments may impact the entire outcome distribution in covariate-dependent ways, for example, by altering the variance or tail risks for specific subpopulations. We propose a novel estimand to capture such conditional distributional treatment effects, and develop a doubly robust estimator that is minimax optimal in the local asymptotic sense. Using this, we develop a test for the global homogeneity of conditional potential outcome distributions that accommodates discrepancies beyond the maximum mean discrepancy (MMD), has provably valid type 1 error, and is consistent against fixed alternatives---the first test, to our knowledge, with such guarantees in this setting. We then provide a test that aggregates evidence across a grid of kernel-bandwidth choices. Furthermore, we derive exact closed-form expressions for two natural discrepancies (including the MMD), and provide a computationally efficient, permutation-free algorithm for our test.

We study the problem of selecting the best heterogeneous treatment effect (HTE) estimator from a collection of candidates in settings where the treatment effect is fundamentally unobserved. We cast estimator selection as a multiple testing problem and introduce a ground-truth-free procedure based on a cross-fitted, exponentially weighted test statistic. A key component of our method is a two-way sample splitting scheme that decouples nuisance estimation from weight learning and ensures the stability required for valid inference. Leveraging a stability-based central limit theorem, we establish asymptotic familywise error rate control under mild regularity conditions. Empirically, our procedure provides reliable error control while substantially reducing false selections compared with commonly used methods across ACIC 2016, IHDP, and Twins benchmarks, demonstrating that our method is feasible and powerful even without ground-truth treatment effects.