Controllable Generative Sandbox for Causal Inference

Qi Zhang; Harsh Parikh; Ashley Naimi; Razieh Nabi; Christopher Kim; Timothy Lash

stat.MEMar 3, 2026

Controllable Generative Sandbox for Causal Inference

Authors: Qi Zhang, Harsh Parikh, Ashley Naimi, Razieh Nabi, Christopher Kim, Timothy Lash

Organizations: Emory University · Yale University · Amgen

Abstract

Method validation and study design in causal inference rely on synthetic data with known counterfactuals. Existing simulators trade off distributional realism, the ability to capture mixed-type and multimodal tabular data, against causal controllability, including explicit control over overlap, unmeasured confounding, and treatment effect heterogeneity. We introduce CausalMix, a variational generative framework that closes this gap by coupling a mixture of Gaussian latent priors with data-type-specific decoders for continuous, binary, and categorical variables. The model incorporates explicit causal controls: an overlap regularizer shaping propensity-score distributions, alongside direct parameterizations of confounding strength and effect heterogeneity. This unified objective preserves fidelity to the observed data while enabling factorial manipulation of causal mechanisms, allowing overlap, confounding strength, and treatment effect heterogeneity to be varied independently at design time. Across benchmarks, CausalMix achieves state-of-the-art distributional metrics on mixed-type tables while providing stable, fine-grained causal control. We demonstrate practical utility in a comparative safety study of metastatic castration-resistant prostate cancer treatments, using CausalMix to compare estimators under calibrated data-generating processes, tune hyperparameters, and conduct simulation-based power analyses under targeted treatment effect heterogeneity scenarios.

Figures & tables

Figure 1: Overview of the CausalMix generative framework.

Panel of Figure 2 — Figure 2: 2D joint embedding of synthetic data under BGMM and Gaussian priors compared with the real mCRPC dataset across causal scenarios. Scenario 1: homogeneous effect, no confounding, perfect overlap; Scenario 2: linear heterogeneous effect, mild confounding, constant overlap; Scenario 3: nonlinear heterogeneity with covariate-dependent confounding and overlap

Figure 3: Comparison of generated and target treatment effects of the mcrpc dataset from CausalMix with a BGMM prior in Scenario 3.

Figure 4: Grouped CATE estimates by age quintile. For each age group, boxplots summarize individual-level CATE estimates from each estimator in the subgroup with Charlson = 0, no prior CVD, under a calibrated synthetic data-generating process without unmeasured confounding (

\kappa=0

). Black diamonds indicate the true group-level mean CATE.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Axis	Category (Var Types)	Metric	Description / Formula
Distributional Fidelity	Marginal (cont.)	Normalized Wasserstein	$\dfrac{W_{1}\!\big(F_{\mathrm{real}}^{(c)},F_{\mathrm{synth}}^{(c)}\big)}{\mathrm{sd}_{\mathrm{real}}^{(c)}+\varepsilon}$ .
	Marginal (cont.)	KSComplement ( sdmetrics )	$1-D_{\mathrm{KS}}$ .
	Marginal (disc.)	TVComplement ( sdmetrics )	$1-\dfrac{1}{2}\sum_{x}\big\|p_{\mathrm{real}}(x)-p_{\mathrm{synth}}(x)\big\|$ .
	Pairwise (all vars)	SU Similarity	$1-\big\|\mathrm{SU}_{\mathrm{real}}(i,j)-\mathrm{SU}_{\mathrm{synth}}(i,j)\big\|$ .
	Pairwise (cont.–cont.)	CorrelationSimilarity ( sdmetrics )	Similarity of Pearson correlations over cont. pairs.
	Pairwise (disc.–disc.)	ContingencySimilarity ( sdmetrics )	Similarity of disc. contingency structure via total variation.

Appendix

Table B.1 : Summary of evaluation metrics across three axes: distributional fidelity, causal-structure fidelity, and privacy.

Figure D.1 : Marginal distributions of all variables in the synthetic data under BGMM and Gaussian priors compared with the real mCRPC dataset (Scenario 3).

Figure D.2 : Pairwise distributions of exposure and age in the synthetic data under BGMM and Gaussian priors compared with the real mCRPC dataset (Scenario 3).

Figure D.3 : Pairwise distributions of exposure and outcome in the synthetic data under BGMM and Gaussian priors compared with the real mCRPC dataset (Scenario 3).

Figure D.4 : Pairwise distributions of exposure and treatment history in the synthetic data under BGMM and Gaussian priors compared with the real mCRPC dataset (Scenario 3).

Figure D.5 : Comparison of generated and target unmeasured confounding of the mcrpc dataset from CausalMix with a BGMM prior in Scenario 3.

Panel of Figure 12 — Figure D.6 : Generated overlap of the mcrpc datasets from CausalMix with a BGMM prior across causal scenarios. Scenario 1: perfect overlap $\log\alpha(X)=0$ ; Scenario 2: moderate constant overlap $\log\alpha(X)=1$ ; Scenario 3: covariate-dependent overlap $\log\alpha(X)=2\big(2\,\text{Abiraterone\_prev}-1\big)$ .

Figure D.7 : Comparison of ATE bias across estimators under no unmeasured confounding (

\kappa=0

) and moderate unmeasured confounding (

\kappa=0.02

). Points denote mean bias across 50 independent replications and error bars indicate one standard deviation. Estimator groups are defined based on the CATE model.

Figure D.8 : Comparison of PEHE across estimators under no unmeasured confounding (

\kappa=0

) and moderate unmeasured confounding (

\kappa=0.02

). Points denote mean RMSE across 50 independent replications and error bars indicate one standard deviation. Estimator groups are defined based on the CATE model.

Figure D.9 : Sensitivity of CATE accuracy and uncertainty to the minimum leaf size in causal forests (2,000 trees). The solid curve shows mean absolute CATE bias and the dashed curve shows mean CATE confidence interval width, averaged over 50 replications.

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Generative Synthetic Data for Causal Inference: Pitfalls, Remedies, and Opportunities

Yichen Xu

University of California, Berkeley

Causal Effect Estimation Synthetic Data Generation Synthetic Tabular Data Generation Synthetic Data Evaluation Causal Intervention

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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.

Abstract

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