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1. Modern Causal Inference Approaches to Improve Power for Subgroup Analysis in Randomized Controlled Trials

   https://doi.org/10.1002/sim.70436  

   D'Alessandro, Antonio; Kim, Jiyu; Adhikari, Samrachana; Goff, Donald; Bargagli‐Stoffi, Falco J; Santacatterina, Michele (February 2026, Statistics in Medicine)

   ABSTRACT Randomized controlled trials (RCTs) often include subgroup analyses to assess whether treatment effects vary across prespecified patient populations. However, these analyses frequently suffer from small sample sizes, which limit the power to detect heterogeneous effects. Power can be improved by leveraging predictors of the outcome—that is, through covariate adjustment—as well as by borrowing external data from similar RCTs or observational studies. The benefits of covariate adjustment may be limited when the trial sample is small. Borrowing external data can increase the effective sample size and improve power, but it introduces two key challenges: (i) integrating data across sources can lead to model misspecification, and (ii) practical violations of the positivity assumption—where the probability of receiving the target treatment is near zero for some covariate profiles in the external data—can lead to extreme inverse‐probability weights and unstable inferences, ultimately negating potential power gains. To account for these shortcomings, we present an approach to improving power in preplanned subgroup analyses of small RCTs that leverages both baseline predictors and external data. We propose de‐biased estimators that accommodate parametric, machine learning (ML), and nonparametric Bayesian methods. To address practical positivity violations (PPVs), we introduce three estimators: A covariate‐balancing approach, an automated de‐biased machine learning (DML) estimator, and a calibrated‐DML estimator. We show improved power in various simulations and offer practical recommendations for the application of the proposed methods. Finally, we apply them to evaluate the effectiveness of citalopram for negative symptoms in first‐episode schizophrenia (FES) patients across subgroups defined by duration of untreated psychosis (DUP), using data from two small RCTs. 

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2. Semi-Supervised Quantile Estimation: Robust and Efficient Inference in High Dimensional Settings

   Chakrabortty, Abhishek; Dai, Guorong; Carroll, Raymond J (August 2024, arXiv.org)

   We consider quantile estimation in a semi-supervised setting, characterized by two available data sets: (i) a small or moderate sized labeled data set containing observations for a response and a set of possibly high dimensional covariates, and (ii) a much larger unlabeled data set where only the covariates are observed. We propose a family of semi-supervised estimators for the response quantile(s) based on the two data sets, to improve the estimation accuracy compared to the supervised estimator, i.e., the sample quantile from the labeled data. These estimators use a flexible imputation strategy applied to the estimating equation along with a debiasing step that allows for full robustness against misspecification of the imputation model. Further, a one-step update strategy is adopted to enable easy implementation of our method and handle the complexity from the non-linear nature of the quantile estimating equation. Under mild assumptions, our estimators are fully robust to the choice of the nuisance imputation model, in the sense of always maintaining root-n consistency and asymptotic normality, while having improved efficiency relative to the supervised estimator. They also attain semi-parametric optimality if the relation between the response and the covariates is correctly specified via the imputation model. As an illustration of estimating the nuisance imputation function, we consider kernel smoothing type estimators on lower dimensional and possibly estimated transformations of the high dimensional covariates, and we establish novel results on their uniform convergence rates in high dimensions, involving responses indexed by a function class and usage of dimension reduction techniques. These results may be of independent interest. Numerical results on both simulated and real data confirm our semi-supervised approach's improved performance, in terms of both estimation and inference. 

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3. RefiDiff: Progressive Refinement Diffusion for Efficient Missing Data Imputation

   https://doi.org/10.1609/aaai.v40i24.39034  

   Ahamed, Md Atik; Ye, Qiang; Cheng, Qiang (March 2026, Proceedings of the AAAI Conference on Artificial Intelligence)

   Missing values in high-dimensional, mixed-type datasets pose significant challenges for data imputation, particularly under Missing Not At Random (MNAR) mechanisms. Existing methods struggle to integrate local and global data characteristics, limiting performance in MNAR and high-dimensional settings. We propose an innovative framework, RefiDiff, combining local machine learning predictions with a novel Mamba-based denoising network efficiently capturing long-range dependencies among features and samples with low computational complexity. RefiDiff bridges the predictive and generative paradigms of imputation, leveraging pre-refinement for initial warm-up imputations and post-refinement to polish results, enhancing stability and accuracy. By encoding mixed-type data into unified tokens, RefiDiff enables robust imputation without architectural or hyperparameter tuning. RefiDiff outperforms state-of-the-art (SOTA) methods across missing-value settings, demonstrating strong performance in MNAR settings and superior out-of-sample generalization. Extensive evaluations on nine real-world datasets demonstrate its robustness, scalability, and effectiveness in handling complex missingness patterns. 

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4. Parametric Bootstrap for Differentially Private Confidence Intervals

   Ferrando, Cecilia; Wang, Shufan; Sheldon, Daniel (January 2022, Proceedings of The 25th International Conference on Artificial Intelligence and Statistics (AITSTAS))

   The goal of this paper is to develop a practical and general-purpose approach to construct confidence intervals for differentially private parametric estimation. We find that the parametric bootstrap is a simple and effective solution. It cleanly reasons about variability of both the data sample and the randomized privacy mechanism and applies "out of the box" to a wide class of private estimation routines. It can also help correct bias caused by clipping data to limit sensitivity. We prove that the parametric bootstrap gives consistent confidence intervals in two broadly relevant settings, including a novel adaptation to linear regression that avoids accessing the covariate data multiple times. We demonstrate its effectiveness for a variety of estimators, and find empirically that it provides confidence intervals with good coverage even at modest sample sizes and performs better than alternative approaches. 

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5. An encoding generative modeling approach to dimension reduction and covariate adjustment in causal inference with observational studies

   https://doi.org/10.1073/pnas.2322376121  

   Liu, Qiao; Chen, Zhongren; Wong, Wing Hung (June 2024, Proceedings of the National Academy of Sciences)

   In this article, we develop CausalEGM, a deep learning framework for nonlinear dimension reduction and generative modeling of the dependency among covariate features affecting treatment and response. CausalEGM can be used for estimating causal effects in both binary and continuous treatment settings. By learning a bidirectional transformation between the high-dimensional covariate space and a low-dimensional latent space and then modeling the dependencies of different subsets of the latent variables on the treatment and response, CausalEGM can extract the latent covariate features that affect both treatment and response. By conditioning on these features, one can mitigate the confounding effect of the high dimensional covariate on the estimation of the causal relation between treatment and response. In a series of experiments, the proposed method is shown to achieve superior performance over existing methods in both binary and continuous treatment settings. The improvement is substantial when the sample size is large and the covariate is of high dimension. Finally, we established excess risk bounds and consistency results for our method, and discuss how our approach is related to and improves upon other dimension reduction approaches in causal inference. 

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