arXiv subjects

Jiaqi Tong

Publications and source records attributed to Jiaqi Tong.

10 recordsLinked to original sources

arXiv2026

Nonparametric heterogeneous causal mediation with orthogonal machine learning

Causal mediation analysis decomposes the total effect of an intervention on an outcome into a direct pathway and an indirect pathway transmitted through a mediator, but standard methods typically summarize these pathways using population average effects. In many applications, however, the indirect effect may vary substantially across individual profiles. We propose an orthogonal statistical learning framework for estimating heterogeneous causal mediation effects conditional on individual characteristics. The method constructs a class of weighted Neyman orthogonal losses motivated by influence function representations of weighted population average effects. These losses directly target conditional mediation estimands whose minimizers are locally insensitive to nuisance estimation errors. We implement the resulting learners under a two-stage meta-learning framework with regularized linear sieves as second-stage smoothers, and introduce a combination of targeted learning and orthogonal learning designed to improve stability when mediator density ratios are unstable. We establish $L^2$ and uniform limit theory and develop pointwise and uniform confidence bands. Simulation studies show that the proposed orthogonal learners reduce the mean integrated squared error by more than $50\%$ compared with existing model-based methods and provide computationally efficient inference in nonlinear settings. The CARDIA, PSACR, and STAR analyses reveal heterogeneous mediated effects across cardiometabolic, psychological, and educational settings.

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arXiv2026

Orthogonal double residual learning for optimal individualized treatment rules

Individualized treatment rules (ITRs) map baseline characteristics to treatment recommendations, with the optimal ITR maximizing expected reward or policy welfare. Indirect methods may require restrictive modeling assumptions, whereas direct methods can be sensitive to nuisance estimation error and limited overlap. We propose orthogonal double residual learning (ODRL), a two-stage, cross-fitted framework that directly targets the optimal ITR through cost-sensitive classification using the product of treatment and outcome residuals. To our knowledge, ODRL is the first direct method with a universally Neyman orthogonal objective requiring neither restrictive modeling assumptions nor inverse propensity score weighting. Thus, nuisance estimation errors affect regret through a second-order product, and ODRL remains robust under limited overlap. The Fisher consistent objective accommodates general decision rule sieves. We establish nonasymptotic high probability value function regret bounds relative to the Bayes classifier for VC classes, including linear rules and decision trees, and calibrated regret bounds for surrogate relaxations using support vector machines and deep ReLU neural networks. We further show that generic surrogate relaxations need not preserve orthogonality, whereas bounded score hinge learning does. Simulations demonstrate strong performance across complex and linear decision boundaries, limited overlap, and working model misspecification. Applications to the Right Heart Catheterization study and the Oxford Net Zero experiment illustrate interpretable treatment or policy recommendations. The \texttt{odrlITR} R package implements ODRL.

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arXiv2026

Doubly cross-fit debiased machine learning of heterogeneous treatment effects under principal stratification

Principal stratification provides a foundational framework for causal inference with intermediate outcomes by defining causal effects within subpopulations, yet existing work has largely focused on average effects across strata rather than treatment effect heterogeneity within strata. Such within-stratum heterogeneity informs individualized treatment decisions but the associated methods are sparse. We address this gap by studying the identification and estimation of the conditional principal causal effects under principal ignorability combined with an odds ratio sensitivity parameterization, which relaxes the monotonicity assumption. To efficiently learn these estimands, we propose a novel doubly cross-fit doubly robust machine learner that resolves the nested nuisance structure inherent to principal stratification. Leveraging sequential orthogonal debiased machine learning with regularized least-squares sieves, we derive $\mathcal{L}^2$ and uniform limit theory, establish oracle efficiency, and construct uniform confidence bands for the proposed estimator. We use simulations to demonstrate the finite-sample performance of our estimator, and provide an empirical analysis of a randomized trial in acute lung injury, revealing informative patterns of treatment effect heterogeneity within the always-survivor subpopulation.

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arXiv2026

Causal mediation in cluster-randomized trials with multiple mediators: spillover-aware decomposition, identification, and semiparametric efficient inference

Causal mediation analysis in cluster-randomized trials (CRTs) is complicated by the presence of multiple mediators, intracluster correlation, and within-cluster interference. Existing mediation methods often fall short in accommodating these features simultaneously, and semiparametric efficient estimators that fully address them remain unavailable. We develop a unified framework that defines a class of mediation effect estimands, including exit indirect effects, exit spillover mediation effects, and their interaction effects, to investigate causal mechanisms in CRTs with an arbitrary number of mediators under an unknown causal structure. We introduce a set of interpretable causal assumptions for point identification of each estimand. For optimal inference, we first derive the efficient influence functions for the proposed estimands and construct corresponding one-step and debiased machine learning estimators. In particular, to flexibly model the joint mediator density, we employ an elliptical copula marginal regression model that combines a nonparametric marginal regression with an interpretable association structure. We assess the finite-sample performance of the proposed estimators through simulation studies and illustrate the methodology by reanalyzing the PPACT CRT data with three causally unordered mediators.

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arXiv2026

Optimal Sample Size Calculation in Cost-Effectiveness Longitudinal Cluster Randomized Trials

Longitudinal cluster randomized trials (L-CRTs) are increasingly used to evaluate the cost-effectiveness of healthcare interventions across multiple assessment periods, yet design methods for powering these trials remain underdeveloped. Existing methods for cost-effectiveness analyses in cluster settings are limited to simple parallel-arm cluster randomized trials with a single follow-up assessment period. These methods cannot accommodate the complex correlation structures in L-CRTs conducted over multiple periods, which require differentiation between within-period and between-period correlations for both clinical and cost outcomes, as well as between-outcome correlations. Moreover, while substantial methodological advances have been made for the design of L-CRTs with univariate outcomes, none specifically address cost-effectiveness objectives where clinical and cost outcomes must be jointly modeled. We provide a design-stage framework for powering cost-effectiveness L-CRTs across three design variants: parallel-arm, crossover, and stepped wedge designs. We derive closed-form variance expressions for the generalized least squares estimator of the average incremental net monetary benefit under a bivariate linear mixed model. We propose a standardized ceiling ratio that adjusts willingness-to-pay for relative outcome variability to inform optimal design. We then develop local optimal designs that maximize statistical power under known correlation parameters and MaxiMin designs that ensure robust performance across parameter uncertainty for all three design variants. Through a real stepped wedge trial data example, we demonstrate the sample size calculation for testing intervention cost-effectiveness under local optimal and MaxiMin designs.

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arXiv2026

On the permutation equivariance principle for causal estimands

In many causal inference problems, multiple action variables, such as factors, mediators, or network units, often share a common causal role yet lack a natural ordering. To avoid ambiguity, the scientific interpretation of a vector of estimands should remain invariant under relabeling, an implicit principle we refer to as permutation equivariance. Permutation equivariance can be understood as the property that permuting the variables permutes the estimands in a trackable manner, such that scientific meaning is preserved. We formally characterize this principle and study its combinatorial algebra. We present a class of weighted estimands that project unstructured potential outcome means into a vector of permutation equivariant and interpretable estimands capturing all orders of interaction. To guide practice, we discuss the implications and choices of weights and define residual-free estimands, whose inclusion-exclusion sums capture the maximal effect, which is useful in context such as causal mediation and network interference. We present the application of our general theory to three canonical examples and extend our results to ratio effect measures.

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arXiv2025

Semiparametric principal stratification analysis beyond monotonicity

Intercurrent events, common in clinical trials and observational studies, affect the existence or interpretation of final outcomes. Principal stratification addresses this challenge by defining local average treatment effect estimands within subpopulations, but often relies on restrictive assumptions such as monotonicity and counterfactual intermediate independence. To overcome these limitations, we propose a semiparametric framework for principal stratification analysis leveraging a margin-free, conditional odds ratio sensitivity parameter. Under principal ignorability, we derive nonparametric identification formulas and efficient estimation methods, including a conditionally doubly robust parametric estimator and a debiased machine learning estimator with data-adaptive nuisance learners. Our simulations show that incorrectly assuming monotonicity can frequently lead to biased inference, but incorrectly assuming non-monotonicity when monotonicity holds may maintain approximately valid inference. We demonstrate our methods in the context of a critical care trial, where monotonicity is unlikely to be valid.

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arXiv2025

Model-robust standardization in cluster-randomized trials

In cluster-randomized trials, generalized linear mixed models and generalized estimating equations have conventionally been the default analytic methods for estimating the average treatment effect as routine practice. However, recent studies have demonstrated that their treatment effect coefficient estimators may correspond to ambiguous estimands when the models are misspecified or when there exists informative cluster sizes. In this article, we present a unified approach that standardizes output from a given regression model to ensure estimand-aligned inference for the treatment effect parameters in cluster-randomized trials. We introduce estimators for both the cluster-average and the individual-average treatment effects (marginal estimands) that are always consistent regardless of whether the specified working regression models align with the unknown data generating process. We further explore the use of a deletion-based jackknife variance estimator for inference. The development of our approach also motivates a natural test for informative cluster size. Extensive simulation experiments are designed to demonstrate the advantage of the proposed estimators under a variety of scenarios. The proposed model-robust standardization methods are implemented in the MRStdCRT R package.

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arXiv2025

Doubly robust estimation and sensitivity analysis with outcomes truncated by death in multi-arm clinical trials

In clinical trials, the observation of participant outcomes may frequently be hindered by death, leading to ambiguity in defining a scientifically meaningful final outcome for those who die. Principal stratification methods are valuable tools for addressing the average causal effect among always-survivors, i.e., the average treatment effect among a subpopulation defined as those who would survive regardless of treatment assignment. Although robust methods for the truncation-by-death problem in two-arm clinical trials have been previously studied, its expansion to multi-arm clinical trials remains elusive. In this article, we study the identification of a class of survivor average causal effect estimands with multiple treatments under monotonicity and principal ignorability, and first propose simple weighting and regression approaches for point estimation. As a further improvement, we derive the efficient influence function to motivate doubly robust estimators for the survivor average causal effects in multi-arm clinical trials. We also propose sensitivity methods under violations of key causal assumptions. Extensive simulations are conducted to investigate the finite-sample performance of the proposed methods against the existing methods, and a real data example is used to illustrate how to operationalize the proposed estimators and the sensitivity methods in practice.

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arXiv2023

On the mixed-model analysis of covariance in cluster-randomized trials

In the analyses of cluster-randomized trials, mixed-model analysis of covariance (ANCOVA) is a standard approach for covariate adjustment and handling within-cluster correlations. However, when the normality, linearity, or the random-intercept assumption is violated, the validity and efficiency of the mixed-model ANCOVA estimators for estimating the average treatment effect remain unclear. Under the potential outcomes framework, we prove that the mixed-model ANCOVA estimators for the average treatment effect are consistent and asymptotically normal under arbitrary misspecification of its working model. If the probability of receiving treatment is 0.5 for each cluster, we further show that the model-based variance estimator under mixed-model ANCOVA1 (ANCOVA without treatment-covariate interactions) remains consistent, clarifying that the confidence interval given by standard software is asymptotically valid even under model misspecification. Beyond robustness, we discuss several insights on precision among classical methods for analyzing cluster-randomized trials, including the mixed-model ANCOVA, individual-level ANCOVA, and cluster-level ANCOVA estimators. These insights may inform the choice of methods in practice. Our analytical results and insights are illustrated via simulation studies and analyses of three cluster-randomized trials.

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