factorial randomized trial

Traditional randomized controlled trials (RCTs) suffer from cross-group spillovers and interference in multi-population interaction settings—e.g., buyer-seller or creator-subscriber systems—leading to biased estimation of the average treatment effect (ATE). This paper introduces the first systematic multidimensional randomization design framework, relaxing the conventional single-layer randomization assumption. By integrating hierarchical randomization, cross-group assignment, and potential outcomes modeling, it jointly identifies both the ATE and cross-group interference effects. We establish theoretical guarantees: the proposed unbiased estimator is consistent and asymptotically normal. Simulation results demonstrate substantially higher statistical power compared to standard RCTs. This work extends the scope of causal questions addressable through experimental design and provides a rigorous foundation for causal inference in complex intervention environments—particularly platform economies—where interdependent user behaviors induce non-negligible interference.

In large-scale aggregate-unit experiments (e.g., markets), conventional randomized treatment assignment often yields severe baseline imbalance due to extremely few treated units, leading to biased causal estimates. To address this, we systematically integrate the synthetic control method into experimental design, proposing a non-randomized treatment allocation mechanism: dynamically constructing a weighted synthetic control group based on pre-treatment covariates. We further develop配套 components—including counterfactual prediction, distance-driven unit matching, robust variance estimation, and a novel confidence interval construction procedure. Theoretically, our estimator is proven consistent and asymptotically normal. Empirically, it reduces estimation bias by 40–65% relative to standard randomization and substantially improves statistical power. Our core contribution is a new causal inference paradigm for small-N aggregate experiments—rigorous in inference, unbiased under mild assumptions, and highly interpretable.

This paper investigates the performance of the difference-in-means estimator in two-arm randomized experiments under continuous, binary, proportion, and survival endpoints, considering both equal and unequal allocation within Neyman and superpopulation modeling frameworks. Methodologically, it integrates randomization inference, minimax analysis, asymptotic statistics, and NP-hardness arguments, complemented by Monte Carlo simulations. The study establishes, for the first time, that Fisher’s blocked design is asymptotically optimal under Kapelner’s tail criterion. It systematically characterizes the theoretical boundaries between complete randomization (Neyman model) and deterministic perfect balance (superpopulation model), identifying blocked design as the optimal compromise. Both theoretical analysis and simulation results consistently demonstrate that blocking substantially reduces estimation error and robustly outperforms complete randomization and pairwise matching across all endpoint types and allocation ratios.

Multifactor causal inference in observational studies faces two key challenges: sparse or missing factor combinations hinder interaction effect identification, while covariate and factor imbalance induces estimation bias. This paper proposes Doubly Balanced Weighting (DBW), the first method to elevate factor balance to theoretical parity with covariate balance in observational factorial studies. DBW jointly optimizes an inverse-probability-weighting objective to simultaneously balance both covariate distributions and factor combination distributions. It enables robust estimation of main and interaction effects—even under missing treatment combinations—and provides consistent asymptotic variance estimation. Simulation and empirical analyses demonstrate that DBW substantially improves estimation accuracy and achieves nominal 95% confidence interval coverage. The framework offers a theoretically grounded, generalizable solution for causal inference in multifactor observational studies.

This paper identifies a causal inference bias in service-intervention randomized controlled trials (RCTs) arising from provider capacity constraints: limited resources induce cross-participant interference and treatment dose heterogeneity, rendering the average treatment effect dependent on both sample size and capacity, and causing effect attenuation beyond a critical threshold—yielding non-monotonic, inverted-U-shaped statistical power. We formally characterize this capacity-constrained, queue-based interference mechanism for the first time, integrating queuing theory (square-root staffing rule), causal inference, and experimental design. Our method jointly optimizes provider capacity and sample size to maximize power under resource constraints. Results demonstrate substantial gains in statistical power, reduced required resources and participant enrollment, and provide a mechanistic explanation for the common phenomenon of intervention efficacy fading upon scaling—from RCT success to real-world failure.

This study addresses the challenge of accurately inferring the distribution of individual treatment effects—such as the proportion benefiting, the median effect, or the maximum impact—in randomized experiments, without suffering power loss due to suboptimal pre-specified test statistics. The authors propose an adaptive randomization test that combines multiple rank-based statistics, ensuring finite-sample validity without requiring prior knowledge of the optimal statistic. Innovatively integrating adaptive statistic combination with stratified weighting, the method effectively circumvents the power degradation typically induced by multiple comparison corrections and accommodates heterogeneous stratified experimental designs. In an empirical application to a teacher training program, the approach reveals that approximately half of the teachers experience significant benefits, demonstrating superior detection power and interpretability compared to conventional single rank-based tests.

This study addresses the challenge in randomized controlled trials of complex interventions—such as psychotherapy—where conventional designs struggle to disentangle the intervention effect from therapist-specific effects. The authors introduce, for the first time, an orthogonal factorial design that treats the intervention (as a fixed effect) and therapist (as a random effect) as potentially interacting factors. Each therapist delivers all intervention conditions, and patients are randomly assigned to specific intervention–therapist combinations. Grounded in Design of Experiments (DoE) theory, the approach integrates ANOVA and regression modeling to establish a tailored randomization scheme and statistical analysis framework. Simulation results demonstrate that this method accurately estimates the main intervention effect, its standard error, between-therapist variance, and therapist-level heterogeneity in intervention effects, thereby substantially enhancing the reliability of evidence generated from complex interventions.

Classical randomized experiments struggle to identify causal effects in market platforms featuring cross-group strategic interactions and complex spillovers. To address this, we propose a novel multi-stage randomization design and the first finite-sample valid inferential framework that explicitly accounts for interference. We define composite causal parameters—including average direct, primary, and multiple types of spillover effects—that are both identifiable and substantively interpretable. Our method integrates graph-based randomization, hierarchical–clustered randomization, inverse-probability weighting, and Hájek-type bias correction, and establishes a finite-sample central limit theorem. We prove that all estimators achieve √n-consistency and asymptotic normality, ensuring statistical validity while substantially improving estimation precision for spillover effects. The framework is scalable and directly applicable to large-scale online marketplace experiments.

研究通过因子回归、双向聚类和协变量调整方法，解决双侧随机设计中的因果推断问题，适用于市场买卖双方等互动群体。

This study addresses the challenge of causal effect estimation in multiply randomized designs (MRD) for two-sided markets, where interference complicates inference. The authors propose a regression adjustment framework that avoids linear assumptions on potential outcomes. By constructing an optimal estimation strategy analogous to classical randomized experiments, they derive a linearly adjusted estimator with minimal asymptotic variance and establish its robust inference theory. Notably, the optimal adjustment form—such as a weighted two-way fixed effects regression with interaction terms—can be adaptively estimated from data, marking a significant departure from conventional approaches. The theoretical analysis integrates an enhanced central limit theorem for MRD with weighted regression techniques, and numerical simulations demonstrate that the proposed method substantially improves estimation efficiency over existing simple estimators, enabling more precise inference on total, direct, and spillover effects.