perform interval analysis

This study addresses the challenge of constructing valid confidence intervals in two-stage adaptive enrichment clinical trials, where patient subgroups are selected based on interim data, thereby compromising the nominal coverage of conventional intervals. The authors propose a novel method that constructs confidence intervals conditional on the interim selection decision, leveraging conditional inference and inversion of uniformly most accurate unbiased (UMAU) tests to guarantee exact coverage within the selected subgroup. The approach is broadly applicable to various adaptive enrichment designs and is implemented via an efficient numerical algorithm. Extensive simulation studies demonstrate that the proposed intervals consistently achieve the desired coverage probability across diverse design configurations, substantially outperforming existing methods in both validity and precision.

Existing exact confidence interval methods for the average treatment effect (ATE) with binary outcomes in randomized experiments are computationally expensive and often incorrectly assume a binomial distribution. Method: We propose the first exact, asymptotics-free confidence interval construction framework that dispenses with the binomial assumption. Our approach models the finite-population distribution using the hypergeometric distribution and combines combinatorial counting with boundary search, accelerated via a divide-and-conquer optimization strategy. Contribution/Results: The algorithm achieves $O(n log n)$ time complexity, enabling millisecond-scale computation for $n leq 1000$—over 100× faster than prior exact methods—while rigorously guaranteeing nominal coverage. It is especially suited for small-sample settings where asymptotic approximations fail and exact inference is critical.

This study addresses the limitations of existing confidence interval methods based on asymptotic normality, which fail to adequately capture the skewed sampling distribution of risk difference estimators in small-sample settings—particularly in paired-organ studies with unilateral and bilateral binary outcomes. To overcome the restrictive normality assumption, this work proposes a distribution-driven approach that explicitly models the true sampling distribution of the risk difference. The method integrates a modified MOVER procedure accounting for within-subject correlation with Monte Carlo simulation. Extensive simulations demonstrate that the proposed intervals achieve coverage probabilities close to the nominal level across various parameter configurations, with widths comparable to existing methods while more accurately reflecting distributional skewness in small samples. Its inferential consistency and practical utility are further corroborated through applications to two real datasets.

This work addresses the poor coverage performance of traditional confidence intervals in small-sample settings or with complex models, where reliance on asymptotic approximations often fails. The authors propose a novel confidence interval construction grounded in optimal transport theory, which minimizes coverage bias through optimal coupling and incorporates data-driven hyperparameter selection to enhance practical applicability. By moving beyond conventional quantile-based approaches, the method achieves substantially improved coverage accuracy and robustness across a range of estimation problems. The theoretical analysis rigorously establishes results concerning comparisons of probability measures, consistency, and finite-sample error bounds, providing a solid foundation for the proposed framework.

This study addresses the challenge of constructing confidence intervals for the average treatment effect (ATE) in multi-center observational healthcare data (e.g., heterogeneous electronic health records across hospitals). We propose a prediction-driven shrinkage inference method that enables valid ATE estimation and interval construction across disparate data sources under weak assumptions. Theoretically, we establish its unbiasedness and asymptotic interval validity for the first time, and extend it to hybrid experimental–observational settings. By integrating bias correction with variance shrinkage, our approach substantially narrows confidence intervals while improving uncertainty quantification accuracy. It guarantees nominal coverage probability under mild conditions. Numerical experiments demonstrate superior performance over naive data pooling. This work provides a statistically rigorous and practically applicable tool for real-world, multi-center evaluation of drug efficacy and safety.

This study addresses the frequentist prohibition against assigning a probability to the coverage of a parameter by an observed confidence interval, which limits nuanced interpretation of coverage events. By embedding confidence interval construction within a unified probabilistic framework through thought experiments and formal modeling, the work introduces a coverage indicator variable and, from a multi-level conditional probability perspective, demonstrates the coherence of assigning intermediate probabilities to single-instance coverage events under specific regularity conditions. This approach transcends the strict behaviorist constraints traditionally imposed on confidence intervals, revealing a tension between the exclusive reliance on design-stage coverage probability and the definition of long-run error rates. The result is a more flexible and internally consistent theoretical foundation for interpreting confidence intervals.

This study addresses the efficient computation of simultaneous confidence intervals under family-wise error rate (FWER) control in multiple hypothesis testing. By extending, for the first time, the concept of coherence from closed testing procedures to the partitioning principle, the authors establish a formal algorithmic equivalence between these two frameworks, thereby unifying the construction of multiple testing procedures and simultaneous confidence intervals. Leveraging this theoretical connection, they propose a computationally efficient and practically feasible algorithm for constructing simultaneous confidence intervals. The method’s validity and advantages are demonstrated through illustrative examples, highlighting its effectiveness in real-world applications.

Traditional hybrid experimental designs struggle to robustly control the frequentist operating characteristics of Bayesian decisions under model misspecification and lack efficient sample size determination methods applicable to generalized posteriors. This work proposes a computationally efficient experimental design framework that requires simulations at only two sample sizes and leverages extrapolation modeling of posterior summary functions to infer performance across the entire sample size space. This approach enables identification of the minimal sample size and decision rule satisfying desired operating characteristics. It represents the first general and scalable method for sample size planning under generalized posteriors, substantially reducing computational burden while enhancing robustness to model misspecification. The method’s validity and broad applicability within Bayesian M-estimation–type experiments are demonstrated through the redesign of an adaptive clinical trial with time-to-event outcomes.

该研究针对存在缺失数据时构建总体均值的置信区间问题，采用重新参数化的污染模型方法，并提供了适应未知参数变化的有效置信区间构造方案。

This study addresses a critical limitation in existing design-based simulations used to evaluate inference methods, which often overstate bias induced by spatial correlation due to unrealistic data-generating mechanisms. In particular, share-shift designs that fix outcomes and resample shocks conflate true treatment effects with error dependence structures, leading to misleading assessments. To remedy this, the paper proposes an improved simulation framework that more accurately models error dependence and avoids spurious entanglement between treatment effects and error terms, thereby better approximating real-world data-generating processes. Integrating resampling techniques with share-shift analysis, the proposed approach substantially enhances the reliability of inference evaluation across multiple empirical applications, underscoring the essential role of aligning simulation designs with genuine underlying mechanisms for valid inference assessment.