Data missing caused by non-response or drop-out appears routinely in modern medical studies. With the rapid development of information technology, medical data are becoming more and more massive in volume, and thus usually require distributed analysis in real-world applications, especially for cases where the data are collected from multiple centers or contain patient privacy. In this paper, we focus on developing efficient distributed algorithms to support quantile regression analysis in missing big data, which provides a powerful tool to model the skew and heterogeneous medical samples in reality, but currently remains a challenging issue. We employ the weighted quantile regression (WQR) technique to incorporate the missing information into the model and propose two two-stage distributed algorithms, IPW-ADMM and IPW-renewable, for efficient and privacy-preserving estimation of WQR. Both methods first estimate the missingness mechanism using a logistic model and then solve the WQR problem in a communication-efficient manner without sharing raw individual-level data. The IPW-ADMM algorithm parallelizes estimation using a multi-block alternating direction method of multipliers (ADMM), reformulating the nonsmooth WQR objective into a set of local subproblems. The IPW-renewable algorithm adopts a sequential renewable estimation framework with the smoothing technique, making it suitable for streaming or incremental data settings. Simulation studies demonstrate that both proposed methods achieve estimation accuracy comparable to the classical centralized interior point (IP) method, while offering substantial computational speedups in distributed environments. An application to the UK Biobank dataset further illustrates their practical utility in detecting heterogeneous genetic associations across quantiles under covariate missingness.

Meta-analysis with continuous outcomes presents a range of methodological challenges. Among these, two issues have received increasing attention: (i) integrating studies that report only the five-number summary (such as the median, interquartile range, and range) rather than the sample mean and standard deviation (SD), and (ii) accurately quantifying between-study heterogeneity. This review first summarizes recent advances in estimating the sample mean and SD from the five-number summary, covering both normality- and non-normality-based estimation methods. We also review recently developed skewness tests that help determine when normality-based estimators are appropriate and present a practical flow chart for integrating studies with five-number summaries into meta-analysis. Building on this, we discuss methods for quantifying the heterogeneity, focusing on the widely used relative heterogeneity statistic I 2 ${{I}^2}$ and its limitations, particularly its dependence on study sample sizes. We then review the absolute heterogeneity statistic I A 2 $I_A^2$ , which quantifies population-level variation across studies and is invariant to study sample sizes, thus complementing traditional measures. By synthesizing these methodological developments and providing practical guidelines and tools, this review aims to support more rigorous and transparent meta-analytic practice for continuous outcomes, especially in the presence of nonstandard reporting formats and varying degrees of heterogeneity.

Causal mediation analysis is an effective method for understanding the mechanism between the exposure and the outcome, often assuming that the mediation model is consistent for each individual in the target population. In practice, however, the natural indirect effect (NIE) may vary across individuals due to their distinct characteristics. As a result, the population can be partitioned into subgroups according to the varying sizes of the NIEs. Distinguishing subgroups within the study population enables the development of more precise and targeted treatment strategies. In this paper, we propose an identifiable mixture mediation model with latent subgroups for the survival data, where the outcome follows an accelerated failure time model and the mediator is Gaussian distributed. We further employ three information criteria including the AIC, BIC, and singular BIC (sBIC) to select the number of subgroups, followed by the expectation-maximization (EM) algorithm to estimate the model parameters and NIEs. Simulation study shows that the sBIC is the most robust and efficient criterion for selecting the number of subgroups; therefore, we recommend the sBIC-EM algorithm for practical use. Lastly, we apply our algorithm to the lung cancer data and discover two latent groups with opposing NIEs.

Meta-analysis is a cornerstone of evidence synthesis, yet challenges arise when studies report heterogeneous summary statistics, such as means and standard deviations (SDs) versus medians, interquartile ranges (IQRs), or other percentiles. Excluding studies that report only medians and IQRs can introduce bias and reduce precision, particularly when outcomes are skewed, which is common in clinical research. Although several methods exist to estimate means and SDs from alternative summaries, many rely on strong normality assumptions, exhibit computational burden, or fail to adequately account for the precision of reported quantiles (e.g., extreme values versus medians). To address these limitations, we propose two flexible weighted estimators for estimating the mean and SD from reported quantiles. The methods leverage inverse-variance and inverse-variance-covariance weighting, respectively, to enhance both accuracy and precision. Additionally, our methods are flexible enough to accommodate any set of reported quantiles and various underlying distributions, and they can be readily implemented using standard statistical software. Simulation studies demonstrate that the weighted estimators provide nearly unbiased estimates of the mean and SD with high precision in most cases, especially for large sample sizes. In a real-world meta-analysis, the estimates obtained using the proposed estimators closely aligned with those derived from true sample statistics. These approaches are particularly valuable for skewed outcomes and offer a practical and user-friendly solution for researchers seeking to integrate heterogeneous data while improving accuracy and precision.

Tukey's boxplot is widely used for outlier detection; however, its classic fixed-fence rule tends to flag an excessive number of outliers as the sample size grows. To address this, we introduce two new R packages, ChauBoxplot and AdaptiveBoxplot, which implement more robust and statistically principled outlier detection methods. We illustrate their advantages and practical implications through comprehensive simulation studies and a real-world analysis of provincial university admission rates from China's National College Entrance Examination. Based on these findings, we provide practical guidance to help practitioners select appropriate boxplot methods, achieving a balance between interpretability and statistical reliability.

For clinical trials with continuous outcomes, researchers may opt to report the whole or part of the five-number summary rather than the sample mean and standard deviation, especially when the outcome data are skewed. To include such studies in meta-analysis, several popular methods have been proposed in the literature that convert the five-number summary back to the sample mean and standard deviation. Nevertheless, most existing methods are based on the normality assumption, which may not hold for the clinical studies with the five-number summary being reported. Recently, Shi et al. (2023, Stat Methods Med Res, 32, 1338-1360) and Balakrishnan et al. (2023, Math Methods Stat, 32, 260-273) proposed methods for detecting the skewness of data that utilize the whole or part of the five-number summary, together with the sample size. In this article, we show that the max-type test of Shi et al. is not only structurally complex but also conservative in controlling the type I error rate, whereas the test of Balakrishnan et al. has difficulty controlling the type I error rate with small sample sizes. Inspired by these findings, we develop a novel test statistic that leverages the ratio of two tails, a measure known for its heightened sensitivity to data skewness. Simulation results demonstrate that our ratio-based test is both less conservative and more powerful compared to the existing methods, especially when the alternative distribution exhibits mild skewness. Additionally, simulated meta-analyses and real-world data examples are presented to demonstrate the utility of our new method in the context of meta-analysis.

The bagplot, also known as the "bag-and-bolster plot", is a notable extension of the boxplot from univariate to bivariate data. Although widely used, its practical application is hindered by two key limitations: the fixed inflation factor for outlier detection that does not adapt to the sample size, and the unstable convex hull used to visualize its fence. In this paper, we propose a new bagplot, namely the "bag-and-whisker plot”, as an improvement method to address these limitations. Our framework recasts outlier detection as a multiple testing problem, yielding a data-adaptive fence that controls statistical error rates and enhances the reliability of outlier identification. To further resolve graphical instability, we introduce a refined visualization that abandons the convex hull (the bolster) with a direct rendering of the statistical fence, complemented by granular whiskers that effectively illustrate the data's spread. Extensive simulations and real-world data analyses demonstrate that our new bagplot exhibits superior adaptivity and robustness compared to the existing standard, and thus can be highly recommended for practical use.

The standardized mean difference (SMD) is a widely used measure of effect size, particularly common in psychology, clinical trials, and meta-analysis involving continuous outcomes. Traditionally, under the equal variance assumption, the SMD is defined as the mean difference divided by a common standard deviation. This approach is prevalent in meta-analysis but can be overly restrictive in clinical practice. To accommodate unequal variances, the conventional method averages the two variances arithmetically, which does not allow for an unbiased estimation of the SMD. Inspired by this, we propose a geometric approach to averaging the variances, resulting in a novel measure for standardizing the mean difference with unequal variances. We further propose the Cohen-type and Hedges-type estimators for the new SMD, and derive their statistical properties including the confidence intervals. Simulation results show that the Hedges-type estimator performs optimally across various scenarios, demonstrating lower bias, lower mean squared error, and improved coverage probability. A real-world meta-analysis also illustrates that our new SMD and its estimators provide valuable insights to the existing literature and can be highly recommended for practical use.

Quantifying the heterogeneity is an important issue in meta-analysis, and among the existing measures, the I^2 statistic is most commonly used. In this paper, we first illustrate with a simple example that the I^2 statistic is heavily dependent on the study sample sizes, mainly because it is used to quantify the heterogeneity between the observed effect sizes. To reduce the influence of sample sizes, we introduce an alternative measure that aims to directly measure the heterogeneity between the study populations involved in the meta-analysis. We further propose a new estimator, namely the I_A^2 statistic, to estimate the newly defined measure of heterogeneity. For practical implementation, the exact formulas of the I_A^2 statistic are also derived under two common scenarios with the effect size as the mean difference (MD) or the standardized mean difference (SMD). Simulations and real data analysis demonstrate that the I_A^2 statistic provides an asymptotically unbiased estimator for the absolute heterogeneity between the study populations, and it is also independent of the study sample sizes as expected. To conclude, our newly defined I_A^2 statistic can be used as a supplemental measure of heterogeneity to monitor the situations where the study effect sizes are indeed similar with little biological difference. In such scenario, the fixed-effect model can be appropriate; nevertheless, when the sample sizes are sufficiently large, the I^2 statistic may still increase to 1 and subsequently suggest the random-effects model for meta-analysis.

Tukey's boxplot is a foundational tool for exploratory data analysis, but its classic outlier-flagging rule does not account for the sample size, and subsequent modifications have often been presented as separate, heuristic adjustments. In this paper, we propose a unifying framework that recasts the boxplot and its variants as graphical implementations of multiple testing procedures. We demonstrate that Tukey's original method is equivalent to an unadjusted procedure, while existing sample-size-aware modifications correspond to controlling the Family-Wise Error Rate (FWER) or the Per-Family Error Rate (PFER). This perspective not only systematizes existing methods but also naturally leads to new, more adaptive constructions. We introduce a boxplot motivated by the False Discovery Rate (FDR), and show how our framework provides a flexible pipeline for integrating state-of-the-art robust estimation techniques directly into the boxplot's graphical format. By connecting a classic graphical tool to the principles of multiple testing, our work provides a principled language for comparing, critiquing, and extending outlier detection rules for modern exploratory analysis.

Evidence is a core element of evidence-based medicine, with diverse classifications and extensive sources. Most of it is based on journals and is commonly found in databases or websites such as PubMed, Web of Science, and CNKI. The number of literatures is countless, which also puts enormous pressure on researchers to consult and read literature. The field of urology is no exception. This article started with analyzing the characteristics of common clinical questions in the field, introduced the four criteria for their screening and two types of structured templates, clarified the definition, categories, identification, and three requirements for the application of the four evidence classification methods, and explained the selection of retrieval resources, construction of retrieval strategies, specific operational steps, and precautions for the retrieval process to develop and use evidence. In addition, combined with artificial intelligence technology, the future development trend of evidence classification and retrieval in the field of evidence-based urology has been clarified, which provided reference for further promoting the development of evidence-based urology.

Systematic reviews play a critical role in synthesizing evidence across numerous studies, providing a foundation for informed decision-making in medical practice. However, the process is resource-intensive, requiring proficiency in constructing Boolean queries and screening extensive literature, which are time-consuming and susceptible to inconsistencies, especially for non-expert researchers. While large language models (LLMs) offer a potential solution, their tendency to generate inaccurate or hallucinated content restricts their direct application in systematic reviews. This study introduces and evaluates MedRAGent, a novel system that integrates LLMs with retrieval-augmented generation (RAG), designed to automate and enhance the efficiency and accuracy of Boolean query formulation and title/abstract screening in systematic reviews. MedRAGent employs DeepSeek-V3-0324 and Kimi-K2-0711-preview LLMs within an RAG framework tailored for PubMed. The system utilizes the official Medical Subject Headings (MeSH) database to construct precise Boolean queries. For screening, it employs the LLMs with a structured prompt to automatically evaluate the relevance of retrieved articles based on predefined inclusion and exclusion criteria. Its performance was assessed using 53,054 articles from 6 research topics. Our results showed that MedRAGent achieved an overall precision of 0.0271, recall of 0.8308, and F1-score of 0.0525 in Boolean query construction. For automated literature screening, the system attained an overall sensitivity of 0.8131, specificity of 0.9891, and G-mean of 0.8968 when using DeepSeek-V3-0324 as the underlying LLM. Performance improved when using Kimi-K2-0711-preview, with sensitivity of 0.8582, specificity of 0.9919, and G-mean of 0.9226. It efficiently processed 4,000-7,000 articles per day at low operational cost. MedRAGent demonstrates strong potential for automating Boolean query construction and abstract-level screening in systematic reviews. It effectively accelerates literature processing, supporting researchers in conducting efficient and evidence-based medical reviews.

Sample size calculation is crucial in biomedical in vivo research investigations mainly for two reasons: to design the most resource-efficient studies and to safeguard ethical issues when alive animals are subjects of testing. In this context, power analysis has been widely applied to compute the sample size by predetermining the desired statistical power and the significance level. To verify whether the assumption of a null hypothesis is true, repeated measures analysis of variance (ANOVA) is used to test the differences between multiple experimental groups and control group(s). In this article, we focus on the a priori power analysis, for testing multiple parameters and calculating the power of experimental designs, which is suitable to compute the sample size of trial groups in repeated measures ANOVA. We first describe repeated measures ANOVA and the statistical power from a practical aspect of biomedical research. Furthermore, we apply the G*Power software to conduct the a priori power analysis using examples of repeated measures ANOVA with three groups and five time points. We aim not to use the typical technically adapted statistical language. This will enable experimentalists to confidently formulate power calculation and sample size calculation easier and more accurately.

Mediation analysis is one of the most popularly used methods in social sciences and related areas. To estimate the indirect effect, the least-squares regression is routinely applied, which is also the most efficient when the errors are normally distributed. In practice, however, real data sets are often non-normally distributed, either heavy-tailed or skewed, so that the least-squares estimators may behave very badly. To overcome this problem, we propose a robust M-estimation for the indirect effect via a general loss function, with a main focus on the Huber loss which is more slowly varying at large values than the squared loss. We further propose a data-driven procedure to select the optimal tuning constant by minimizing the asymptotic variance of the Huber estimator, which is more robust than the least-squares estimator facing outliers and non-normal data, and more efficient than the least-absolute-deviation estimator. Simulation studies compare the finite sample performance of the Huber loss with the existing competitors in terms of the mean square error, the type I error rate, and the statistical power. Finally, the usefulness of the proposed method is also illustrated using two real data examples.

The box-and-whisker plot, introduced by Tukey (1977), is one of the most popular graphical methods in descriptive statistics. On the other hand, however, Tukey's boxplot is free of sample size, yielding the so-called "one-size-fits-all" fences for outlier detection. Although improvements on the sample size adjusted boxplots do exist in the literature, most of them are either not easy to implement or lack justification. As another common rule for outlier detection, Chauvenet's criterion uses the sample mean and standard derivation to perform the test, but it is often sensitive to the included outliers and hence is not robust. In this paper, by combining Tukey's boxplot and Chauvenet's criterion, we introduce a new boxplot, namely the Chauvenet-type boxplot, with the fence coefficient determined by an exact control of the outside rate per observation. Our new outlier criterion not only maintains the simplicity of the boxplot from a practical perspective, but also serves as a robust Chauvenet's criterion. Simulation study and a real data analysis on the civil service pay adjustment in Hong Kong demonstrate that the Chauvenet-type boxplot performs extremely well regardless of the sample size, and can therefore be highly recommended for practical use to replace both Tukey's boxplot and Chauvenet's criterion. Lastly, to increase the visibility of the work, a user-friendly R package named `ChauBoxplot' has also been officially released on CRAN.

In financial econometrics, the Sharpe ratio function serves as a gold standard to measure the return-to-risk ratio for comparing different assets or trading strategies. In the recent literature, several methods have been developed to directly or indirectly estimate the Sharpe ratio function, yet none of them apply to the scenario where the covariates are measured with error. To handle this problem, we propose a new method by incorporating the local polynomial smoothing and SIMEX to simultaneously estimate the Sharpe ratio function and the negative log-volatility function in the presence of measurement error. The asymptotic bias and variance of the proposed estimators are also derived under some regularity conditions. We further conduct Monte Carlo simulations to evaluate the finite sample performance, and apply two real data examples to illustrate the usefulness of our new method.

For high-dimensional small sample size data, Hotelling's T2 test is not applicable for testing mean vectors due to the singularity problem in the sample covariance matrix. To overcome the problem, there are three main approaches in the literature. Note, however, that each of the existing approaches may have serious limitations and only works well in certain situations. Inspired by this, we propose a pairwise Hotelling method for testing high-dimensional mean vectors, which, in essence, provides a good balance between the existing approaches. To effectively utilize the correlation information, we construct the new test statistics as the summation of Hotelling's test statistics for the covariate pairs with strong correlations and the squared $t$ statistics for the individual covariates that have little correlation with others. We further derive the asymptotic null distributions and power functions for the proposed Hotelling tests under some regularity conditions. Numerical results show that our new tests are able to control the type I error rates, and can achieve a higher statistical power compared to existing methods, especially when the covariates are highly correlated. Two real data examples are also analyzed and they both demonstrate the efficacy of our pairwise Hotelling tests.