arXiv subjects

Jiandong Shi

Publications and source records attributed to Jiandong Shi.

5 recordsLinked to original sources

arXiv2025

Geometric standardized mean difference and its application to meta-analysis

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.

stat.ME↗

arXiv2023

Detecting the skewness of data from the five-number summary and its application in meta-analysis

For clinical studies with continuous outcomes, when the data are potentially skewed, researchers may choose to report the whole or part of the five-number summary (the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation. In the recent literature, it is often suggested to transform the five-number summary back to the sample mean and standard deviation, which can be subsequently used in a meta-analysis. However, if a study contains skewed data, this transformation and hence the conclusions from the meta-analysis are unreliable. Therefore, we introduce a novel method for detecting the skewness of data using only the five-number summary and the sample size, and meanwhile propose a new flow chart to handle the skewed studies in a different manner. We further show by simulations that our skewness tests are able to control the type I error rates and provide good statistical power, followed by a simulated meta-analysis and a real data example that illustrate the usefulness of our new method in meta-analysis and evidence-based medicine.

stat.ME↗

arXiv2020

Optimally estimating the sample standard deviation from the five-number summary

When reporting the results of clinical studies, some researchers may choose the five-number summary (including the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation, particularly for skewed data. For these studies, when included in a meta-analysis, it is often desired to convert the five-number summary back to the sample mean and standard deviation. For this purpose, several methods have been proposed in the recent literature and they are increasingly used nowadays. In this paper, we propose to further advance the literature by developing a smoothly weighted estimator for the sample standard deviation that fully utilizes the sample size information. For ease of implementation, we also derive an approximation formula for the optimal weight, as well as a shortcut formula for the sample standard deviation. Numerical results show that our new estimator provides a more accurate estimate for normal data and also performs favorably for non-normal data. Together with the optimal sample mean estimator in Luo et al., our new methods have dramatically improved the existing methods for data transformation, and they are capable to serve as "rules of thumb" in meta-analysis for studies reported with the five-number summary. Finally for practical use, an Excel spreadsheet and an online calculator are also provided for implementing our optimal estimators.

stat.ME↗

arXiv2019

A new paradox in random-effects meta-analysis

Meta-analysis is an important tool for combining results from multiple studies and has been widely used in evidence-based medicine for several decades. This paper reports, for the first time, an interesting and valuable paradox in random-effects meta-analysis that is likely to occur when the number of studies is small and/or the heterogeneity is large. With the incredible paradox, we hence advocate meta-analysts to be extremely cautious when interpreting the final results from the random-effects meta-analysis. And more importantly, with the unexpected dilemma in making decisions, the new paradox has raised an open question whether the current random-effects model is reasonable and tenable for meta-analysis, or it needs to be abandoned or further improved to some extent.

stat.AP↗

arXiv2018

How to estimate the sample mean and standard deviation from the five number summary?

In some clinical studies, researchers may report the five number summary (including the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation. To conduct meta-analysis for pooling studies, one needs to first estimate the sample mean and standard deviation from the five number summary. A number of studies have been proposed in the recent literature to solve this problem. However, none of the existing estimators for the standard deviation is satisfactory for practical use. After a brief review of the existing literature, we point out that Wan et al.'s method (BMC Med Res Methodol 14:135, 2014) has a serious limitation in estimating the standard deviation from the five number summary. To improve it, we propose a smoothly weighted estimator by incorporating the sample size information and derive the optimal weight for the new estimator. For ease of implementation, we also provide an approximation formula of the optimal weight and a shortcut formula for estimating the standard deviation from the five number summary. The performance of the proposed estimator is evaluated through two simulation studies. In comparison with Wan et al.'s estimator, our new estimator provides a more accurate estimate for normal data and performs favorably for non-normal data. In real data analysis, our new method is also able to provide a more accurate estimate of the true sample standard deviation than the existing method. In this paper, we propose an optimal estimator of the standard deviation from the five number summary. Together with the optimal mean estimator in Luo et al. (Stat Methods Med Res, in press, 2017), our new methods have improved the existing literature and will make a solid contribution to meta-analysis and evidence-based medicine.

stat.ME↗