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تسجيل مستخدم جديدDetecting the skewness of data from the sample size and the five-number summary
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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. For the studies with skewed data, if we include them in the classical meta-analysis for normal data, it may yield misleading or even wrong conclusions. In this paper, we develop a flow chart and three new tests for detecting the skewness of data from the sample size and the five-number summary. Simulation studies demonstrate that our new tests are able to control the type I error rates, and meanwhile provide good statistical power. A real data example is also analyzed to demonstrate the usefulness of the skewness tests in meta-analysis and evidence-based practice.
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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, p
articularly 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.
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.
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values, and/or the first and third quartiles. Hence, in order to combine results, one may have to estimate the sample mean and standard deviation for such trials. In this paper, we propose to improve the existing literature in several directions. First, we show that the sample standard deviation estimation in Hozo et al. (2005) has some serious limitations and is always less satisfactory in practice. Inspired by this, we propose a new estimation method by incorporating the sample size. Second, we systematically study the sample mean and standard deviation estimation problem under more general settings where the first and third quartiles are also available for the trials. Through simulation studies, we demonstrate that the proposed methods greatly improve the existing methods and enrich the literature. We conclude our work with a summary table that serves as a comprehensive guidance for performing meta-analysis in different situations.
The era of big data is coming, and evidence-based medicine is attracting increasing attention to improve decision making in medical practice via integrating evidence from well designed and conducted clinical research. Meta-analysis is a statistical t
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