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 technique widely used in evidence-based medicine for analytically combining the findings from independent clinical trials to provide an overall estimation of a treatment effectiveness. The sample mean and standard deviation are two commonly used statistics in meta-analysis but some trials use the median, the minimum and maximum values, or sometimes the first and third quartiles to report the results. Thus, to pool results in a consistent format, researchers need to transform those information back to the sample mean and standard deviation. In this article, we investigate the optimal estimation of the sample mean for meta-analysis from both theoretical and empirical perspectives. A major drawback in the literature is that the sample size, needless to say its imp...

Optimally estimating the sample mean from the sample size, median, mid-range, and/or mid-quartile range

Summary Background Viral load kinetics and duration of viral shedding are important determinants for disease transmission. We aimed to characterise viral load dynamics, duration of viral RNA shedding, and viable virus shedding of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in various body fluids, and to compare SARS-CoV-2, SARS-CoV, and Middle East respiratory syndrome coronavirus (MERS-CoV) viral dynamics. Methods In this systematic review and meta-analysis, we searched databases, including MEDLINE, Embase, Europe PubMed Central, medRxiv, and bioRxiv, and the grey literature, for research articles published between Jan 1, 2003, and June 6, 2020. We included case series (with five or more participants), cohort studies, and randomised controlled trials that reported SARS-CoV-2, SARS-CoV, or MERS-CoV infection, and reported viral load kinetics, duration of viral shedding, or viable virus. Two authors independently extracted data from published studies, or contacted authors to request data, and assessed study quality and risk of bias using the Joanna Briggs Institute Critical Appraisal Checklist tools. We calculated the mean duration of viral shedding and 95% CIs for every study included and applied the random-effects model to estimate a pooled effect size. We used a weighted meta-regression with an unrestricted maximum likelihood model to assess the effect of potential moderators on the pooled effect size. This study is registered with PROSPERO, CRD42020181914. Findings 79 studies (5340 individuals) on SARS-CoV-2, eight studies (1858 individuals) on SARS-CoV, and 11 studies (799 individuals) on MERS-CoV were included. Mean duration of SARS-CoV-2 RNA shedding was 17·0 days (95% CI 15·5–18·6; 43 studies, 3229 individuals) in upper respiratory tract, 14·6 days (9·3–20·0; seven studies, 260 individuals) in lower respiratory tract, 17·2 days (14·4–20·1; 13 studies, 586 individuals) in stool, and 16·6 days (3·6–29·7; two studies, 108 individuals) in serum samples. Maximum shedding duration was 83 days in the upper respiratory tract, 59 days in the lower respiratory tract, 126 days in stools, and 60 days in serum. Pooled mean SARS-CoV-2 shedding duration was positively associated with age (slope 0·304 [95% CI 0·115–0·493]; p=0·0016). No study detected live virus beyond day 9 of illness, despite persistently high viral loads, which were inferred from cycle threshold values. SARS-CoV-2 viral load in the upper respiratory tract appeared to peak in the first week of illness, whereas that of SARS-CoV peaked at days 10–14 and that of MERS-CoV peaked at days 7–10. Interpretation Although SARS-CoV-2 RNA shedding in respiratory and stool samples can be prolonged, duration of viable virus is relatively short-lived. SARS-CoV-2 titres in the upper respiratory tract peak in the first week of illness. Early case finding and isolation, and public education on the spectrum of illness and period of infectiousness are key to the effective containment of SARS-CoV-2. Funding None.

SARS-CoV-2, SARS-CoV, and MERS-CoV viral load dynamics, duration of viral shedding, and infectiousness: a systematic review and meta-analysis

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Mathematical Methods Of Statistics

https://academicworks.medicine.hofstra.edu/cgi/viewcontent.cgi?article=7937&context=articles

Cytokine elevation in severe and critical COVID-19: a rapid systematic review, meta-analysis, and comparison with other inflammatory syndromes.

Choosing effect measures and computing estimates of effect

In systematic reviews and meta-analysis, researchers often pool the results of the sample mean and standard deviation from a set of similar clinical trials. A number of the trials, however, reported the study using the median, the minimum and maximum 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.’s method (BMC Med Res Methodol 5:13, 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 several other interesting settings where the interquartile range is also available for the trials. We demonstrate the performance of the proposed methods through simulation studies for the three frequently encountered scenarios, respectively. For the first two scenarios, our method greatly improves existing methods and provides a nearly unbiased estimate of the true sample standard deviation for normal data and a slightly biased estimate for skewed data. For the third scenario, our method still performs very well for both normal data and skewed data. Furthermore, we compare the estimators of the sample mean and standard deviation under all three scenarios and present some suggestions on which scenario is preferred in real-world applications. In this paper, we discuss different approximation methods in the estimation of the sample mean and standard deviation and propose some new estimation methods to improve the existing literature. We conclude our work with a summary table (an Excel spread sheet including all formulas) that serves as a comprehensive guidance for performing meta-analysis in different situations.

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Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range

In systematic reviews and meta-analysis, researchers often pool the results of the sample mean and standard deviation from a set of similar clinical trials. A number of the trials, however, reported the study using the median, the minimum and maximum 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.

Wenqian Wang

Papers

Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range

Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range