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Ten circumstances and solutions for finding the sample mean and standard deviation for meta-analysis.

ABSTRACT: A common problem in meta-analyses is the unavailability of mean and standard deviation (SD). Unfortunately, only having values of the median, interquartile range (IQR), or range cannot be directly utilized for meta-analysis. Although some estimation and conversion methods have been proposed in the past two decades, there were no published and user-friendly tools developed based on multiple scenarios of missing SD. Therefore, this study aimed to provide a collection of possible circumstances of missing sample means or SD with solutions for teaching and research. A total of 10 common circumstances of missing SD or mean could have available statistics of p value, t value, z score, confidence interval, standard error, median, IQR, and range. Teachers and investigators can use relevant formulas for finding the sample mean and SD according to the available circumstance. Due to the complicated computations, our team provides a free available spreadsheet. With ever-evolving statistical methods, some formulas may be further improved in the future; therefore, it is recommended to involve statisticians in evidence-based practice or systematic reviews.

SUBMITTER: Chi KY

PROVIDER: S-EPMC10068165 | biostudies-literature | 2023 Apr

REPOSITORIES: biostudies-literature

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Ten circumstances and solutions for finding the sample mean and standard deviation for meta-analysis.

Chi Kuan-Yu KY Li Man-Yun MY Chen Chiehfeng C Kang Enoch E

Systematic reviews 20230401 1

A common problem in meta-analyses is the unavailability of mean and standard deviation (SD). Unfortunately, only having values of the median, interquartile range (IQR), or range cannot be directly utilized for meta-analysis. Although some estimation and conversion methods have been proposed in the past two decades, there were no published and user-friendly tools developed based on multiple scenarios of missing SD. Therefore, this study aimed to provide a collection of possible circumstances of m ...[more]

PMID: 37005690

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Project description:BackgroundIn 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.MethodsIn 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.ResultsWe 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.ConclusionsIn 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.

Project description:BackgroundRigorous, informative meta-analyses rely on availability of appropriate summary statistics or individual participant data. For continuous outcomes, especially those with naturally skewed distributions, summary information on the mean or variability often goes unreported. While full reporting of original trial data is the ideal, we sought to identify methods for handling unreported mean or variability summary statistics in meta-analysis.MethodsWe undertook two systematic literature reviews to identify methodological approaches used to deal with missing mean or variability summary statistics. Five electronic databases were searched, in addition to the Cochrane Colloquium abstract books and the Cochrane Statistics Methods Group mailing list archive. We also conducted cited reference searching and emailed topic experts to identify recent methodological developments. Details recorded included the description of the method, the information required to implement the method, any underlying assumptions and whether the method could be readily applied in standard statistical software. We provided a summary description of the methods identified, illustrating selected methods in example meta-analysis scenarios.ResultsFor missing standard deviations (SDs), following screening of 503 articles, fifteen methods were identified in addition to those reported in a previous review. These included Bayesian hierarchical modelling at the meta-analysis level; summary statistic level imputation based on observed SD values from other trials in the meta-analysis; a practical approximation based on the range; and algebraic estimation of the SD based on other summary statistics. Following screening of 1124 articles for methods estimating the mean, one approximate Bayesian computation approach and three papers based on alternative summary statistics were identified. Illustrative meta-analyses showed that when replacing a missing SD the approximation using the range minimised loss of precision and generally performed better than omitting trials. When estimating missing means, a formula using the median, lower quartile and upper quartile performed best in preserving the precision of the meta-analysis findings, although in some scenarios, omitting trials gave superior results.ConclusionsMethods based on summary statistics (minimum, maximum, lower quartile, upper quartile, median) reported in the literature facilitate more comprehensive inclusion of randomised controlled trials with missing mean or variability summary statistics within meta-analyses.

Project description:BackgroundA recent review found that 45% of meta-analyses included statistical errors, of which, the most common was the calculation of effect sizes based on standard error (SE) rather than standard deviation (SD) [the SE/SD mix-up].ObjectivesThe first aim of this study was to assess the impact of the SE/SD mix-up on the results of one highly cited meta-analysis. Our second aim was to identify one potential source of the SE/SD mix-up, by assessing how often SE is reported as a measure of sample variability in randomised controlled trials in sports medicine.MethodsWe checked for potential SE/SD mix-ups in a 2015 meta-analysis of randomised controlled trials reporting the effects of recreational football interventions on aerobic fitness in adults. We corrected effect sizes affected by SE/SD mix-ups and re-analysed the data according to the original methodology. We compared pooled estimates of effect sizes from our re-analysis of corrected values with those of the original study. To assess how often SE was reported instead of SD as a measure of sample variance, we text mined results of randomised controlled trials from seven sports medicine journals and reported the proportion reporting of SE versus SD.ResultsWe identified potential SE/SD mix-ups in 9/16 effect sizes included in the meta-analysis describing the effects of football-based interventions versus non-exercise control. The published effect size was standardised mean difference (SMD) = 1.46 (95% confidence interval [CI] 0.91, 2.01). After correcting for SE/SD mix-ups, our re-analysis produced a smaller pooled estimate (SMD = 0.54 [95% CI 0.37, 0.71]). The original pooled estimate for trials comparing football versus running interventions was SMD = 0.68 (95% CI 0.06, 1.4). After correcting for SE/SD mix-ups and re-analysis, the effect was no longer statistically significant (SMD = 0.20 [95% CI - 0.10, 0.49)]). We found that 19.3% of randomised controlled trials reported SE rather than SD to describe sample variability. The relative frequency of the practice ranged from 0 to 25% across the seven journals sampled.ConclusionsWe found the SE/SD mix-up had inflated estimates for the effects of football on aerobic fitness. Meta-analysts should be vigilant to avoid miscalculating effect sizes. Authors, reviewers and editors should avoid and discourage (respectively) the practice of reporting SE as a measure of sample variability in sports medicine research.

Project description:IntroductionResponse to treatment, according to Clinical Global Impression-Improvement (CGI-I) scale, is an easily interpretable outcome in clinical trials of autism spectrum disorder (ASD). Yet, the CGI-I rating is sometimes reported as a continuous outcome, and converting it to dichotomous would allow meta-analysis to incorporate more evidence.MethodsClinical trials investigating medications for ASD and presenting both dichotomous and continuous CGI-I data were included. The number of patients with at least much improvement (CGI-I ≤ 2) were imputed from the CGI-I scale, assuming an underlying normal distribution of a latent continuous score using a primary threshold θ = 2.5 instead of θ = 2, which is the original cut-off in the CGI-I scale. The original and imputed values were used to calculate responder rates and odds ratios. The performance of the imputation method was investigated with a concordance correlation coefficient (CCC), linear regression, Bland-Altman plots, and subgroup differences of summary estimates obtained from random-effects meta-analysis.ResultsData from 27 studies, 58 arms, and 1428 participants were used. The imputation method using the primary threshold (θ = 2.5) had good performance for the responder rates (CCC = 0.93 95% confidence intervals [0.86, 0.96]; β of linear regression = 1.04 [0.95, 1.13]; bias and limits of agreements = 4.32% [-8.1%, 16.74%]; no subgroup differences χ2 = 1.24, p-value = 0.266) and odds ratios (CCC = 0.91 [0.86, 0.96]; β = 0.96 [0.78, 1.14]; bias = 0.09 [-0.87, 1.04]; χ2 = 0.02, p-value = 0.894). The imputation method had poorer performance when the secondary threshold (θ = 2) was used.DiscussionAssuming a normal distribution of the CGI-I scale, the number of responders could be imputed from the mean and standard deviation and used in meta-analysis. Due to the wide limits of agreement of the imputation method, sensitivity analysis excluding studies with imputed values should be performed.

Dataset Information

Ten circumstances and solutions for finding the sample mean and standard deviation for meta-analysis.

Publications

Ten circumstances and solutions for finding the sample mean and standard deviation for meta-analysis.

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