Dataset Information

Estimating the mean and variance from the median, range, and the size of a sample.

ABSTRACT:

Background

Usually the researchers performing meta-analysis of continuous outcomes from clinical trials need their mean value and the variance (or standard deviation) in order to pool data. However, sometimes the published reports of clinical trials only report the median, range and the size of the trial.

Methods

In this article we use simple and elementary inequalities and approximations in order to estimate the mean and the variance for such trials. Our estimation is distribution-free, i.e., it makes no assumption on the distribution of the underlying data.

Results

We found two simple formulas that estimate the mean using the values of the median (m), low and high end of the range (a and b, respectively), and n (the sample size). Using simulations, we show that median can be used to estimate mean when the sample size is larger than 25. For smaller samples our new formula, devised in this paper, should be used. We also estimated the variance of an unknown sample using the median, low and high end of the range, and the sample size. Our estimate is performing as the best estimate in our simulations for very small samples (n < or = 15). For moderately sized samples (15 < n < or = 70), our simulations show that the formula range/4 is the best estimator for the standard deviation (variance). For large samples (n > 70), the formula range/6 gives the best estimator for the standard deviation (variance). We also include an illustrative example of the potential value of our method using reports from the Cochrane review on the role of erythropoietin in anemia due to malignancy.

Conclusion

Using these formulas, we hope to help meta-analysts use clinical trials in their analysis even when not all of the information is available and/or reported.

SUBMITTER: Hozo SP

PROVIDER: S-EPMC1097734 | biostudies-literature | 2005 Apr

REPOSITORIES: biostudies-literature

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Publications

Estimating the mean and variance from the median, range, and the size of a sample.

Hozo Stela Pudar SP Djulbegovic Benjamin B Hozo Iztok I

BMC medical research methodology 20050420

<h4>Background</h4>Usually the researchers performing meta-analysis of continuous outcomes from clinical trials need their mean value and the variance (or standard deviation) in order to pool data. However, sometimes the published reports of clinical trials only report the median, range and the size of the trial.<h4>Methods</h4>In this article we use simple and elementary inequalities and approximations in order to estimate the mean and the variance for such trials. Our estimation is distributio ...[more]

PMID: 15840177

Similar Datasets

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:Introduction: The multi-copied genes coding for the human 18, 5.8, and 28S ribosomal RNA (rRNA) are located in five pairs of acrocentric chromosomes forming so-called rDNA. Human genome contains unmethylated, slightly methylated, and hypermethylated copies of rDNA. The major research question: What is the rDNA copy number (rDNA CN) and the content of hypermethylated rDNA as a function of age? Materials and Methods: We determined the rDNA CN in the blood leukocyte genomes of 651 subjects aged 17 to 91 years. The subjects were divided into two subgroups: "elderly" group (E-group, N = 126) - individuals over 72 years of age (the age of the population's mean lifetime for Russia) and "non-elderly" group (NE-group, N = 525). The hypermethylated rDNA content was determined in the 40 DNA samples from the each group. The change in rDNA during replicative cell senescence was studied for the cultured skin fibroblast lines of five subjects from NE-group. Non-radioactive quantitative dot- and blot-hybridization techniques (NQH) were applied. Results: In the subjects from the E-group the mean rDNA CN was the same, but the range of variation was narrower compared to the NE-group: a range of 272 to 541 copies in E-group vs. 200 to 711 copies in NE-group. Unlike NE-group, the E-group genomes contained almost no hypermethylated rDNA copies. A case study of cultured skin fibroblasts from five subjects has shown that during the replicative senescence the genome lost hypermethylated rDNA copies only. Conclusion: In the elderly group, the mean rDNA CN is the same, but the range of variation is narrower compared with the younger subjects. During replicative senescence, the human fibroblast genome loses hypermethylated copies of rDNA. Two hypotheses were put forward: (1) individuals with either very low or very high rDNA content in their genomes do not survive till the age of the population's mean lifetime; and/or (2) during the aging, the human genome eliminates hypermethylated copies of rDNA.

Dataset Information

Estimating the mean and variance from the median, range, and the size of a sample.

Background

Methods

Results

Conclusion

Publications

Estimating the mean and variance from the median, range, and the size of a sample.

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