Source-linked AI summary
Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range
Xiang Wan, Wenqian Wang, Jiming Liu, Tiejun Tong
TL;DR
Meta-analyses require means and standard deviations, but clinical trials may report only medians, ranges, and quartiles. This paper develops sample-size-aware estimators across reporting scenarios and finds that the proposed methods improve existing approaches in simulations, while recommending quartile-based reporting when possible.
Problem
Clinical trials may report medians, ranges, and quartiles instead of the means and standard deviations required for pooling in meta-analysis.
Method
The paper develops sample-size-aware estimators of means and standard deviations for scenarios using medians, ranges, and interquartile ranges.
Results
Simulations show that the proposed standard-deviation estimator is nearly unbiased and usually has relative error below 10%, even for highly skewed log-normal data.
Takeaways & Limitations
The authors recommend reporting the median, first and third quartiles, and sample size when estimating means and standard deviations for meta-analysis.
Takeaways & Limitations
When distributions are very asymmetric, estimated means and standard deviations may not adequately represent location and dispersion for meta-analysis.
Abstract
from arXiv · showhide
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.