Estimating the mean and variance from the median, range, and the size of a sample.
Estimating the mean and variance from the median, range, and the size of a sample.
复制标题
DOI：
10.1186/1471-2288-5-13
复制
发表时间：
2005-04-20
影响因子：
4
通讯作者：
Hozo I
中科院分区：
文献类型：
--
作者：
Hozo SP;Djulbegovic B;Hozo I
通常，对临床试验的连续结果进行荟萃分析的研究人员需要它们的平均值和方差(或标准差)，以便汇集数据。然而，有时已发表的临床试验报告只报告了试验的中位数、范围和规模。在这篇文章中，我们使用简单和初等的不等式和近似来估计这种试验的均值和方差。我们的估计是无分布的，也就是说，它不假设基础数据的分布。我们发现了两个简单的公式，它们使用中位数(M)、范围的低端和高端(分别为a和b)以及n(样本大小)的值来估计平均值。通过模拟，我们发现当样本容量大于25时，中位数可以用来估计均值。对于较小的样品，应使用本文设计的新公式。我们还使用范围的中值、低端和高端以及样本大小估计了未知样本的方差。在我们的模拟中，对于非常小的样本(n≤15)，我们的估计是最佳估计。对于中等大小的样本(15<；n≤70)，我们的模拟表明公式Range/4是标准差(方差)的最佳估计器。对于大样本(n>；70)，公式Range/6给出标准差(方差)的最佳估计值。我们还使用Cochrane综述中关于促红细胞生成素在恶性肿瘤引起的贫血中的作用的报告，列举了我们的方法的潜在价值的说明性例子。使用这些公式，我们希望帮助元分析师在他们的分析中使用临床试验，即使不是所有的信息都可用和/或报告。
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. 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. 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 ≤ 15). For moderately sized samples (15 <n ≤ 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. 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.