Estimating the sample mean and standard deviation from order statistics and sample size in meta-analysis

In recent years, a growing number of researchers have attempted to overcome the constraints of size and scope in different medical studies to find out the overall treatment effects. As a widespread technique to combine results of multiple studies, commonly used meta-analytic approaches for continuous outcomes demand sample means and standard deviations of primary studies, which are absent sometimes, especially when the outcome is skewed. Instead, the median, the extrema, and/or the quartiles are reported. One feasible solution is to convert the preceding order statistics to demanded statistics to keep effect measures consistent. In this article, we propose new methods based on maximum likelihood estimation for known distributions with unknown parameters. For unknown underlying distributions, the Box-Cox transformation is applied to the reported order statistics so that the techniques for normal distribution can be utilized. Two approaches for estimating the power parameter in Box-Cox transformation are provided. Both simulation studies and real data analysis indicate that in most cases, the proposed methods outperform the existing methods in estimation accuracy.