Generalized Box-Cox method to estimate sample mean and standard deviation for Meta-analysis

Meta-analysis is the aggregation of data from multiple studies to find patterns across a broad range relating to a particular subject. It is becoming increasingly useful to apply meta-analysis to summarize these studies being done across various fields. In meta-analysis, it is common to use the mean and standard deviation from each study to compare for analysis. While many studies reported mean and standard deviation for their summary statistics, some report other values including the minimum, maximum, median, and first and third quantiles. Often, the quantiles and median are reported when the data is skewed and does not follow a normal distribution. In order to correctly summarize the data and draw conclusions from multiple studies, it is necessary to estimate the mean and standard deviation from each study, considering variation and skewness within each study. In past literature, methods have been proposed to estimate the mean and standard deviation, but do not consider negative values. Data that include negative values are common and would increase the accuracy and impact of the me-ta-analysis. We propose a method that implements a generalized Box-Cox transformation to estimate the mean and standard deviation accounting for such negative values while maintaining similar accuracy.