Minimum distance estimation of mean and standard deviation from reported quantiles

Meta-analysis is a cornerstone of evidence synthesis, yet challenges arise when studies report heterogeneous summary statistics, such as means and standard deviations (SDs) versus medians, interquartile ranges (IQRs), or other percentiles. Excluding studies that report only medians and IQRs can introduce bias and reduce precision, particularly when outcomes are skewed, which is common in clinical research. Although several methods exist to estimate means and SDs from alternative summaries, many rely on strong normality assumptions, exhibit computational burden, or fail to adequately account for the precision of reported quantiles (e.g., extreme values versus medians). To address these limitations, we propose two flexible weighted estimators for estimating the mean and SD from reported quantiles. The methods leverage inverse-variance and inverse-variance-covariance weighting, respectively, to enhance both accuracy and precision. Additionally, our methods are flexible enough to accommodate any set of reported quantiles and various underlying distributions, and they can be readily implemented using standard statistical software. Simulation studies demonstrate that the weighted estimators provide nearly unbiased estimates of the mean and SD with high precision in most cases, especially for large sample sizes. In a real-world meta-analysis, the estimates obtained using the proposed estimators closely aligned with those derived from true sample statistics. These approaches are particularly valuable for skewed outcomes and offer a practical and user-friendly solution for researchers seeking to integrate heterogeneous data while improving accuracy and precision.