How to impute study-specific standard deviations in meta-analyses of skewed continuous endpoints?

Figure 2 Value of each standardized estimate, θstand_ijk, for each number of dataset included in the corresponding meta-analysis simulated. A: Exponential (mean = 5 and lambda = 0.2 for the treatment group; mean = 7 and lambda = 0.14 for the control group); B: Bimodal (50% Normal distribution (with mean = 5 and SD = 2) and 50% Standardized Normal for the treatment group; 50% Normal distribution (with mean = 7 and SD = 2) and 50% standardized normal for the control group); C and D: Real distribution of intensive care unit stay and hospital stay of an Italian cardiology dataset with 7471 patients. The X-axis represents the number of studies (datasets) included in the meta-analysis. For each approximation method (blue line for the conservative estimate of SD, green line for the less conservative estimate of SD, pink line for the mean estimate of SD, and red line for the interquartile range), the Y-axis reports the difference between the standardized estimate and the reference (black line). IQR: Interquartile range.