Source: McGrath, S, Sohn, H, Steele, R, Benedetti, A. Meta‐analysis of the difference of medians. Biometrical Journal . 2020; 62: 69– 98. https://doi.org/10.1002/bimj.201900036
I thought this was a good survey on the lag between the use of alternative measures of central tendency in primary studies, vs. the synthesis of these reports in meta-analysis.
I am still curious as to why there are very few mentions in the literature of the Hodges-Lehmann estimator as a meta-analytic tool. If I were concerned about the validity of a mean effect, why not compute the median of the pair-wise mean estimates from the primary studies? Or in this case, the HL estimate of the median effect?
Dr. Harrell has pointed out in numerous venues that this has natural connections to the Wilcoxon-Mann-Whitney test, the proportional odds model, and is a natural and robust measure of effect regardless of the distribution. It is simultaneously more robust than the mean, yet more efficient than the sample median.
Addendum: A weighted version of the HL estimate would be attractive from a theoretical POV. This paper explores the possibility of a weighted HL estimate based on measurement precision.