Journal Article: Meta-analysis of Difference in Medians

[R_cubed]

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.

Hodges–Lehmann estimates in deformation analyses

Related:

Nonparametric Effect Size estimation, Likelihood Methods, and Meta Analysis

Posted as a new topic at Prof. Harrell’s request. Study heterogeneity is a big issue in research synthesis, and is related to various issues in robust statistics. I have an intuition that those involved in research synthesis might be better served by using nonparametric estimates of effect (Hodges-Lehmann estimates/generalized odds ratios, etc), instead of necessarily relying upon standardized mean differences reported by primary researchers. But I am also persuaded by the work of Richard Roy…

[f2harrell]

Except for the case where there are heavy ties in the data, the Hodges-Lehmann estimator is a wonderful estimator and is very much underused. I’m glad you are bringing this up. H-L is the median of all pairwise differences between two groups in raw data values. It has high efficiency (unlike the sample median).