I agree but the counterargument from their side is that these PRO scores are sums of ordinal scales that can be treated as interval.
This is a common assumption in psychometrics, but I’ve never been able to find any rigorous mathematical argument in favor of it.
On the contrary, much like the literature on “significance” testing vs. p values as surprise measures, there is a debate within social science on whether it is permissible to treat ordinal data as interval.
Representational measurement theory would advise analysis that takes into account only the order properties when spacing cannot be verified as equal at all points of the scale.
Joel Mitchell (a mathematical psychologist) as written numerous papers on this issue and considers psychometrics a “pathological science” because of it.
Michell J. Normal Science, Pathological Science and Psychometrics. Theory & Psychology. 2000;10(5):639-667. doi:10.1177/0959354300105004
The consequences of treating these ordinal scales as interval has been explored in this paper:
After reading this, I’ve come to the unfortunate conclusion that parametric analysis of PRO measures at the individual study level makes any synthesis or meta-analysis (without access to individual data) unreliable.
If researchers would simply use ordinal methods at the individual study level, then meta-analysis could be a useful tool. The methods recommended by @f2harrell seem correct if the goal is to learn at both the individual level, and to aggregate studies via meta-analysis.
Of note, the authors from the paper I mentioned before cite this another article, where they describe this concept:
“The proposed Wilcoxon-Mann-Whitney generalised odds ratio (WMW GenOR) follows the same logic as Agresti’s GenOR but does not ignore the ties; tied observations are split evenly between better and worse outcomes”
You can easily convert the regular PO model odds ratio to the concordance probability (that counts ties as 1/2) as detailed here. I hope that someone can figure out how that relates to GenOR or Agresti’s.