Stratified Wilcoxon Mann Whitney Generalised Odds Ratios for Repeated Measures Data

[James Lebowski]

Dear Statalist,

Hope you're all well.

I have a dataset with repeated measures of the modified Rankin Scale (mRS), which is an ordinal measure (0 = independence to 6 = death) and I am attempting to find associations between baseline demographic variables (e.g. sex, age, comorbidities) with the mRS at Day 365.

Using the repeated measures of mRS (Day 1, 28, 90, 180, 365), I am attempting to show that there is a benefit to using the additional data, as opposed to just using Day 365 data.
- My current approach was to use meologit in STATA using Day 365 data only, and then comparing to meologit using Day 1, 28, 90, 180, 365.
- I then compared odds ratios and the McKelvey & Zavoinas R2.

However, the journal I have submitted to has rejected this statistical approach on the grounds that it violates the proportional odds assumption and that logistical odds was not the right approach.
- previous attempts at using partial proportional odds and generalised logistic regression did not work due to the number of parameters and struggle to converge / production of negative probabilties.

Searching for alternatives, I have reviewed the literature and come across the Wilcoxon Mann Whitney Generalised Odds Ratios
- Churilov L, Arnup S, Johns H, Leung T, Roberts S, Campbell BC, Davis SM, Donnan GA. An improved method for simple, assumption-free ordinal analysis of the modified Rankin Scale using generalized odds ratios. Int J Stroke. 2014 Dec;9(8):999-1005. doi: 10.1111/ijs.12364. Epub 2014 Sep 4. PMID: 25196780.

I think that this may hold promise, however I will have to stratify the odds ratios in STATA (I think using somersd, as ranksum cannot support this).

However I am unsure how to use the Wilcoxon Mann Whitney Generalised Odds Ratios in a repeated measures analysis.
- Would I stratify by time and adjust for all variables?
- It seems as though that the vanElten method can only adjust for 1 additional strata. I am unsure whether or not somersd can adjust for multiple strata.

Would be very grateful for any insights into alternative approaches for finding associations using repeated measures of ordinal data; and if the generalised odds ratio approach would be suitable.

Many thanks.

[Joseph Coveney]

What's your research question? It would seem as if to find associations between baseline demographic variables (e.g., sex, age, comorbidities) with the mRS score at Day 365 would have been done before.

If you've got an experimental treatment condition that you're determining the effectiveness of against a control treatment condition (e.g., standard of care) and you want to adjust for multiple patient characteristics (sex, age etc.), then you'll need to consider fitting a regression model, repeated measures or no. Does the method of Churilov et al. accommodate covariates?

The thing about stroke is that the higher mRS scores (four and above) tend sadly to be one-way streets (certainly a score of six is), and so you might want to dichotomize your scores into something like three or less versus four or greater, and then use conventional logistic regression methods (-melogit-, -xtlogit-). Such a dichotomization approach to mRS scores has been done before in clinical studies of stroke interventions, if you need to defend it with the referees. An added benefit with logistic regression: they're not going to be able to harp on proportional odds and whatnot.

Depending upon your study's eligibility criteria, you might have sufficient mortality to fit a time-to-event regression model, if that will clarify the influences of patient characteristics on your treatment's effectiveness.