Hello Virginia De Martin Topranin. Can you share the 3x3 table with us?

One approach to consider is the adaptation of the Mann-Whitney test Alan Agresti describes in this article:

• http://users.stat.ufl.edu/~aa/articles/agresti_1983.pdf

HTH.

In my opinion, make the comparisons in pairs using the McNemar-Bowker test and use Bonfrone correction for meaning.

In my opinion, you could use the Friedman aligned ranks test. In attachment a small example for your design.

-1 = negative

0 = netral

1 = postive

Thanks for your suggestions. I provided the table in the question, and I have a few doubts:

- does it make sense to perform the Bonferroni correction when the result from the McNemar-Bowker test is NaN?

- if using Friedman aligned ranks test, how do you correct for ties? Moreover, isn't one of the assumptions that the dependent variable is ordinal or continuous? It is not the case as we have the three conditions "Negative" "Positive" or "Neutral" as outcome.

Hello Virginia De Martin Topranin. Having had time to think about it, and having seen your 3x3 table, I now see that your question is structurally identical to one I posted to StataList in May 2020:

https://www.statalist.org/forums/forum/general-stata-discussion/general/1552729-3-level-ordinal-outcome-measured-at-3-time-points-repeated-measures

I ended up liking the Somers' D approach suggested by Mike Lacy in post #8. I am not a useR, so do not know if there is an implementation of Somers' D that has the wstrata(id) option that Mike showed:

somersd time y, wstrata(id) // stratify by patient id

HTH.

Thanks again.

It's worth mentioning that we also considered using generalized linear mixed model (R “lme4” package), treating time points as fixed effect and participants as random effect. However, this method is commonly used for dichotomous dependent variables, do you know if it exists an extension for more than two conditions in the dependent variable and whether this could be a valid option?

Hello Virginia De Martin Topranin. I'll have to leave your last question about "lme4" to any useRs who are following this thread.

Meanwhile, I dug up a Stata DO file I wrote in the wake of that Statalist discussion I pointed you to. The attached text file has some code and output showing how I analyzed 3-level ordinal ratings over three time points for n=17 patients. The -somersd- command is a user-written command contributed by Roger Newson. The reference section near the bottom of the output lists 3 articles by Newson that you may find helpful if you decide to go this route.

Cheers,

Bruce

Hello , Virginia De Martin Topranin

I guess that time is ordered factor with 3 levels ( before-during-after).

possible answers is exactly ordered factor with 3 levels.

R package hmmm (hierarchical multinomial marginal (HMM) models for categorical variables) may be usefull.

The McNemar-Bowker test seems appropriate:

See Salvatore S. Mangiafico's Handbook

https://rcompanion.org/handbook/H_05.html

McNemar-Bowker Test of Symmetry intend for paired measurements.

so this Virginia De Martin Topranin case need three copmrarison

before-during

during-after

before-after

This test analyzes the discordance pairs.

Table1.webarchive seems to be wrong for McNemar-Bowker Test of Symmetry.

In attachment an example with many zero values, inspired by the R companion book.

Thank you once again for all your valuable feedback! :)

It seems like McNemar-Bowker test is the most appropriate.

The Somer's D approach is interesting, but I am not sure it applies to our case. Time points in our design are indeed not necessarily ordered: they refer to different phases of the menstrual cycle ("during menstruation", "after menstruation", "before menstruation) which are supposed to be linked to different hormonal concentrations. We are interested in understanding the difference between the phases rather than how ratings are changing over time.