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I have an medical test which has been repeatedly administered to patients over time that I would like to analyze.

The tests results are ordinal (Neg, Scanty, 1, 2, and 3).

The testing schedule was irregular - daily for the first two weeks, weekly for the next two weeks and then monthly for a total of six months.

I have data from 25 patients.

An example would look like this: enter image description here

I have used Mann-Kendall & Theil-Sen Slopes to analyze non-parametric trend data. This seems somewhat correct because they are rank tests.

Is this appropriate with ordinal data?

Additionally, I would like to see if some of the clinical data regarding the patients is associated with their outcome and I am not at all confident that either of those tests will assist me in that.

If not, are there suggestions for alternative trend detection?

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    $\begingroup$ If you want to stay close to regression techniques (but still want to do something which is difficult IMO) you could look at random effects ordinal regression model such as in this paper: ncbi.nlm.nih.gov/pubmed/7787006. I cannot vouch for consistency, but the longitudinal version of their models seems closely related to your test. $\endgroup$ – IWS Oct 31 '17 at 15:42
  • $\begingroup$ ps. In R such models can for example be fit using the clmm function from the 'ordinal' package $\endgroup$ – IWS Oct 31 '17 at 15:46
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The first and most critical thing to do is provide a visual inspection of the trend; plotting time on the X-axis and the ordinal response on the Y-axis achieves this.

The limitations of using the non-parametric tests you mention is that they do not summarize the strength or direction of trend, they require uncorrelated data, and they may be inefficient.

You may instead consider summarizing a possibly non-linear (rather than non-parametric) trend. I presume there is some form of an S-shaped trend where, over time, participants tend toward a top-response of 3 or the bottom response of 'negative'.

There is nothing wrong with using linear least squares to summarize the first order trend of that S-shaped curve. This approach is frequently used with ordinal data. If the tendency is toward a higher response, the least squares slope will be positive. Generalized estimating equations (GEEs) will allow you to both account for repeated measures within participant as well as the the fact that a linear regression may, over certain time intervals, predict responses beyond the observable range. That is of no concern, since a non-parametric test predicts nothing at all.

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