Welcome to datamethods Rob.
As discussed here framing MCID in terms of change in a patient’s status is problematic, and as discussed here change from baseline is problematic in general. When using ordinal models, we need the response variable to be ordinal, and a difference between two ordinal variables (baseline and follow-up) is not necessarily ordinal. For example a change from 1 to 2 on an ordinal scale that runs from 1-10 may not be comparable to a change from 8 to 9.
One other general problem is which model is likely to fit the correlation structure of your data. As argued here, it is not necessarily natural to think of random effects to handle within-person correlation. Random intercepts induces a compound symmetric correlation structure, e.g., it assumes that the within-person correlation in responses measured at 2 months and 3 months is the same as the correlation between 2 and 24 months. This is very unlikely to fit the data. Ordinal Markov longitudinal models are excellent choices for handling the more likely-to-fit serial correlations we see in practice. See this and this.
To get at your question of how to use an ordinal model to get estimates on the original scale, see one of the replies posted earlier on this page where I talk about estimating the mean or differences in means. To estimate quantiles instead (which make a strong assumption that Y is continuous, i.e., has few ties in the data) use the Quantile function instead of the Mean function. The contrast function (rms::contrast.rms) can come into play here. If doing Bayesian ordinal modeling with rmsb::blrm it is easier to deal with uncertainty intervals of complex nonlinear transformations of the original ordinal model parameters (on the log-odds scale).
For simple examples of using ordinal models to estimate means and quantiles see this.
On your question about nonlinear baseline covariate effects, we try to think of these as general effects that have the same shape over time, i.e., hope for no covariate by time interaction (though that can be extended, if the sample size allows). So having for example a restricted cubic spline function of baseline with 4 knots should pose no problem.
It’s good to recall the reasons for going to this trouble.
- The effect of the baseline measurement of Y is frequently nonlinear when predicting follow-up Y as exempified here.
- The baseline variable is so dominating in predictive value that underfitting it will lose efficiency.