Given the (I think appropriate) emphasis on ordinal COVID-19 outcomes, I’m trying to figure out how to work through the usual regression modelling strategies for prediction model building and validation with ordinal outcomes. In this case, I’m looking at a 5-point ordinal outcome ranging from no COVID infection all the way up to COVID-associated death.
How to estimate the discrimination performance of a model predicting an ordinal outcome.
…I read f2harrell’s Ch.13 in Regression Modelling Strategies and it looks like can use Somers D and C-statistic as usual.
How to estimate the value of adding a variable (e.g. a biomarker) to a existing model?
…I like likelihood ratio tests to establish statistical significance and I think I can use that here, but wonder how best to quantify the added value using net benefit ala Andrew Vickers. Perhaps will have to do by calculating probability of outcome at each level and above. Maybe will just have to use (the less attractive to me but of interest to many readers) change in AUC.
Sample size considerations.
…I have been using lately the excellent pmsampsize package from Richard Riley’s group, but this only informs binary, time to event, and continuous outcomes. So far I have been assuming that sample size requirements are LOWER when fitting models for ordinal outcomes than for binary outcomes. Is this correct? I will try to use penalized maximum likelihood estimation to lower the effective degrees of freedom, but the (forward continuous ratio) model will likely need extensions to work around the proportional odds assumption.
Any guidance would be most welcome.