it has become convention to analyse components separately, im pretty sure EMA guidelines demand it, but see eg chapter “Composite endpoints in clinical trials” in Methods and Applications of Statistics in Clinical Trials.
also, from experience id anticipate that the clinicians will became very interested in any “result” and it will incite secondary analyses in the hope of understanding it precisely, and when this fails it will invite discussion and promote sceptism
regarding why we would analyse components separately, you made a point in the quality-of-remdesivir-trials thread: “we know from the international survey of thousands of patients that they place great weight on shortness of breath”
i appreciate this point, however i think eg Sun et al. showed in their paper that dyspnea can dominate a composite: Evaluating Treatment Efficacy by Multiple End Points in Phase II Acute Heart Failure Clinical Trials
you can see in table 4 that VAS AUC is superior to the clinical composite on power. And that is fine, i would just want it made explicit what is driving the result, rather than being hidden in the mechanism of the calculation for the composite
I tried to show, by defining “Influence”, that patient reported outcomes can drive the difference observed on the composite measure, and how this Influence is sensitive to the arbitray cut-offs used: Examining the Influence of Component Outcomes on the Composite at the Design Stage
im not sure to what extent any of this is relevant for the covid ordinal outcome, but one common issue with these rankings is what to do at the lowest rank. Some have suggested using eg a biomarker to discriminate between these indiviuals rather than leave some large % of the sample with a tied rank (when clinical events are low). But then the biomarker overwhlems the composite (i tried to illustrate that here: cjc, see global rank in fig2)
i just dont think many will be satsified with a conclusion of the kind: the intervention is superior on some conglomerate of outcomes, it’s inviting scepticism and people like to practice scepticism