A recent pre-print has studied this by measuring 86 accredited diagnostic parameters and plasma proteomes at 687 sampling points, in a cohort of 139 patients during hospitalisation.
We identified 26 protein biomarkers and 14 routine diagnostic markers
(Fig. 4a, Supp. Fig. SF20) that correlate with the time between the
first sampling point and release from inpatient care. The proteomic
signature associated with longer duration of inpatient treatment and
hence more severe COVID-19 progression includes upregulated components
of the complement system (C1QA, C1QB, C1QC) and reflects altered
coagulation (KLKB1, PLG, SERPIND1) and inflammation (CD14, B2M,
SERPINA3, CRP, GPLD1, PGLYRP2, AHSG).
They used a learning classifier to then predict survival in critically ill patients:
In a last step, we established a machine learning model based on
parenclitic networks52,53 (Methods) to predict survival in critically
ill patients (WHO grade 7, n=49) from the proteome of the earliest
single time point sample at WHO grade 7 for a particular patient. On
the test subjects (the data of whom were excluded when training the
machine learning model), high prediction accuracy was achieved, with
AUC = 0.81 for the receiver-operating characteristic (ROC) curve. Of
note, the model correctly predicted survival or adverse outcome weeks
in advance (median time from prediction to outcome 39 days,
interquartile range 16 - 64 days).
The 'predictive power' can be captured (not in a perfect way) by the AUC value - a value of 0 has the worst power to separate patients and 1 has perfect power, so 0.81 is pretty good overall. I haven't read the paper fully, but from a brief scan it looks as though their methodology is at least reasonably sound.