The RECOVERY trial in Oxford, with 5795 patients who were randomly allocated to receive convalescent plasma treatment and 5763 who received usual care alone, found that there was no statistically significant difference for 28-day mortality (24% for both groups, p-0.93) or the proportion of patients discharged from hospital within 28 days (66% CP vs 67% control, p=0.50) for the two groups. Additonally for patients without mechanical ventilation, there was no stastically significant difference in the intubation rate (28% CP vs 29% control, p=0.79).

https://doi.org/10.1101/2021.03.09.21252736

The trial showed convalescent plasma therapy had no benefit to patients with COVID-19. As a result the UK's health service has stopped collecting convalescent plasma from patients who had recovered from COVID-19.

https://www.bbc.co.uk/news/health-55681051

Additonally the NIH have halted a convalescent plasma trial for COVID-19 patients with mild symptoms stating that the "study shows that the treatment is safe, but provides no signifcant benefit in this group".

https://www.nih.gov/news-events/news-releases/nih-halts-trial-covid-19-convalescent-plasma-emergency-department-patients-mild-symptoms

Kominers, S. D., Pathak, P. A., Sönmez, T., & Ünver, M. U. (2020). Paying It Backward and Forward: Expanding Access to Convalescent Plasma Therapy Through Market Design (Working Paper No. 27143; Working Paper Series). National Bureau of Economic Research. https://doi.org/10.3386/w27143