An Eli Lilly drug for rheumatoid arthritis carries a warning on its label saying patients with infections should not take it because it can make infections worse. Yet the National Institutes of Health is about to test it in people hospitalized with coronavirus infections.

The study, whose innovative design is meant to find out — fast — what works, began at the end of February with the antiviral drug remdesivir made by Gilead Sciences. Four hundred patients have been treated either with remdesivir or a placebo. The results are now being analyzed and will be known within a few weeks.

Then the study will move on to baricitinib, made by Eli Lilly and Company, the company said.

Jennifer Routh, a spokeswoman at the National Institute of Allergy and Infectious Diseases, confirmed that the drug would now be tested in the federal trial but said the institute could offer no further comment.

Dan Skovronsky, chief scientific officer at Lilly, explained how and why baricitinib was chosen.

In February, when the new coronavirus was emerging as a pandemic threat, a company in the United Kingdom called Benevolent AI began using its artificial intelligence system to look for approved drugs that could possibly help people with coronavirus infections. It pointed toward baricitinib precisely because it suppresses the immune system. That, the company suggested, might allow it to quell a cytokine storm, a disastrous immune system response that kills patients.