Food and Drug Administration Commissioner Steven Hahn, having been battered around for his egregiously inaccurate endorsement Sunday of a purported COVID-19 treatment pushed by President Donald Trump, walked that endorsement back Monday and Tuesday.

It isn’t enough. Hahn has damaged his credibility, possibly beyond repair, and taken the credibility of the FDA down with him — at a crucial moment when the agency’s trustworthiness may be more important than at any time in its 114-year history.

He has not behaved like the head of an independent, science-based arm of the federal government, and for that he has to go.

“I have been criticized for remarks I made Sunday night about the benefits of convalescent plasma,” Hahn tweeted Monday, at the start of an apology round that also took him to “CBS This Morning.” “The criticism is entirely justified,” he tweeted. “What I should have said better is that the data show a relative risk reduction, not an absolute risk reduction.”

On CBS, he said, “I could have done a better job and should have done a better job at that press conference explaining what the data show.”

Let’s take a closer look at what this is all about, and why Hahn’s most recent statements are insufficient.

The issue involved convalescent plasma, which is blood fluid taken from patients who have recovered from COVID-19. It’s then transfused into new COVID-19 patients, with the aim of allowing antibodies the original patients developed during their illness to fight the infection in the new patients.

Sunday’s White House press conference was called to announce that the FDA had issued an “emergency use authorization” for convalescent plasma in COVID-19 cases. This move isn’t tantamount to FDA clinical approval and has little practical effect, since researchers already were using the substance in clinical trials.

But it does raise the possibility that the general public will think that the FDA has concluded that it works for COVID-19 patients, for which there is still no evidence.

Convalescent plasma has been used for about 100 years as treatment for other diseases. It has never been a “miracle” drug or a “breakthrough.” as Trump has described it. Though researchers have seen some evidence that it may help seriously ill COVID-19 patients, medical experts strongly doubt that it will be a “breakthrough” drug now.

That brings us to Hahn’s original error.

At a White House press conference Sunday, Hahn stated that for patients treated with convalescent plasma there was a 35% improvement in survival, which he called “a significant clinical benefit.” He tried to explain what he meant by adding that, of “100 people who are sick with COVID-19, 35 would have been saved because of the administration of plasma.”

None of that is true. The Mayo Clinic study on which his remarks were based says nothing of the kind. It says that preliminary results from its trial show that patients given convalescent plasma with a high concentration of antibodies and receive it within three days of diagnosis with COVID-19 have a 35% better survival rate than those given plasma with a low concentration of antibodies and who receive it four days or more after diagnosis.

The best one could say is that five out of 100 people in the trial — but really only three out of 100 — would have better survival rates. Even that conclusion is dubious, however, because the Mayo study doesn’t compare the patients who received plasma to those who didn’t receive it at all — it merely compares those who receive different versions of the plasma and on different schedules to each other.

From that, it’s impossible to tell what benefit convalescent plasma has on COVID-19 patients, if any.

Hahn’s statement instantly drew a pushback from medical experts. Jonathan Reiner of George Washington University medical school called it “shockingly wrong.”

Hahn’s original statement was so profoundly wrong that his walkback Monday and Tuesday can’t help but increase public confusion.

The importance of the FDA’s credibility at this moment can’t be overstated. At some point within the next year, the agency will be called on to validate the safety and efficacy of any vaccines for COVID-19 that emerge from clinical testing.

In an era in which conspiracy theories animate resistance even to vaccines of proven safety and efficacy, doubts about a new vaccine against a novel disease will threaten public health if they prompt people to refuse immunization. Hahn is making it impossible to trust the FDA’s judgment on COVID-19 vaccines.

Michael Hiltzik is a columnist for the Los Angeles Times.