At NewYork-Presbyterian Hospital, the chief of surgery, Dr. Craig R. Smith, wrote in a memo that was released by the hospital, “We are hurtling into weeks predicted to be our worst.” But he also offered a small dose of optimism. “Scanning the daily statistics for the NYP system I can squint, angulate the page, and see the hint of a suggestion that the new-case curve has flattened slightly over the past few days.”

Dr. Jim Malatras, the president of SUNY Empire State College who previously served in Mr. Cuomo’s administration as director of state operations, appeared with the governor on Monday and said New York officials had been looking at projections that listed a possible peak to occur anywhere within 7 to 30 days.

“It looks like we’re at toward the earlier side of that time frame based on the current projections and modeling that we’ve been looking at,” Dr. Malatras said.

That seems to suggest the worst is almost behind us, right?

There are reasons to treat the data with caution.

The number of hospitalizations, for instance, depends not only on the number of new arrivals but also on hospital admission standards. As hospitals have teetered on the brink of being overwhelmed, they have sent home people whom they would have admitted just a few weeks earlier, several New York doctors said in interviews.

So even if the number of hospitalizations appears to have plateaued, that could be because the number of sick people turning up has lessened, or it may have to do with changing hospital admissions standards — or both.

And it’s difficult to know what to make of the slight dip in deaths in recent days. There are indications that deaths related to the coronavirus are being undercounted — especially those who die of the illness at home.

Patients can die of the illness several weeks after they were infected — some after a lengthy period of time in a medically induced coma while a mechanical ventilator breathes for them.