The death toll from coronavirus in New York City jumped by nearly 4,000 on Tuesday, to a cumulative total of more than 10,000. Health officials revised previous numbers to account for presumed cases: individuals who had died with symptoms of the virus but not tested positive for it. The revisions highlight the difficulty of interpreting official health figures in the fog of the pandemic. Nations and localities have some discretion in determining cause of death, which may cause discrepancies in the data.

Independent of New York City’s revisions, new cases and deaths also increased nationally yesterday, with an especially large spike in New Jersey. The next week or so is projected to take a large toll as the U.S. approaches the peak of its domestic outbreak.

Testing increased on Tuesday, with more than 145,000 tests administered. However, it remains considerably below last week’s level as states grapple with shortages of test tubes and swabs. Another factor causing that decrease is the CDC’s testing criteria, which call for hospitalized patients, health-care workers, and vulnerable populations to be prioritized.

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