The truth is that all "public health" is driven by statistics. Seven deaths is a tragedy but 7/n of shots given is a statistic. The people determining whether these vaccines are safe won't stop until that ratio is "proven" by a statistical procedure to be more than could be expected by chance. The bad news is that will take a big sample. The good news is that the bigger the sample, the smaller the difference necessary to show "statistical significance," which should not be confused with substantive significance.