When U.S. officials paused administration of the Johnson & Johnson vaccine after six cases of a rare clotting disorder, one fatal, among the 6.9 million people who had received the vaccine, many critics noted that the chance of a serious ailment was so rare as to be negligible ¡ª less frequent than being struck by lightning.

But that roughly one-in-a-million rate is far from certain. Doctors may ultimately find the vaccine is not responsible for the ailment. However, if the two are linked, it¡¯s also possible that the chance of an adverse effect will be higher, even if it remains low.

¡°Numbers seem quite solid, like, ¡®Oh, it¡¯s 10,¡¯¡± said Caitlin Rivers, an assistant professor at Johns Hopkins University, who studies infectious disease. She said epidemiologists deal with similar matters of uncertainty at the beginning of disease outbreaks. ¡°But they¡¯re estimates, and they will need to be refined, and they may need to be refined a lot, especially since they are small numbers.¡±