Earlier today, I wrote about the U.S. Food and Drug Administration’s recommendation that federal and state governments stop administering Johnson & Johnson’s COVID-19 vaccine because the agency was “reviewing data involving six reported U.S. cases of a rare and severe type of blood clot…called cerebral venous sinus thrombosis (CVST).” Here, I thought I would do a back-of-the-envelope comparison of this risk to that of another category of products on which the FDA has not placed a hold: oral contraceptives.

According to one literature review, the baseline risk of CVST among women is 3 per million per year and “the pooled odds of developing CVST in women of reproductive age taking oral contraceptives was 7.59 times the odds of developing CVST for those not taking oral contraceptives.” If so, the risk of CVST among oral contraceptives users is roughly 23 per million per year.

In a recent white paper, my colleague Jeff Singer and I explain that oral contraceptives pose such large benefits and such low risks that American College of Obstetricians and Gynecologists, the American Academy of Family Physicians, and a majority of reproductive health care providers support making them available over the counter.

Now let’s consider the data on CVST and the J&J vaccine. Since the FDA acknowledges those six incidents occurred in a pool of “more than 6.8 million doses,” that means the FDA has evidence that CVSTs have occurred in J&J vaccine recipients at a rate of about 0.9 per million recipients. If we assume half of recipients were women, the CVST rate among female recipients would be about 1.8 per million. Since the FDA approved the J&J vaccine on February 27, and those six cases all occurred before April 12, let’s then conservatively multiply by nine to arrive at an annual estimate of 16.2 CVSTs per million female J&J vaccine recipients per year. That is nearly 30 percent lower than the risk of CVST from taking a product that many physicians and consumers think should be available over the counter.

So why is the FDA putting a hold on the J&J vaccine on this basis?