The point of that napkin math is not to get an exact prediction, it's to get a order-of-magnitude estimate to see if this study is different from any other of the large amount of "promising drug cures X" articles that never actually turn out to work.

I concede that if a quick remission is extremely rare that does change the outcome, though I don't know how common that it.

Picking 'Total number of "cancer studies"' was not arbitrary. A similar article could have been crated for e.g. "promising drug cures breast cancer" so you need to take all of them into account. Actually probably every study conducted of all high-profile diseases that are likely to wind up on the HN frontpage - in a counterfactual universe we could be discussing a miracle Alzheimer drug or the like.