I wish i could remember where I saw it, but some years ago I read about a study of "miraculous" cures from cancer in people who had visited Lourdes which showed that the proportion of certified-miracle cancer cures was actually less than the rate of spontaneous remission from cancer in the general population.
The authors of the study pointed out that the finding could be explained by the fact that most of the cancer victims who go to Lourdes are likely to be in the terminal stages of the illness. But even so....
I don't know if this is what you had in mind, but in
The Demon-Haunted World, Carl Sagan wrote:
Since 1858 something like a hundred million people have come to Lourdes in the hope of being cured, many with illnesses that the medicine of the time was helpless to defeat. The Roman Catholic Church rejected the authenticity of large numbers of claimed miraculous cures, accepting only 65 in nearly a century and a half .... The odds of a miraculous cure in Lourdes then are about one in a million; you are roughly as likely to recover after visiting Lourdes as you are to win the lottery, or to die in the crash of a randomly selected regularly scheduled airplane flight - including the one taking you to Lourdes.
The spontaneous remission rates of all cancers ... is estimated to be something between 1 in 10,000 and 1 in 100,000. If no more than 5% of those who come to Lourdes were there to treat their cancers, there should have been something between 50 and 500 "miraculous" cures of cancer alone. Since only 3 of the attested 65 cures are of cancer, the rate of remission at Lourdes seems to be lower than if the victims had just stayed at home.
I seem to recall an old commentary of Randi's mentioning this observation of Sagan's. Unfortunately, I suspect Sagan was guilty of some faulty reasoning here.
Published figures suggest that 100 million (the rough accuracy of which at the time of writing I don't question) corresponds to the total number of
visitors or at least pilgrims having traveled to Lourdes. The overwhelming majority of these people were not, pre-visit, even eligible for subsequent consideration as miracle case. Most of them were simply religious tourists who did not go there in the hope of being cured of anything.
Based on data on the Lourdes website, roughly 6 million people visit the shrine each year nowadays, and about 31,000 of them are hosted at the facilities offered for sick and disabled pilgrims, where we might expect most such people to stay. Let's guesstimate that maybe 35,000 annual visitors suffer from a serious illness or disability. That's less than 0.6% of the total visitors, and one might reasonably extrapolate that perhaps only 600,000 of Sagan's cited 100,000,000 million people were seriously sick or disabled. Sagan's arbitrary estimate of 5% applied to this figure yields 30,000 visitors hoping for a cancer cure. Also using Sagan's cited 1:10,000 to 1:100,000 spontaneous remission rate, we would then expect the number of pilgrims coincidentally going into spontaneous remission to be,
not between 50 and 500, but between zero and three. In fact, as Sagan points out, there were three "miraculous" cancer cures during the period in question.
So Dr. Sagan (or his source) appears to have made a mistake. It seems unlikely, based on this informal examination, that the rate of remission at Lourdes is
less than what one would expect in the general population, and it's just possible that the rate is considerably higher - though, obviously, the likely reasons for that would not include "divine intervention".
I suspect he has a lot on his plate. Another description of how you tried to verify a miracle would probably be welcomed.
