Randomised trials cannot be used in this way
The wealth of responses you have had to Prof Leibovici's paper
suggests that not everyone regards it as a hoax. There is therefore some
justification for looking at the study more closely.
It is an essential feature of randomised trials that they can be
replicated. For prospective studies this involves a further set of
subjects; but in a retrospective study of a retroactive effect there is no
reason not to replicate the study by randomising the population again and
repeating the prayers by either the same or a different person. If the
results were consistent on a number of occasions this would enhance their
However, it is not necessary to put Prof Leibovici to the trouble of
repeating the experiment because a little further thought shows that it
cannot give a meaningful result.
If a population of 3393 subjects is randomised into two groups on n
occasions, the probability (p) of any subject being placed in only one of
the groups is (0.5)^n; and the probability that the subject falls into
both groups is therefore (1-p). The probability that all 3393 subjects
fall into both groups is (1-p)^3393 and the probability that any one
subject does not fall into both groups (q) is 1-(1-p)^3393.
For n=20 q= .00323 or 1/310
For n=30 q= .0000031 or 1/323,237
For n=40 q falls below the limits of my calculator!
Thus, quite modest numbers of repeat randomisations show that no
meaningful result is possible because all subjects occur in both groups.
If this were not to be the case, then the randomisation is faulty and the
study fails on that account.
A retrospective randomised study simply cannot answer the question
that Prof Leibovici is posing. This says nothing, one way or the other,
about the efficacy of prayer.
Competing interests: No competing interests