Meadow's law

In a note to his mathematical analysis of the Sally Clark case, Professor Ray Hill endorses a claim that Meadow did not originate the rule:

Professor Meadow did not originate the law. It appears to be attributable to D. J. and V. J. M. Di Maio, two American pathologists who state in their book:[6] It is the authors’ opinion that while a second SIDS death from a mother is improbable, it is possible and she should be given the benefit of the doubt. A third case, in our opinion, is not possible and is a case of homicide. It is clear that the statement is the authors’ opinion. It is not a conclusion reached by analysis of their observations; no supportive data are presented and there are no illustrative case histories, or references to earlier publications. This is in striking contrast with the rest of the book which is replete with illustrative case histories and cites many references throughout. A recent examination of Meadow’s own contributions to the medical literature has likewise failed to uncover supportive pathological evidence or references to it

— Dr Glynn Walters[7], Letter to Professor Ray Hill, published in Multiple sudden infant deaths – coincidence or beyond coincidence?[8]

The precept was published in the United States by DiMaio and DiMaio in 1989, without mention of Meadow. In ABC of Child Abuse, first published in the same year, Meadow wrote his formulation:

'One sudden infant death is a tragedy, two is suspicious and three is murder until proved otherwise' is a crude aphorism but a sensible working rule for anyone encountering these tragedies

— Dr Roy Meadow, ABC of Child Abuse[1]

The formula is "clearly fallacious" according to Bob Carpenter, Professor of Medical Statistics at the London School of Hygiene and Tropical Medicine, an expert witness in some of the trials where infant cot deaths were prosecuted as homicides.[9]

Firstly, Meadow was accused of espousing the so-called prosecutor's fallacy in which the probability of "cause given effect" (i.e. the true likelihood of a suspect's innocence) is confused with that of "effect given cause" (the likelihood that innocence will result in the observed double-cot-death). In reality, these quantities can only be equated when the likelihood of the alternative hypothesis, in this case murder, is close to certainty. Since murder (and especially double murder) is itself a rare event, the probability of Clark's innocence was certainly far greater than Meadow's figure suggested.

An equivalent error is to accuse anybody who wins a lottery of fraud.

The second criticism was that Meadow's calculation had assumed that cot deaths within a single family were statistically independent events, governed by a probability common to the entire affluent non-smoking population. No account had been taken of conditions specific to individual families (such as a hypothesised "cot death gene") which might make some more vulnerable than others. The occurrence of one cot-death makes it likely that such conditions exist, and the probability of subsequent deaths is therefore greater than the group average (estimates are mostly in the region of 1:100).

Combining these corrections with estimates of successive murder probabilities by affluent non-smokers, Mathematics Professor Ray Hill found that the probability of Clark's guilt could be as low as 10% (based solely on the fact of two unexplained child deaths, and before any other evidence was considered).[8] In any case, a legal verdict is not to be rendered on the basis of statistics; Hill wrote, "guilt must be proved on the basis of forensic and other evidence and not on the basis of these statistics alone. My own personal view that she is innocent is based on my subjective assessment of all the aspects".[10]