## Statistics — a question of life and death

29 Feb, 2016 at 10:19 | Posted in Statistics & Econometrics | 1 Comment

In 1997, Christopher, the eleven-week-old child of a young lawyer named Sally Clark, died in his sleep: an apparent case of Sudden Infant Death Sybdrome (SIDS) … One year later, Sally’s second child, Harry, also died, aged just eight weeks. Sally was arrested and accused of killing the children. She was convicted of murdering them, and in 1999 was given a life sentence …

Now … I want to show how a simple mistaken assumption led to incorrect probabilities.

In this case the mistaken evidence came from Sir Roy Meadow, a paediatrician. Despite not being an expert statistician or probabilist, he felt able to make a statement about probabilities … He asserted that the probability of two SIDS deaths in a family like Sally Clark’s was 1 in 73 million. A probability as small as this suggests we might apply Borel’s law: we shouldn’t expect to see an improbable event …

Unfortunately, however, Meadow’s 1 in 73 million probability is based on a crucial assumption: that the deaths are independent; that one such death in a family does not make it more or less likely that there will be another …

Now … that assumption does seem unjustified: data show that if one SIDS death has occurred, then a subsequent child is about ten times more likely to die of SIDS … To arrive at a valid conclusion, we would have to compare the probability that the two children had been murdered with the probability that they had both died from SIDS … There is a factor-of-ten differeence between Meadow’s estimate and the estimate based on recognizing that SIDS events in the same family are not independent, and that difference shifts the probability from favouring homicide to favouring SIDS deaths …

Following widespread criticism of the misuse and indeed misunderstanding of statistical evidence, Sally Clark’s conviction was overturned, and she was released in 2003.

## 1 Comment

1. They will kill again…

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