I was quoting the statistics, I wasn't pretending to be a statistician
Sir Roy Meadow struck off by GMC
BBC News, 15 July 2005
Beyond reasonable doubt
Plus Magazine, 2002
Flawed Statistics in Murder Trial May Cost Expert His Medical License
Science, 22 July 2005
Multiple sudden infant deaths--coincidence or beyond coincidence
Paediatric and Perinatal Epidemiology 2004, 18, 320-326
Sir Roy Meadow is a pediatrician, well known for his research in child abuse. The BBC article reports that the UK General Medical Council (GMC) has found Sir Roy guilty of serious professional misconduct and has "struck him off" the medical registry. If upheld under appeal, this will prevent Meadow from practicing medicine in the UK.
This decision was based on a flawed statistical estimate that Meadow made while testifying as an expert witness in a 1999 trial in which a Sally Clark was found guilty of murdering her two baby boys and given a life sentence.
To understand Meadow's testimony we need to know what a SIDS (sudden infant death syndrome) is. The name SIDS was proposed by the pathologist Bruce Beckwih at a conference in 1969 and the definition, which is still current, along with many others,was formulated at the conference by Beckwith and others as follows:
The sudden death of a baby that is unexpected by history and in whom a thorough post-mortem examination fails to demonstrate an adequate cause of death.
The death of Sally Clark's first baby was reported as a cot death, which is another name for SIDS. Then when her second baby died she was arrested and tried for murdering both her children.
We were not able to find a transcript for the original trial but from Lexis Nexis we found transcripts of two appeals that the Clarks made, one in October 2000 that they lost, and the other in April 2003 which they won releasing Sally after four anda half years in jail. The 2003 transcript reported on the statistical testimony in the original trial as follows:
Professor Meadow was asked about some statistical information as to the happening of two cot deaths within the
same family, which at that time was about to be published in a report of a government funded multi--disciplinary research team, the Confidential Enquiry into Sudden Death in Infancy (CESDI) entitled 'Sudden Unexpected Deaths in Infancy' to which the professor was then writing a Preface. Professor Meadow said that it was 'the most reliable study and easily the largest and in that sense the latest and the best' ever done in this country.
It was explained to the jury that there were factors that were suggested as relevant to the chances of a SIDS death within a given family; namely the age of the mother, whether there was a smoker in the household and the absence of a wage-earner in the family.
None of these factors had relevance to the Clark family and Professor Meadow was asked if a figure of 1 in 8,543 reflected the risk of there being a single SIDS within such a family. He agreed that it was. A table from the CESDI report was placed before the jury. He was then asked if the report calculated the risk of two infants dying of SIDS in that family by chance. His reply was: 'Yes, you have to multiply 1 in 8,543 times 1 in 8,543 and I think it gives that in the penultimate paragraph. It points out that it's approximately a chance of 1 in 73 million.'
It seems that at this point Professor Meadow's voice was dropping and so the figure was repeated and then Professor Meadow added: 'In England, Wales and Scotland there are about say 700,000 live births a year, so it is saying by chance that happening will occur about once every hundred years.'
Mr. Spencer [for the prosecution] then pointed to the suspicious features alleged by the Crown in this present case and asked: 'So is this right, not only would the chance be 1 in 73 million but in addition in these two deaths there are features, which wuld be regarded as suspicious in any event?' He elicited the reply 'I believe so'.
All of this evidence was given without objection from the defence but Mr. Bevan (who represented the Appellant at trial and at the first appeal but not at ours) cross--examined the doctor. He put to him figures from other research that suggested that the figure of 1 in 8,543 for a single cot death might be much too high. He then dealt with the chance of two cot deaths and Professor Meadow responded: 'This is why you take what's happened to all the children into account, and that is why you end up saying the chance of the children dying naturally in these circumstances is very, very long odds indeed one in 73 million.' He then added:
'. . . it's the chance of backing that long odds outsider at the Grand National, yu know; let's say it's a 80 to 1 chance, you back the winner last year, then the next year there's another horse at 80 to 1 and it is still 80 to 1 and you back it again and it wins. Now here we're in a situation that, you know, to get to these odds of 73 million you've got to back that 1 in 80 chance four years running, so yes, you might be very, very lucky because each time it's just been a 1 in 80 chance and you know, you've happened to have won it, but the chance of it happening four years running we all know is extraordinarily unlikely. So it's the same with these deaths. You have to say two unlikely events have happened and together it's very, very, very unlikely.'
The trial judge clearly tried to divert the jury away from reliance on this statistical evidence. He said: 'I should, I think, members of the jury just sound a word of caution about the statistics. However compelling you may find them to be, we do not convict people in these courts on statistics. It would be a terrible day if that were so. If there is
one SIDS death in a family, it does not mean that there cannot be another one in the same family.'
Note that Meadow obtained the odds of 73 million to one from the CESDI report so there is some truth to the statement "I was quoting the statistics, I wasn't pretending to be a statistician” that Meadow made to the General Medical Council. Note also that both Meadow and the Judge took this statistic seriously and must have felt that it was evidence that Sally Clark was guilty. This was also true of the press. The Sunday Mail (Queenstand, Australia) had an article titled "Mum killed her babies" in which we read:
Medical experts gave damning evidence that the odds of both children dying from cot death were 73 million to one.
There are two obvious problems with this 1 in 73 million statistic: (1) Because of environmental and genetics effects it seems very unlikely that the a SIDS death for a families the first baby and for their second baby are independent and (2) These odds might suggest to the jury that there is a 1 in 74 million chance that Sally Clark is innocent. This is, the well-known prosecuter's paradox. The medical experts testimonies were very technical and some were contradictory. The 1 in 73 million odds were something the jury would at least feel that they understood.
Of course these odds of 73 million to 1 for SIDS teaths are useless to the jury in assessing guilt unless they are also given the corresponding odds that the deaths were the result of murders. In his article on the Sally Clark trial Professor Roy Hill estimated that, for a randomly chosen family with two baby deaths, the probability that the deaths are the result of SIDS is about 10 times more likely than the probability that they are the result of murders. Thus, if this kind of statistical evidence means anything, it suggests that Sally Clark is innocent.
The Clarks had their first appeal in 2 October 2000. By this time they realized that they had to have there own statisticians as expert witnesses. They chose Ian Evett from the Forensic Science Service and Philip Dawid, Professor of Statistics at the Department of Statistical Science, University College London. Both of these statisticians have specialized in statistical evidence in the courts. In his report Dawid gave a very clear description of what would be required to obtain a reasonable estimate of the probability of two SIDS deaths in a randomly chosen family with two babies. He emphasized that it would be important also to have some estimate of the variability of this estimate. Then he gave an equally clear discussion on the relevance of this probability, emphasizing the need for the corresponding probability of two murders in a family with two children. His conclusion was:
The figure 1 in 73 million quoted in Sir Roy Meadow's testimony at trial, as the probability of two babies both dying of SIDS in a family like Sally Clark's, was highly misleading and prejudicial. The value of this probability has not been estimated with anything like the precision suggested, and could well be very much higher. But, more important, the figure was presented with no explanation of the logically correct use of such information - which is very different from what a simple intuitive reaction might suggest. In particular, such a figure could only be useful if compared with a similar figure calculated under the alternative hypothesis that both babies were murdered. Even though assessment of the relevant probabilities may be difficult, there is a clear and well-established statistical logic for combining them and making appropriate inferences from them, which was not appreciated by the court.
These two statisticians were not allowed to appear in the court proceedings but only to have their reports read.
The Clarks grounds for appeal included medical and statistical errors. In particular they included Meadow's incorrect calculation and the Judge's failing to warn the jury against the "prosecutor's fallacy".
Concerning the miscalulation of the odds for two SIDS in a family of two children, the judge remarks that this was already known and all that really mattered was that appearance of two SIDS deaths is unusual.
The judge then dismisses the prosecutors fallacy with the remark:
He [Everett] makes the obvious point that the evidential material in Table 3.58 tell us nothing whatsoever as to the guilt or innocence of the appellant.
The judge concludes:
Thus we do not think that the matters raised under Ground 3(a) (the statistical issues) are capable of affecting the safety of the
convictions. They do not undermine what was put before the jury or cast a fundamentally different light on it. Even if they had been raised at trial, the most that could be expected to have resulted would be a direction to the jury that the issue
was the broad one of rarity, to which the precise degree of probability was unnecessary.
After this the mathematics and statistical communities it was necessary to explain these statistical issues to the legal community and the press. On 23 October Royal Stistical Society put out the following news release:
The Royal Statistical Society today issued a statement, prompted by issues raised by the Sally Clark
case, expressing its concern at the misuse of statistics in the courts.
"In the recent highly-publicised case of R v. Sally Clark, a medical expert witness drew on published studies to obtain a figure for the frequency of sudden infant death syndrome (SIDS, or "cot death") in families having some of the characteristics of the defendant's family. He went on to square this figure to obtain a value of 1 in 73 million for the frequency of two cases of SIDS in such a family.
"This approach is, in general, statistically invalid. It would only be valid if SIDS cases arose independently within families, an assumption that would need to be justified empirically. Not only was no such empirical justification provided in the case, but there are very strong a priori reasons for supposing that the assumption will be false. There may well be unknown genetic or environmental factors that predispose families to SIDS, so that a second case within the family becomes much more likely.
"The well-publicised figure of 1 in 73 million thus has no statistical basis. Its use cannot reasonably be justified as a "ballpark" figure because the error involved is likely to be very large, and in one particular direction. The true frequency of families with two cases of SIDS may be very much less incriminating than the figure presented to the jury at trial.
"Aside from its invalidity, figures such as the 1 in 73 million are very easily misinterpreted. Some press reports at the time stated that this was the chance that the deaths of Sally Clark's two children were accidental. This (mis-)interpretation is a serious error of logic known as the Prosecutor's Fallacy. The jury needs to weigh up two competing explanations for the babies' deaths: SIDS or murder. Two deaths by SIDS or two murders are each quite unlikely, but one has apparently happened in this case. What matters is the relative likelihood of the deaths under each explanation, not just how unlikely they are under one explanation (in this case SIDS, according to the evidence as presented).
"The Court of Appeal has recognised these dangers (R v. Deen 1993, R v. Doheny/Adams 1996) in connection with probabilities used for DNA profile evidence, and has put in place clear guidelines for the presentation of such evidence. The dangers extend more widely, and there is a real possibility that without proper guidance, and well-informed presentation, frequency estimates presented in court could be misinterpreted by the jury in ways that are very prejudicial to defendants.
"Society does not tolerate doctors making serious clinical errors because it is widely understood that such errors could mean the difference between life and death. The case of R v. Sally Clark is one example of a medical expert witness making a serious statistical error, one which may have had a profound effect on the outcome of the case.
"Although many scientists have some familiarity with statistical methods, statistics remains a specialised area. The Society urges the Courts to ensure that statistical evidence is presented only by appropriately qualified statistical experts, as would be the case for any other form of expert evidence."
Transcript for the 2000 and 2003 appeals can be obtained from Lexis Nexis following the following route:
Open Lexis Nexis
Choose "Legal Research" from the sidebar
From "Case Law" choose "Get a Case"
Choose" Commonwealth and Foreign Nations" from the sidebar
Choose "Sally Clark” for the " Keyword"
Choose "UK Cases" for the "Source"
Choose "Previous five years” for the "Date."
The two " r v Clarks" are the appeals.
To be continued
Retrieved from "http://chance.dartmouth.edu/chancewiki/index.php/I_was_quoting_the_statistics%2C_I_wasn%27t_pretending_to_be_a_statisitcian" The two " r v Clarks" are the appeals. To be continued