Cot Deaths

A serious misunderstanding of conditional probability by Sir Roy Meadow, the inventor of the psychological condition called "Munchausen's syndrome by proxy", might already have led to widespread miscarriages of justice. Over 200 women in the UK in the last two decades have been convicted of the murder or mistreatment of 1 or 2 of their infants, who died without known cause in what is known as "cot deaths", also known as Sudden Infant Death Syndrome (SIDS). A few years ago, about one baby in 8400 died a cot death in the UK every year. Among families with 2 or more children it is about 1 in 1,600. Sir Roy has said that one cot death is a tragedy, two is suspicious and three is murder. He has calculated that the chance that two further cot deaths occur in a family in which one baby has already died a cot death is 1 in 73 million, which is so small (if it is chance) that it must be murder. Other medics have criticised his arithmetic, since it is evident that he has assumed that the second (and third) events are independent of the first, and simply multiplied 8,400 by itself. They are not independent; the rate of cot-deaths is higher in families in which there is a smoker, and among babies whose mothers put them to sleep face down. There is also a genetic component. So the rate of two further cot deaths is much larger than 1 in 73 million. Because of this error, and because some evidence of genetic susceptibility was witheld from the defence, three convicted mothers have been released by the Appeal Court, on the grounds that the murder convictions are unsafe. The Attorney General has started a legal review of all cases.

However, the error of Sir Roy is much more serious than his rough assumption that the events, the two (or 3) cot deaths, are independent. In an unprecedented intervention, the Royal Statistical Society criticised the incorrect use of statistics. They gave the following analogy. Suppose an unskilled archer fires one hundred arrows at a target of size 1 cm. times 1 cm., drawn on a board 1 metre by 1 metre, and his aim is so bad that the arrows are distributed with uniform probability over the metre square. Assume (with Sir Roy) that each shot is independent of the others. There is then a chance of 1/10000 that a single arrow hit the target, but a reasonable chance, about 1/100, that one of the 100 arrows find the target. There is only a small chance that two arrows hit the target. If however, after the archer has fired his 100 arrows, one looks at the distribution, and chooses to draw the target round the two arrows that are closest together, one find a much better chance that both will lie inside a square 1 cm. times 1 cm. [this trick is known as "moving the goalposts"]. Sir Roy's mistake is not to recognise that in the case of cot deaths, one has moved the target by selecting a family with two cot deaths for investigation.

If the chance of a cot death is 1/1600, and given that there is some innocent cause giving rise to the failure of independence of the first and second death, then in a population as large as Britain's, one might expect several double cot deaths a year to arise purely by chance. One can then pick out a case of double cot death, but it would be wrong to say that the chance of an accidental death of the two babies in the case in hand is very low: the case is selected by the very property whose chance one is assessing. One should use conditional probability to assess the chances that the selected sample have various properties. Thus, among the population consisting of families with two cot deaths, one can ask what is the proportion in which there is medical evidence that one or both of them was murdered? Put this way, it is low, perhaps 3%, and almost certainly less than 10%, of the cases, given that there have been two deaths (this figure is based on US data; the UK figures are distorted by the spate of recent convictions). One can also ask, what is the proportion in which one or both parents smoke? and so on, with each possible cause of death, given that there have been two deaths. But the fact that there have been two deaths, by itself, provides no evidence WHATEVER of murder, for the simple reason that the conditional probability that there are two deaths, given that there are two deaths, is unity, 1, 100%. One may then estimate the probability that it is accidental, in the absence of any other information, to be better than 90%, assuming that the proportion with evidence of murder is smaller than 10% at the very most. This is a far cry from 1 in 73 million. What the prosecution needs is evidence that a murder took place, not evidence that the chosen family suffered two deaths. It follows that if in a trial, the rarity of double deaths is assumed to provide supporting evidence, the argument is erroneous, and an appeal to the European Court should reverse the decision.

There have been many further cases in which there have been one or two cot deaths or other injuries, with no prosecution for murder or abuse, perhaps because the medical evidence is weak, but nevertheless the other children in the family have been seized by the social services. According to Margaret Hodge, the numbers of cases might run into thousands, or even tens of thousands. There have even been cases in which a prosecution for murder has failed, and the mother found NOT GUILTY, in which the remaining children have been taken into care for their safety. This is said to occur because the burden of proof in civil cases is less than in criminal cases; the social services only need to show that on the balance of probability, the remaining children are in danger, not that this is true beyond reasonable doubt. But it is likely that another important factor is that the family courts act in secret, and the parents are not allowed to see all the evidence on which the care order is based. [in a documented case, the social worker destroyed one of three tapes made during disclosure sessions with a child; this seems to have been quite legal!] They and their advisors are not even allowed to discuss the case in any detail with their Member of Parliament or even the Commissioner for Children [Margaret Hodge], without the permission of the Court. It is likely that the success of local MPs in solving the Cleveland scandal has been countered by applications to the court to exclude everyone (except the social services, the SS) including the MP. In a recent case, the state-appointed solicitor, purportedly acting for the child, as well as the solicitor for Kent Social Services, argued against any papers being sent to Margaret Hodge, and the judge concurred. That they were sent was pronounced to be contempt of court, even though it was done by the Solicitor General, my good-hearted MP, Harriet Harman. The parent was not allowed to reveal the name of the doctor who had diagnosed her as suffering from MSP. One of the objections put forward by social workers (according to the press) to speedy review of these cases is that, where adoption is pending, it will be interrupted if the case is found for the mother. Of course, the reader will understand that once a child is sent to an adoptive family (rather than just a foster home), the SS can argue that (in spite of a ghastly mistake having been made) it is now in the best interests of the child to remain in the new family. This argument has been made by Mrs. Hodge herself, who is a former social worker. Indeed, in a recent trial for perjury, a senior social worker pleaded guilty to perjury; she had said in a family court that the process of adoption of three childern had progressed further than it actually had. She was given 12 months community service, because her statement was judged not to have changed the decision. She said that she did not know why she had told a lie. It might have been to influence the outcome of the trial; or it might have been because she was worried that she had not followed the instructions of her line manager to get those kids adopted fast.

If it should happen that weak evidence of actual bodily harm is routinely enhanced by the claim that a double death is unlikely, then, as remarked above, the decision would be flawed: the `balance of probability' may have been incorrectly assessed. See also the analysis by Frank Ward, an actuary. I think that there should be a review of such cases as well as those in which the mother is in jail for life (55 cases or more). It is difficult to see how a review can be done (by the Solicitor General, assisted by the Commissioner for Children) if no papers on the case can be sent to them. What were the solicitor acting for the child, and that acting for Kent Social Services, afraid of? That the adoption process will be stopped and then reversed? This would have prevented the Social Services Dept. of Kent County Council from achieving its target for adoptions that year. We all know that there is a great shortage of babies for adoption, and that barren parents are tempted to treat as gods those wonderful people from Social Services who provide them with a child at last. These thoughts might well be entertained by the deprived birth parents [but not, of course, by this author]. Another thought they might have is that that some remnant of the infamous 1:73 million might have been mentioned in the argument that, on balance, murder is more probable than not. There is no evidence that the Social Services would be swayed at all by such a figure; after all, the Appeal Court judge in the latest case asserted that the original jury was not swayed by the figure, simply because they had been warned by the judge who sat the case. And we all know that the Social Services of Kent and all other places consist of entirely professionally trained experts, who understand correlations and conditional probability, and can assess the balance of probabilities correctly, don't we? Even when not warned by a judge.

The BBC reported (May, 2004) that many of the Departments of Social Services, which have secured convictions for murder or abuse of babies suffering cot-deaths, do not intend to reopen any of the cases. No surprise there, then.

So the Social Services, which already has taken over the task of the police in rooting out children not already in care, and in conducting cross-examination of the children, who have already taken over the duties of the CPS in deciding which cases to bring to the family courts, who have already assumed the duties of the defence counsel in deciding which evidence to allow the court to see, and who already have assumed the duties of the jury in deciding on the case, will now assume the duties of the appeal courts by deciding which cases will be reopened [none].

The NSPCC advocates that the rules of assessment should be altered, so that care orders can be issued when the carer's MSB is not just found to more probable than not, but its absence is not beyond reasonable doubt. This would, if implemented, reverse the burden of of proof from the State to the parents. If this had been used up till now, the number of guilty parents not prosecuted would be higher, and the number of miscarriages of justice would be much higher.

Following recent advice to put children to sleep on their backs or side, the number of cot-deaths in the USA, New Zealand, Tasmania and Scandinavia fell "dramatically" lately, and in the UK the number has been reduced by 70%. We can say, on these figures, that until recently, about 70% of cot deaths are caused by placing the child to sleep on its face. Other causes, such as genetic predisposition, premature birth, parental smoking, use of clamps in the birth... must account for some of the remaining 30%. So the number of murders among double cot deaths could well be 10% at most, during the period of many of the cases that worried Lord Howe. So the balance of probabilities, with no other evidence, would then be 9:1 in favour of the mother. My source cautions against the automatic murder charge for cot-deaths, unless there is evidence; it is remarked that the vast majority of cot-deaths have an innocent explanation. It does mention that if the cot death is discovered to be the second to be suffered by the family, then that might constitute evidence. I would suggest that this is a fallacious argument, as explained above. The RSS point out that in assessing whether a rare event like two cot deaths is suspicious, we should not just find its probability. We should compare the chances of the very rare event, two murders, with the chance of an innocent reason for the deaths. This can be expressed in terms of frequencies, and is accessible to empirical evaluation. The revelation that there was an earlier death changes the chance, in the absence of evidence, of murder in the second case of death from p(1) = m(1)/t(1) to p(2) = m(2)/t(2), where m(1) is the number of murders among a total of t(1) families with one cot death, and m(2) is the number of murders of the later child among the total of t(2) families with two cot deaths. It is not clear that p(2) is larger than p(1). Thus is is not clear whether the revelation that there was an earlier cot-death in the same family is evidence for, or evidence against, murder in the case at hand. It could be evidence that a genetic defect is more likely than in the general population, thus reducing the chance that the second death is murder. It, roughly, depends on whether the correlation between murders is higher, or lower, than the correlation between second deaths due to genetic (or other, innocent) factors. Thus, the suggestion in the article that the revelation that the family has already suffered a previous cot-death provides evidence of murder is not justified, even though it is official policy of a reputable body, the American Academy of Pediatrics.

It has been remarked that some ot the doctors' reports say that the deaths were due to suffocation, "consistent with having been smothered by a soft pillow". Any gas, if it is not oxygen, could exclude oxygen and suffocate a baby. This could be carbon dioxide and methane given out by the baby or others, or a heating device, or other gases exhaled by smokers. There is a great difference between evidence "consistent with having been smothered by a soft pillow", and evidence of murder, which would also have to be "inconsistent with having been suffocated by lack of oxygen due to ambient gases". The article quoted above asserts that nearly all SIDS cases reveal "upper airways obstruction" as the final event causing death, and that this happens whatever the reason for the lack of oxygen.

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