Eminent paediatrician Professor Sir Roy Meadow was struck off the medical register on Friday for serious professional misconduct in the latest stage of a saga that showed the power and danger of statistics.

The retired expert, from Leeds, who had played a role in government initiatives to cut deaths from Sudden Infant Death Syndrome, known as cot death, learnt his fate at a disciplinary hearing before the General Medical Council’s fitness to practise panel.

The committee ruled that Prof Meadow gave “erroneous” and “misleading” evidence in the trial of solicitor Sally Clark, who was found guilty in 1999 of murdering her sons Christopher and Harry, but later had her conviction quashed by the Court of Appeal in 2003. He had also been an expert witness in other similar cases where convictions had been over-turned on appeal.

Prof Meadow, 72, told the jury at the Clark trial that the chance of two babies dying of SIDS in an affluent family was “one in 73 million”. The figure was derived from assuming that the two deaths were independent - he had squared the one in 8,500 probability of one death occurring in an affluent non-smoking family. This has been described as an “arithmetically correct but statistically grossly erroneous observation” by one legal academic.

But research has shown that a second child is at greater risk of cot death if one has already died of the syndrome. In other words, the first death in a family is very unlikely but a second is much more likely.

The case has caused so much concern among statisticians, who feel that it has severely damaged the perception of the validity of statistical evidence in general, that the Royal Statistical Society has engaged in a number of initiatives to reinforce the value of statistics in law and more widely.

As one statistician said, “statistical information, properly acquired, understood, and considered, with conclusions properly expressed, and informed by good understanding of statistical principles, is sound” and valuable, but clearly Prof Meadow “got it wrong” with his evidence in this case.

Prof Meadow was told by the GMC that he had a duty to familiarise himself with all relevant data and published work in order to provide competent evidence. “Your errors, compounded by repetition over a considerable period of time were so fundamental and so serious it is the panel’s view that a period of suspension would be inadequate, not in the public interest and would fail to maintain public confidence in the profession.’’

According to Professor Ray Hill of Salford University, an expert on cot death cases, “The danger in avoiding statistics altogether is that jurors may well draw incorrect conclusions for themselves, believing that occurrences of rare events are somehow beyond coincidence.”

The panel also said he failed in his duty as an expert witness and was wrong to compare the possibility of Mrs Clark’s two children dying natural deaths to the odds of horses winning the Grand National, telling the jury that the odds of both Clark children dying natural deaths could be compared with four different horses winning the Grand National in consecutive years at odds of 80-1.

The RSS drew attention to this “serious error of logic” known as the prosecutor’s fallacy. It says that the jury needs to weigh up two competing explanations for the babies’ deaths - cot death or murder. It says that “two deaths by SIDS or two murders are each quite unlikely and what matters is the relative likelihood of the deaths under each explanation, not just how unlikely they are.”

The GMC ruled that Prof Meadow “failed to provide a fair context for the limited relevance” of his findings and relied on erroneous statistics. Notably, he was wrong to imply that the risk of a second cot death in a family was unrelated to common environmental factors or genetics.

The difficulty of accurately classifying unexplained and unexpected deaths means that reliable figures are impossible to come by. But, while the chance of any one baby dying in a family type, such as Mrs Clark’s, might be as low as 0.01 per cent, studies now suggest that the chance of a second dying in a family could be many times higher.

Professor Hill’s own “rough estimates” suggest that single cot deaths outnumber single murders by about 17 to 1, double cot deaths outnumber double murders by about 9 to 1, and triple cot deaths outnumber triple murders by about 2 to 1. Each death does give rise to greater suspicion but arguably not to the extent of the dictum known as Meadow’s law, namely that “One cot death is a tragedy, two cot deaths is suspicious and, until the contrary is proved, three cot deaths is murder”.