Professor Sir Roy Meadow, a child abuse expert, gave evidence in the trial of Sally Clark that the chances of two babies dying of cot death within an affluent family was one in 73 million.
But he quoted the figure out of context and in a way that it was never intended to be used, the hearing before the General Medical Council was told.
Sally Clark was jailed for life for the murder of her two baby sons in 1999, but freed on appeal in 2003. Sir Roy is charged with serious professional misconduct, which he denies.
The GMC heard that the one in 73 million statistic was not calculated by Sir Roy, but came from a report into sudden infant deaths known as the Cesdi Sudi study.
Peter Fleming of the University of Bristol, the chief author of the study and an expert on cot death, told the hearing that although his study contained the one in 73 million figure, it was "somewhat unreliable" because of the "extreme rarity" of double cot deaths. "It was never intended as a real statistical estimate," he told the hearing. The true rate could range between 1 in 214 and 1 in 8,500, he said.
Sir Roy was invited to write the preface for the publication in August 1999 and had been given a draft of the study, the hearing was told.
Professor Fleming was shocked when Sally Clark's defence team informed him that the one in 73 million statistic was being used as part of the case against her and faxed a letter to the Clark defence team the same morning highlighting his concerns.
"I was trying to make the context of that sentence clearer," he said. "My intention was that the barrister would have the opportunity to raise these points if that particular sentence was raised in court. The content of previous paragraphs made it clear we were making assumptions for it we knew were not correct."
The statistics were meant to show how genetic as well as environmental factors, such as parents who smoke, came into play. "We were increasingly becoming aware it seemed that many ... were assuming where a second death was occurring there was a very high likelihood of neglect and abuse."
Professor Fleming said his study was "trying to balance" that assumption. It should have been "quite clear" that the one in 73 million figure was purely illustrative, he said.
Sir Roy was knightedon his retirement from St James' University Hospital, Leeds, in 1998. He faces being struck off the medical register if found guilty.
His evidence helped to convict Angela Cannings and Donna Anthony of murdering their children. He was also involved in the failed prosecution of Trupti Patel in 2003. After Mrs Cannings' conviction was quashed, 28 cases were referred to the Criminal Cases Review Commission, which investigates miscarriages of justice.
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