A doctor gave "misleading and flawed" evidence in the trial of a mother wrongly convicted of murder, the General Medical Council has heard.
Paediatrician Professor Sir Roy Meadow is accused of misusing statistics during the 1999 trial of Sally Clark.
Mrs Clark was freed by the Court of Appeal in 2003 after serving more than three years for murdering her two sons.
Sir Roy could be struck off if found guilty of serious professional misconduct - a charge he denies.
Sally Clark: Served three years after being wrongly convicted of killing her two sons
Angela Cannings: Served 18 months after being wrongly convicted of killing her two sons
Donna Anthony: Served six years after being wrongly convicted of killing her son and daughter
Trupti Patel: Cleared of killing three of her children
During the Clark trial, Sir Roy said the probability of two natural unexplained cot deaths in the family was 73 million to one.
His calculation was based on a report by the Confidential Enquiry into Sudden Deaths in Infancy, but was later disputed by the Royal Statistical Society, which wrote to the Lord Chancellor to say there was no statistical basis for the claim.
Others have said that once genetic and environmental factors are taken into consideration, the odds are closer to 200 to one.
Mrs Clark was eventually freed in 2003, but not as a result of Sir Roy's discredited testimony.
Instead, it had become apparent that another witness at her trial, pathologist Alan Williams, had failed to disclose key medical evidence.
Opening the case for the GMC, Robert Seabrook QC said Sir Roy had been a pre-eminent paediatrician and child expert with many achievements during a long career.
However, he said he had been in breach of his duties as an expert witness in the Clark trial.
"He either didn't understand what he was doing, should not have given evidence and was incompetent to do so, or he was using the information carelessly in support of the proposition that Sally Clark smothered her babies."
Mr Seabrook said in relation to Sir Roy's evidence, the result of the trial was not relevant.
"What matters is that when doctors offer themselves as forensic medical experts ... they must be scrupulously fair.
"They are not hired guns, they are not advancing their own pet theories."
Sir Roy also gave evidence as an expert witness in the trials of two other women, Angela Cannings and Donna Anthony, who were both freed on appeal after being convicted of murdering their children.
Sir Roy's calculation
He said the odds of a single cot death in a non-smoking household where the mother was aged over 26 and there was at least one wage-earner were one in 8,543
This meant the odds of both Clark boys dying of natural causes were the square of this figure - 73 million to one
This was equivalent to four different horses winning the Grand National in consecutive years at odds of 80-1
Mrs Cannings, wrongly imprisoned for smothering her two sons in 2002, shouted at Sir Roy as he arrived at the hearing on Tuesday morning.
She said: "Any apologies for the families, Professor Meadow, for the families you destroyed? Apologies, that's what we want."
Speaking outside the court, Mrs Anthony, convicted of killing her daughter, Jordan, and son, Michael, but later freed by the Court of Appeal, said: "I think this is the beginning of the end for some of us.
"We will just have to see what the GMC decides."
However, Sir Roy has received support from colleagues in the field of paediatric medicine.
He is particuarly noted for his work on Munchausen Syndrome by Proxy - a form of child abuse in which a parent induces real or apparent symptoms of a disease in a child.
Professor Sir Alan Craft, President of the Royal College of Paediatrics and Child Health, said: "It is important to remember that the allegations against him are only about his use of certain statistics in the trial of Sally Clark.
"Whatever the outcome, I hope that this hearing does not overshadow all the work he has completed over his long and distinguished career, including on Fabricated or Induced Illness, which was formerly known as Munchausen Syndrome by Proxy.
"His work has undoubtedly saved the lives of many children."
The hearing was adjourned until Thursday.