Statistical Argument

Lucy Letby: police and CPS handling of case raises new concerns about convictions

‘The prosecutor’s fallacy’

At Letby’s first trial, the prosecution used a chart that showed which nurses were on shift when babies were allegedly attacked. The chart was presented to the jury to illustrate the central allegation that Letby was the one constant presence.

Its use has prompted unusually vocal criticism from leading statisticians. They argue that the chart represents a classic example of the “prosecutor’s fallacy”, in which an investigation starts with only a suspicion, and a case is built to support it, rather than all possible evidence and explanations having been rigorously explored.

Jane Hutton, a professor of statistics at the University of Warwick, said of the shift chart and other elements of the case: “It’s a large pile of crockery, much of which is broken. Such a pile does not hold water, however big it is.”

The Thirlwall inquiry has heard that the police investigation was based on statistical coincidence from the beginning.

According to documents seen by the Guardian, seven doctors collaborated on compiling a report to police in May 2017. It presented details of 13 babies who had died and eight more who had deteriorated. They said Letby had been present at 11 of the deaths, adding: “The likelihood of this occurring by chance alone is very low.”

In their opening statement to the inquiry, hospital managers said that when they finally went to Cheshire police, on 5 May 2017: “It was explained that there was a notable high statistical relationship between Letby and babies deteriorating on the unit, but no other evidence.”

At a subsequent meeting a week later, according to the managers’ statement: “Assistant Chief Constable Cheshire [Darren] Martland said: ‘This is uncomfortable as there is no specific allegation at this point to suggest a criminal act.’”

Five days later Cheshire police announced they had opened a criminal investigation.

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