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The “unusual” spike in baby deaths on the neonatal unit where Lucy Letby worked had a 0.008% probability of occurring given its previous mortality rate, a public inquiry has been told.
Sir David Spiegelhalter, the emeritus professor of statistics at the University of Cambridge, said the sudden rise in deaths in 2015 was “surprising” and enough to warrant an internal investigation.
However, he added that from a national perspective the increase was “not very surprising at all” and was “not extreme enough to be considered an outlier”.
The Thirlwall inquiry has heard that three babies died on the Countess of Chester’s neonatal unit in 2012, followed by two in 2013 and three in 2014.
This rose to eight in 2015 and there were a further five deaths in the first six months of 2016. Letby was removed from the neonatal unit in July 2016.
The former nurse, now 34, is serving 15 whole-life prison terms after being convicted of murdering seven babies and attempting to murder seven others between June 2015 and June 2016. She maintains her innocence.
The use of statistics in Letby’s first trial has been one of the central causes of concern raised by experts who believe she is the victim of a miscarriage of justice.
Critics have suggested that the jury was misled by the prosecution’s highlighting of Letby’s name in a shift chart to suggest that she was the only clinician on duty for each of the murders and attempted murders.
Letby’s presence at a series of “unexpected and unexplained” deaths and collapses was what first triggered the suspicions of senior doctors, who raised the alarm to their superiors while acknowledging that they had no further evidence of deliberate harm.
Giving evidence at Liverpool town hall on Wednesday, Spiegelhalter did not comment directly on the interpretation of the shift chart or the use of statistics by the prosecution.
However, he emphasised the need for rigorous analysis and caution before reaching conclusions on data alone.
“The reason why statistics are so important is that numerous studies and personal experience have shown that humans are not very good at judging data,” he said.
“They can miss long-term trends, slowly accumulating changes … and on the other hand they can perhaps pay too much attention to sporadic runs of bad outcomes due to unknown factors and try to find patterns that may not actually exist.
“These are well-know human characteristics and that’s why we need statistical analysis.”
Spiegelhalter, who was a member of the statistical team for the Harold Shipman inquiry, said the rise in neonatal deaths at the Countess of Chester hospital – from under three before 2015 to eight that year – was a “surprising event within the Countess of Chester but from a national event this is not very surprising at all”: “We expect this to happen every year somewhere.”
He said the probability of the unit recording eight deaths a year given its previous mortality rate was “0.008%, which is less than 1%”.
“That would generally be sufficient to trigger an alert but not extreme enough to be considered an outlier,” he said, adding that it would be enough to warrant an internal investigation.
However, Spiegelhalter went on to urge caution because “bad things do tend to cluster” and that “just because numbers have gone up does not mean necessarily that there is a special cause for it”.
Questioned by Peter Skelton KC, representing some of the bereaved families, the statistician said it was important for those interpreting data to show “humility” when dealing with uncertain situations.
“Humility is to try to think I may be wrong, not to have over-confidence about one’s judgments, and … not to be so confident about your judgments that you blind yourself to evidence that might be pointing in another direction.”
The inquiry, by Lady Justice Thirlwall, will conclude hearing evidence on Friday before closing speeches begin in March. The findings are expected to be published in the autumn.
