Experts have challenged the medical case against Lucy Letby. What about the statistical evidence?
An international panel of medical experts have thrust Lucy Letby back into the spotlight. At a press conference convened by Letby’s legal team, the experts cast doubt over the former nurse’s conviction. Letby was given 15 whole-life sentences for murdering seven babies and attempting to murder seven more.
Speaking at the press conference in London, retired neonatologist Dr Shoo Lee told the assembled reporters: “In all cases death or injury were due to natural causes or just bad medical care.”
Why should we take Dr Lee’s word for it? Well, in part, because he is the author of a key paper on air embolisms, one of the methods that Letby was accused of using to kill babies, which formed a key part of the prosecution’s evidence at the trial.
He also claims that the paper’s findings were misinterpreted at the trial and that a newly updated version of the article would help exonerate Letby rather than convict her.
The Letby conviction has always attracted critical attention because there were no witnesses who could confirm they saw her attacking any of the babies she was convicted of murdering. Nor did anyone see her perform actions that could have constituted the attempted murders of seven others.
Consequently, the prosecution used statistics alongside the medical evidence the expert panel has now cast doubt upon. So how solid is that statistical evidence?
A key piece of statistical evidence is a chart which showed that Lucy Letby was on duty every time one of the crimes of which she was accused occurred, but that none of the other nursing staff were.
On the face of it, it seems quite damning. But when you think about it, it’s unsurprising that Letby’s column is the only one full of crosses. Any of the events at which she was not present she would not have been charged with and consequently wouldn’t appear on the chart.
A chart showing the shifts in suspicious activity was suspected and the nurses who were working on each shift.
Cheshire Police
This is an example of what is known in statistics as the Texas sharpshooter fallacy.
The fallacy is named for a story about a Texan cowboy who likes to head out to his barn after a few drinks for target practice. Invariably, the barn wall gets peppered with random bullet holes during the inebriated exercise, and purely by chance some of these holes are clustered.
One morning the savvy “sharpshooter” gets out his paint cans and daubs a target around this cluster of holes to give the impression of accuracy to anyone who didn’t see the process by which they were made and to draw attention away from the other more dispersed bullet holes.
The sharpshooter fallacy occurs when a conclusion is drawn based only on data consistent with a given hypothesis, ignoring data that doesn’t support the proposed conclusion.
Imagine, for example, you made a chart similar to the one used to convict Letby, this time including only those deaths at which a different member of the nursing staff was present. It’s entirely possible – for example, if they were present for deaths at which Letby was not – that their name would be above the only column full of crosses and not Letby’s.
Indeed, it later transpired that the table did not include six other deaths that occurred during the same period and with which Letby was not charged. The jury was not told about these other deaths.
As Jane Hutton, a professor of medical statistics at the University of Warwick argues: “If you want to find out what went wrong, you need to consider all deaths, not just a subset of them.”
She also points out that it’s important to consider how likely the other alternative causes of death were at the struggling Countess of Chester neonatal unit.
The prosecutor’s fallacy
The probability of so many deaths on a neonatal unit in such a short period should be quite low. At first glance, this might seem to make the alternative explanation of murder seem more likely. But this is a classic statistical error.
This mistake is so common in courtrooms that it is known as the prosecutor’s fallacy. The argument starts by showing that, if the suspect is innocent, seeing a particular piece of evidence is extremely unlikely.
For Letby, this is the assertion that if she was innocent of killing these babies, the probability of them dying due to other causes is extremely low. The prosecutor then deduces, incorrectly, that an alternative explanation – the suspect’s guilt – is extremely likely.
The argument neglects to take into account any other possible alternative explanations, in which the suspect is innocent, such as the death of these babies due to inadequate care. It also neglects the possibility that the explanation that the prosecution is proposing, in which the suspect is guilty, may be just as uncommon as the alternative explanations, if not more so.
By just presenting the low probability of these seven babies dying naturally, the inference that an untrained jury is invited to draw runs something along these lines: “The deaths of these babies from natural causes is extremely rare, so the odds that the deaths are the result of murder is correspondingly extremely high.”
However, it must also be taken into account, when weighing up the evidence, that multiple infant murders are also extremely uncommon. What really matters is the relative likelihoods of the different explanations. Weighing these very unusual events against each other is not an easy thing to do.
Criminal cases review
Other statistical issues with the case also deserve more attention: the high number of deaths at the Countess of Chester, even excluding the babies that Letby has been convicted of murdering. Or the possibility of false positive medical identifications of murder, for example.
Whether Letby’s team’s appeal to the Criminal Cases Review Commission will be successful or not remains to be seen. The statistical issues over the case, when taken alongside the doubts about the medical evidence, mean that there is certainly a possibility.
Throughout all this, it’s important to remember the families affected by the events at the Countess of Chester Hospital. Whatever the ultimate truth of the matter, this ongoing case will undoubtedly make dealing with their grief more difficult. Läs mer…
