Lucy Letby and the Texas sharpshooter

I am once again asking the statisticians to stay in their lane

I have a letter in this week’s Spectator responding to an unusually weak column by Rory Sutherland which takes as its premise the idea that Lucy Letby was convicted on the basis of statistics.

Sir: I fear that Rory Sutherland has fallen for the myth that Lucy Letby was convicted because of ‘statistics’ (The Wiki Man, 31 August). Once it was established that someone was deliberately harming children on the ward – a fact that Letby herself conceded – it was highly relevant that she was the only person who was always present. Other evidence presented at the trial, such as her falsification of medical records, strengthened the case but none of this had anything to do with statistics. The jury did not spend ten months staring at a staff rota.

Proving that the defendant was at the scene of the crime is a necessary condition for a conviction but, as Letby’s acquittal on several charges shows, it is not a sufficient condition. If 12 statisticians had been on the jury, she still would have been found guilty.

The Economist published a much worse article last month which more or less claimed that Letby was innocent and asserted that…

… in the Letby trial, a chart was used to show that she had been on duty when babies had died or collapsed unexpectedly; the jury was not told about other deaths for which she was not charged. The statistical weaknesses of this were not sufficiently pointed out. The target was painted around the arrow. She was convicted.

I was first drawn to writing about this case by the misuse of the Texas sharpshooter analogy which has done more than anything to create doubt about the safety of the convictions in the minds of people who, quite understandably, are not inclined to dig into the case. Letby was charged and convicted of seven murders but there were a further nine early neonatal deaths at the hospital during the period in question. We were never told how these babies died or whether Letby was present. This led some to believe that the police had retrospectively cherry-picked the deaths that occurred when Letby was on duty and used the fact that no one else was present as compelling evidence of her guilt. As I wrote in Spiked…

A spreadsheet showing that Letby was present during all the murders and attempted murders was used by the prosecution and widely circulated in the media after her first conviction. Those who knew little else about the case assumed that this was what had persuaded the jury. Concerns were raised about the Texas sharpshooter fallacy – where a man shoots at the side of a barn and then paints a target centred around the tightest cluster of bullet holes. Was it not possible, they said, that the police had looked at the spike in deaths that took place at the Countess of Chester Hospital (CoCH) in 2015 and 2016, cherry-picked the ones at which Letby was present and ignored the rest?

Those who are familiar with the case can see the holes in this theory. When Dewi Evans first identified suspicious collapses and deaths by looking at the medical records, he did so without knowing who was on duty. Each suspicious incident was then handed to a different detective to investigate in isolation. According to Detective Superintendent Paul Hughes, who allocated the cases, it was only when the detectives returned to discuss their cases with each other that the similarities emerged, not least the constant presence of Nurse Letby. What possible motive could the police have to frame an innocent woman anyway?

It is the unexplained and unexpected nature of so many of the collapses and deaths that set them apart from the handful of deaths that the doctors expected to see each year. An unexpected and unexplained death is not necessarily suspicious (the cause of Child A’s death was recorded as ‘unascertained’ at the time, but it did not lead to a murder enquiry), but if the death is also unnatural it can only be homicide, suicide or a fatal accident. A large part of the ten month trial was spent proving that the seven deaths in the Letby case were indeed unnatural and you won’t understand how compelling the evidence is for this by looking at a spreadsheet.

(Letby’s defenders often parrot the claim that all the babies were judged to have died of ‘natural causes’ but, as mentioned, Child A’s death was unascertained, Child P’s death was put down to ‘Sudden Unexpected Postnatal Collapse’ with the pathologist unable to find an underlying cause, and Child O’s cause of death was intra-abominal bleeding which is consistent with the liver injury Letby was accused to causing. Child E did not have a post-mortem and the cause of death was listed as necrotising enterocolitis (NEC) by a doctor who later apologised to the parents for this mistake and acknowledged that an X-ray taken an hour before he died showed no sign of NEC. Letby’s apologists treat the original death certificates as if they were infallible, but there is no reason why pathologists who had probably never seen a case of air embolism, who were not looking for a murderer and who usually did not conduct an autopsy were better placed to identify the cause of death than the expert witnesses who testified at the trial.)

Nevertheless, the nagging thought remains that there may have been some unexpected or suspicious deaths when Letby was not on duty. Or it did until yesterday when Liz Hull revealed that the other nine deaths were not unexplained, unexpected or unnatural.

The source said: ‘Four of the deaths were babies born with a congenital problem or birth defect, another baby was sadly asphyxiated or deprived of oxygen at birth, the remaining four died of infection and their deaths were precipitated with a period of time consistent with infection, they did not suddenly and unexpectedly collapse and die.’

The Mail understands that Letby was on duty at times when at least two of these babies were being treated on the neo-natal unit, although it is not known if she was ever their designated nurse.

Liz Hull is exceptionally well informed and well connected, having been in court for nearly every day of the trial and presented the excellent podcast, The Trial of Lucy Letby, with Caroline Cheetham. I warmly recommend the latest episode which includes a polite but devastating takedown of a statistician who clearly knows next to nothing about the case.

The significance of this new information should be obvious, but I will spell it out. None of the nine deaths were suspicious and therefore no crimes were alleged. Five of them were highly predictable and the other four (from infection) were clearly natural. Letby was not accused of killing these children because they were obviously not murdered. That is why they are not on the spreadsheet. Although Letby was on duty when some of these babies died, she was not prosecuted for them because the police were not, in fact, ‘painting a target around the arrow’.

The ‘Free Lucy’ crowd have been demanding this information for months, but they have shown little interest in it now that it has arrived. Journalists such as Peter Hitchens and Phil Hammond have ignored it (so far) while her anonymous supporters have characteristically grasped the wrong end of the stick.

If these people are serious about freeing Letby, they will need to engage with the evidence presented at the trial at some point. Wanging on about ‘statistics’ and ‘spikes’ is not going to get them anywhere with a judge because this was never what the trial about. Last week, the Telegraph’s scientifically illiterate science editor published an article that was entirely based on her failure to distinguish a spike in inexplicable deaths from an inexplicable spike in deaths. Yesterday, she published an article based on the thoughts of a fund manager (described as ‘a fellow of the Royal Statistical Society’, which anyone can become for £153 a year) who says the ‘spike’ could have happened by chance.

And so it could. No one disputes that. Letby contributed to the spike in deaths but she wasn’t convicted because of the spike. There were other deaths at the hospital that she was never charged with. No one disputes that either, but those deaths were not remotely suspicious or unusual. Miscarriages of justice happen. Of course they do. But wrongful convictions only get overturned when the accused is shown to be innocent because new evidence proves that they couldn’t have done it or that someone else did it. Neither is a realistic proposition for Letby. Her only possible path to freedom is if it shown that no crimes were committed at all, but that will never happen so long as her advocates continue to ignore how the babies died and why Letby was accused of murdering them.

Other posts on this subject:

Is Lucy Letby innocent?

Further thoughts on Lucy Letby

Lucy Letby and the statisticians