Lucy Letby, Private Eye and statistics

Those statistical claims in full

When I first wrote about Lucy Letby last summer, it was largely to point out that the prosecution case was not based on statistics and that any appeal that relied on statistics was doomed to fail. Since then, I have been asking her supporters to tell me what statistic was used to convict her. I have not heard a compelling answer.

Sally Clark was convicted on the deeply flawed assumption that the chances of two cot deaths happening in the same family were 1 in 73 million. Lucia de Berk was convicted of multiple murders because the jury was told that “the probability of so many deaths occurring while de Berk was on duty was only one in 342 million”.

No such statistical claim was ever made in the Letby case and her new defence are focusing more on the medical evidence which, they claim, shows that no crimes were committed, rather than on the supposed statistical evidence. (For a fine explanation of why this is also doomed to fail, read this Substack by Ben Cole.)

But the statisticians will not go away. Eight of them, including the usually sensible Stephen Senn and the rarely sensible Richard Gill, have endorsed an analysis by Phil Hammond in the current issue of Private Eye. Hammond reckons that there were three statistical claims made by the prosecution and has given ten reasons why he thinks they are wrong. Let’s go through them.

We don’t know whether this claim “sunk in the minds of the jury” because we don’t know what they were thinking. What we do know is that the jury in the first trial found her not guilty of two attempted murders and could not reach a verdict on several other charges. She was charged with 22 offences and “only” convicted of 14, so her mere presence on the ward was clearly not seen as sufficient evidence of guilt. Either the jury didn’t think there was enough evidence to convict her of eight offences or they thought she was definitely innocent or they thought that they were not crimes at all. It is possible, though vanishingly unlikely, that they thought someone else committed the offences. We will never know. But they obviously did not convict on the basis of “statistics” otherwise they would have convicted her of everything.

What is the statistic here anyway? That she had the opportunity to commit the crime 100% of the time? If so, every court case is based on statistics.

The statistical fallacy is, supposedly, that the prosecution ignored all the deaths and collapses that Letby wasn’t present for. The obvious explanation for this is that the other deaths and collapses were not the result of inflicted harm. Hammond claims that Evans alone decided what a suspicious incident was “without any objective definition or independent corroboration”. This is not true. His interpretation of events was endorsed in two peer reviews by the neonatologists Martin Ward Platt and Sandie Bohin, and a great deal of objective evidence was provided in court by radiologists, pathologists, etc. A series of unexplained deaths is inherently suspicious. Evidence of air embolism is suspicious. Evidence of exogenous insulin is suspicious. Evidence of blunt trauma is suspicious. There is objective evidence for all of this.

Evans flagged up incidents that had no obvious innocent explanation based on medical records (which are also objective evidence) and recommended that they be investigated further. The pathologist Jane Hawdon had already done the same thing when her review identified five unexplained deaths. Medical records alone are not enough to prove guilt (or innocence), as Letby’s new lawyer is about to find out. Evans’ reports were only the first step in a criminal investigation that involved a huge number of people.

This claim is based on an article in Unherd by David Rose. The evidence for it is not in the public domain and it is unclear where Rose got it from. So many ‘bombshell’ revelations from Letbyists have turned out to be damp squibs that I would need to see it with my own eyes before I took Rose’s interpretation of it seriously. As mentioned above, Evans flagged up incidents for further investigation. For the most part, he did not say decisively that a crime had been committed. If further evidence (eg. from eye witnesses) indicated a natural cause of death or if there was insufficient evidence of a crime, it would not go to court.

Notice, however, that this claim contradicts another argument often made by Letby’s supporters, that Evans only picked the incidents at which Letby was present. It also refutes a similar claim that the police only gave Evans records of events at which Letby was present or - a third variation - that the doctors only gave the police records of events at which Letby was present.

Letby was often given babies to look after in Nursery 2 or 3 rather than the sicker babies in Nursery 1 - and she rather resented it. For example, she was given two of the triplets - known as O and P - to look after in Nursery 2 while the sicker triplet was in Nursery 1. Babies O and P both died while the sicker triplet survived.

It is also notable that several of the deaths and collapses happened while Letby was looking after babies that she was not supposed to be looking after - and that the deaths and collapses occurred shortly after the designated nurse had left the room. This was mentioned in court.

Children who collapsed when designated nurse left or leaving the room: Child C, D, G [first event], I [second event and fourth event], K, N [first event], P [third collapse - when doctors were out of the room], Q [slight variation - when Letby got herself out of the room].

Child I’s mother only found out at the trial how much Letby had been hovering around her daughter, as she told the Thirlwall Inquiry.

“Now I have seen the medical records, I am absolutely shocked at how much ‘care’ she provided to our baby. She is all over her notes. I have noticed a lot of the ‘care’ was when I wasn’t present.”

More reliable sources say that Letby was actually present for 12 of the 13 deaths that occurred at the neonatal unit of the CoCH in 2015 and 2016. There were four (not three) babies born in the hospital who died elsewhere but they are obviously not relevant to the trial. Without the seven murders, there were three deaths per year in the unit, which is about average. In other words, without Letby there was no “spike”.

We have the cause of death for the other babies. They are things like ‘hypoxic-ischaenic encephalopathy’ (a brain injury) and ‘multiple congenital anomalies’. There was nothing ‘suspicious’ about them and there is no unifying factor that explains them.

Letby did a lot of overtime but she wasn’t at the hospital anything close to 90% of the time and yet she was there when 92% of the babies died. The prosecution could have conducted a statistical analysis and given the probability of this being a coincidence but they didn’t because the case was not about statistics and it would be silly to include the deaths of babies from natural causes.

If, as the sceptics claim, natural deaths were turned into suspicious deaths on the basis of Letby’s presence, why wasn’t she prosecuted for 12 of them? Because it wouldn’t have stood up. The prosecution had to prove that inflicted harm had been committed. Only once that was done was Letby’s presence relevant.

The triplets were not “very high-risk”. They were all a good weight and doing well before they crossed paths with Staff Nurse Letby. Babies O and P both collapsed and died while their brother - who was considered to be higher risk - didn’t collapse at all and is still alive today.

Baby E and Baby F also had completely different experiences, with the former dying from air embolism while his twin brother suffered from hypoglycaemia and survived. The hypoglycaemia is an agreed fact, although Letbyists claim it was natural rather than caused by Letby administering insulin. Baby E’s death was initially assumed to be necrotising entercolitis (subsequently disproven by X-ray evidence) and the ‘independent panel’ claim that it was actually due to a haemorrhage. Whatever you conclude about Baby E’s death, it had no connection to Baby F’s hypoglycaemia. Their being twins is of no relevance, aside from Letby’s penchant for attacking twins.

The statisticians are getting well beyond their field of expertise now, aren’t they? What have deaths in the maternity ward - mostly stillbirths - got to do with the price of fish? There was an unusually high number of stillbirths in 2015, but an unusually low number in 2016. There is no correlation with what was going on in the neonatal unit and why should there be? How could there be?

That sound you can hear is a barrel being scraped. Anyone who is familiar with the incidents that occurred at the CoCH in 2015-16 knows that senior doctors were on hand to resuscitate the babies. Letbyists are keen to blame under-staffing, but this is not an excuse that Letby used much herself. During cross-examination, Nick Johnson KC went through every incident one at a time, asking Letby if she could pinpoint a lack of staff or any incompetence that could explain the collapses. She generally could not.

Onto the second alleged statistical claim…

In chronological order, these four deaths were due to ‘severe multiple congenital abnormalities’, ‘congenital pneumonia with inflammatory response syndrome’, ‘pulmonary hypoplasia’ and ‘multiple congenital anomalies (including dysplasia)’. Hammond correctly notes that the prosecution “argued that suspicious incidents followed Letby” (emphasis added). The incidents above were not suspicious.

This has got nothing to do with Letby being moved to day shifts and, as with nearly everything discussed so far, would not benefit from the insights of statisticians. The deaths of both triplets were highly suspicious. The pathologist who gave evidence in court said that the damage to Baby O’s liver was the kind of thing that would normally only be seen in someone who had been in a car crash.

Finally, the third “statistical claim”…

This is true so far as it goes. The CoCH was downgraded to a Level 1 unit on 7 July 2016 and can now only take babies of a 32 week gestation. However, it is worth noting that Baby D was born at 37 weeks and the triplets were born at 33 weeks. A few others were born prematurely but died or collapsed when they were significantly older (e.g. Baby I was two and a half months old when she died). Three of the seven babies murdered by Letby were born at a sufficient gestation to be admitted to the CoCH today, but no babies of that age died in the unit after Letby left.

I could be wrong, but I can’t find any record of the prosecution making this particular ‘statistical claim’ in the court reports, although the redesignation of the unit to level 1 was mentioned several times. I think it has been mentioned more by the media than it ever was in court.

Incidentally, for all the talk about the CoCH looking after babies that were at death’s door, it was a Level 2 unit. The sickest babies are sent to a Level 3 unit.

Conclusion

You can describe the three claims listed by Hammond as statistics if you like, but I don’t see how a statistician would be able to resolve the questions they supposedly raise. There are no probabilities to critique, no maths to be done, no formulae to devise. Last December, Dewi Evans said that babies were 30 times more likely to die if Letby was looking after them. This is a statistic and it was never mentioned in court. Evans may have only come up with it to wind up statisticians. If so, it worked. Jane Hutton, a statistician who has been commenting on this case for some time despite being ignorant of large parts of it, responded by saying:

“One also needs to know how many babies were on the neonatal intensive care unit, and the severity of illness of each infant, multiplicity (twins/triplets) etc.

“Without confirmation of the data on shifts, particularly times of day, as well as the relevant information about the severity of illness of the infants, this calculation is meaningless.”

Finally, the penny drops! The incidents on the indictment were not random data points that lend themselves to statistical analysis. You need to know what happned to the children. The case would have never gone to trial if it had been based on a staff rota and the coincidence of the deaths drying up once Letby had gone. Once inflicted harm had been proven, Letby’s invariable presence on the ward was highly relevant, as were numerous other ‘coincidences’ such as the strangely large number of collapses that occurred when the parents left the ward.

Hutton has complained that Cheshire Police hired her to do a statistical analysis but then dropped her because, as they explained to her, they were “looking at the validity of statistical evidence again”. For Letbyists, this is further evidence of a conspiracy. A more reasonable interpretation is that the police realised that statistics were going to get them nowhere and wanted to avoid another Sally Clark fiasco.