Talk:Lucy Letby

The confirmation biases

Prominent public supporters of the convictions to date:

• Dr. Jayaram (prosecution witness
• Dr Evans (prosecution expert witness)
• Judith Moritz and Liz Hull
• Christopher Snowden

As the debate has developed their numbers have not risen. All have some personal stake in affirming the convictions other than Snowdon who, as a paid lobbyist for the alcohol and tobacco industries, we might say, is a professional holder of confirmation biases.

Now, true, those professing Letby’s innocence are prone to confirmation bias too. but if you looked at it probabilistically, the competing “confirmation biases” are these:

the likelihood of a healthcare serial murderer (an extremely unlikely scenario) to a very high degree of certainty (>95% confidence level)

the likelihood of a spike in neonatal deaths in a specific location with any other cause at all, to a very low degree of certainty (>5% confidence level).

Now it is true that there is more evidence than just a statistical spike: there were also specific forensic findings, documentation irregularities, and behavioural evidence that factor into the overall probability assessment. And the "reasonable doubt" standard isn’t purely mathematical — it’s about whether alternative explanations are reasonable given all available evidence, not just whether they're statistically possible.

In the absence of direct evidence, all circumstantial evidence amounts to an inference that makes the allegation more or less likely. In cases built on circumstantial evidence, what we’re doing is building a probabilistic case through multiple layers of inference. To be sure, you can’t precisely quantify it, but that is not to say it is not a question of probability. The prosecution’ compiles enough of these probability-modifying factors to cross the beyond reasonable doubt threshold, while the defence only needs to introduce enough doubt in any of these inferential chains to keep the total probability below that threshold.

This is why the “coincidence” argument is so central. The multiplication of improbable coincidences makes the innocent explanation vanishingly unlikely. But this reasoning is vulnerable to several statistical criticisms, such as the Texas sharpshooter fallacy and selection bias.

In the absence of compelling direct or even circumstantial evidence (and much of the forensic evidence has been strongly criticised) it comes down to probabilities. This is where Bayesian reasoning comes in: if you have direct evidence of actual direct harm, that changes the priors. If you don’t then really the prior probabilities are all you have.

And the absence of direct evidence over a sustained period in as heavily controlled, regulated and monitored an environment as a hospital, especially against a person who has no known expertise in serial murder and took no known steps to research methods of killing without leaving evidence, is telling in itself.

There is a kind of paradox here: the very absence of evidence over such a sustained period, in such a tightly monitored environment, against someone with no apparent expertise in committing these crimes let alone avoiding detection, becomes probative in itself. It makes the prosecution narrative require additional unlikely assumptions about extraordinary competence in evidence elimination that nothing else in the case supports.

This fits into a Bayesian framework because the probability of seeing a pattern of “no clear evidence” would be higher under “innocent” explanations — where of course there could be no such evidence — as against the murder hypothesis, where such evidence would potentially exist, so there would be a presumption that a tightly monitored environment would catch it. would expect some physical or direct evidence to emerge given the circumstances.

This is why, i think, the "letby is guilty" faction are at pains to de-escalate the importance of statistical analysis

Letby canards

• Admissions: Ms. Letby admitted someone was poisoning on the ward
• You weren’t there: If you weren’t at the trial you can’t know: “context is everything”, and guilt with events through a combination of interlocking facts. This is a kind of “emergence” argument. It is routinely run, ironically enough, by people who also were not at the trial.
• The Judgment: You haven’t read the Court of Appeal judgment so you can’t possibly know.
• Insulin inference: Regarding the “concrete” insulin evidence, the prosecution argued: “if the jury could agree that Letby had deliberately poisoned two babies, they could also reasonably conclude that she had harmed others using different methods even if the evidence in those cases was less concrete.”: (Sub point: some of those who criticise the trial were at the trial).
• Improbable cluster: The jump in annual deaths from three to seven and eight strongly indicates foul play: not according to the, er, statistics
• This case has nothing to do with statistics: Oh, but it is: this is the fundamental position that guilty case must defend, otherwise the whole case collapses. Factually, that is how the suspicion arose: initially the incidents were not considered suspicious: Nick Johnson KC: “as the deaths continued, with Letby present at every one, consultants realised she was the “common denominator”. So the statistics underlies all other evidence. The Bayesian priors all point away from Lucy Letby. It is the sine qua non of the case. Also an anchoring and confirmation bias. This is how the “Texas sharpshooter” fallacy starts.
• Circumstantial evidence: Circumstantial evidence speaks for itself — oh, there’s that confusion about probabilities again.
• Motivation of innocence campaigners: Innocence campaigners use the families’ grief to build their own reputations.
• Virtual red-hands: Letby was almost caught “virtually red-handed”, standing over the babies.
• Covered tracks: Ms. Letby “covered her tracks” by erasing data from hospital records. In particular, erasing records of Baby E’s mother’s visit and Ms. Letby’s own presence with the baby at the time of its collapse: there seems to be little direct evidence of this — it is inferred from incomplete hospital records or inconsistencies with witnesses who claimed to have been present (i.e., she must have altered them) — which is one explanation: another is that witnesses were mistaken or — given the allegation of under-resourcing and mismanagement, another (and most likely) is that the records were never made, or not kept.
• Circumstantial evidence again: It’s no big deal that the case is only about circumstantial evidence: Lots of people get convicted on circumstantial evidence alone. Differences between circumstantial cases where there definitely was a murder (e.g. David Bain) with circumstantial cases where there was not (Lindy Chamberlain). Witness the Thirlwall kerfuffle about extubation rates while Ms Letby was at the Royal Liverpool. How would extubation data arise? Presumably, it does not auto-generate, but is collected by those observing extubations—e.g., rostered nurses? Even if mandatory there is an element of discretion here: a diligent nurse would generate “worse” stats than a slipshod one. So —. (This is the problem with circumstantial evidence, in a nutshell: it does not “speak for itself” (pace Ken Macdonald KC) but requires an imaginative, narrative act of inference. The same data permits many, contradictory inferences. The difference is not the evidence, but your inference. Circumstantial evidence is not “facts”.)
• That judge’s direction: “You don’t need to be know how she did it as long as you are sure she did it”. There are different scenarios:
  1. Death definitely has 1 of 3 causes, the defendant definitely was responsible for all 3, jury need not be sure which of the 3 it was. Does not apply here: no direct evidence, no finite set of causes. Some natural causes.
  2. Death definitely has 1 of 3 causes, defendant definitely responsible for 2. Jury must be sure it was not the 3rd cause. Between the other 2, 1. above applies. Does not apply here for same reason as 1.
  3. Death definitely has 1 of 3 causes, defendant *may* have been responsible for all of them. If they do not know which it was, Jury must still be certain defendant was responsible for all three. Does not apply here: Same as 1 above. In Ms Letby’s case, there were an unknown set of possible causes, some innocent, some malign, it was not clear she was even responsible for the malign ones. Since you can’t rule out unknown innocent causes, if they don’t know how Ms. Letby committed the acts, the jury can’t be “sure” she committed them.

There’s no need to suggest anyone acted in bad faith. This is the essence of prosecutor’s tunnel vision: a series of cognitive biases lead into a logical cul-de-sac it is hard to get out of. The same biases can also apply to innocence campaigners. but the “guilty” campaign will find it harder to back out of their cul-de-sac. The innocence case commits only to the weak proposition that “there is reasonable doubt”. It is easy enough to walk that back. It is harder to resile from the proposition: “I have no doubt”.

Because of the co-dependency of the circumstantial evidence, the case depends on an all-or-none approach. The argument cannot stand case that Letby was responsible for some collapses, but not others, because evidence for the individual cases would not by itself discharge the burden of proof. That Ms Letby was somehow causative of collapses is a long way short of saying she wilfully inflicted them. She may have been causative by omission. By choosing the wrong option in an emergency situation. Perhaps her clinical practice was ineffective. Perhaps she was negligent — even reckless, in individual cases. The prosecution case obliges us, in those cases, to attribute to malice what is more probably caused by error.

Interlude

Probabilities are confusing things.

Say a nurse works, on average, 56 hours per week. she will be on duty for one-third of the week, or one shift in three. A year comprises 1095 eight-hour shifts. We would expect our nurse to work 365 shifts on average.

How safe is a guess that our nurse will work at least 25 shifts in the year? Yes, barring unexpected events, she almost certainly will. We can choose 25 shifts from the 365 she actually worked quite easily: We have 317,289,491,593,508,738,514,256,079,646,867,087,834 different combinations of twenty-five shifts! Still, that number is minuscule compared to all possible permutations of 25 shifts from the whole 1,095.

Which twenty-five? Well, there are a lot of choices. 365 is a much bigger number than 25, so we can see immediately the odds are very close to one.

The amateur expert serial murderer

The unit’s lead consultant Dr Stephen Brearey first raised concerns about Letby in October 2015.

No action was taken and she went on to attack five more babies, killing two.

— BBC website

On the face of it, the intensive care unit in a neonatal hospital — which must be as tightly controlled, monitored and overwatched as any place in Britain — is the last place you would embark on a regime of surreptitious serial murder. Better, surely to do it like Harold Shipman did, in the privacy of your consulting rooms, or better still, during a house call.

And once the hospital’s lead consultant had his own suspicions about the Nurse, you would think, she would be under even greater surveillance. Wouldn’t she? So does this not make the lack of direct evidence even more remarkable?

Caption text

Category	Daniela Poggiali	Lucia de Berk	Jane Bolding	Lucy Letby
“Incriminating” evidence	Took selfies laughing with dead body She had the ability to switch between wings of hospital Fiery temper, played pranks on colleagues Found patients irritating Allegations of thefts of jewellery	Example	Example	Googled parents That post-it note The increased insulin without corresponding C-peptide in 2 victims Had lots of teddy bears
Motive	“She must have just loved killing people”	Example	Example	Example
Actual evidence	Correlation between shifts and deaths	Example	Example	Correlation between shifts and deaths
Mitigants	Large ward many patients High proportion of very old and terminally ill patients Data collection was pretty ropey	Example	Example	Example
Alleged Method	Pottassium Choloride	Example	Example	Several
Resources	Richard Gill blog	Example	Example	New Yorker article We need to talk about lucy letby podcast

More Witches

{{quote| Peasant 1: We have found a witch may we burn her?
Peasant 2: Burn her!
Bedevere: How do you know she is a witch?
Peasant 1: She looks like one
Bedevere: Bring her forward.
Woman: I am not a witch
Bedevere:But you are dressed as one
Woman: They dressed me up like this
Peasant 1: We didn't!
Woman: And this isn't my nose it's a false one
Bedevere:Well?
Peasant 1: Well, we did do the nose
Bedevere: The nose?
Peasant 2: And the hat but she is a witch
Peasant 1: Burn her!
Bedevere: Did you dress her up like this?
Peasant 1: No.
Peasant 2: Yes.
Peasant 3: Yes.
Peasant 3: A bit. She has got a wart.
Bedevere: What makes you think she is a witch?
Peasant 1: Well, she turned me into a newt.
Bedevere: A newt?
Peasant 1: I got better.
Peasant 2: Burn her anyway!
Peasant 1: Burn her!
Bedevere: Quiet! There are ways of telling whether she is a witch.
Peasant 1: Are there? What are they? Tell us.
Bedevere: Tell me, what do you do with witches?
Peasant 1: Burn them!
Bedevere: What do you burn apart from witches?
Peasant 1: More witches!
Peasant 2: Wood.
Bedevere: So, why do witches burn?
Peasant 1: Because they're made of wood?
Bedevere: Good!
Bedevere: So, how do we tell whether she is made of wood?
Peasant 1: Build a bridge out of her!
Bedevere: Can you not also make bridges of stone?
Peasant 1: Oh, yeah.

David Holmes

JHB: what could have been the tell-tale signs that this woman was a danger? Was there anything that could have given us forewarning? Holmes: “Well, it may not give forewarning but generally speaking, [with] a serial killer of this stature really it’s almost obligatory to have psychopathic traits and they will often show themselves in various ways. ... she was very controlled. She was trying to give the image of a very responsible, caring nurse who would be there in a crisis to save babies and so on and so forth. So she is playing the role of someone who would not be suspected other than the correlation between her and the babies’ deaths.”

“It’s a situation where you have not got any really concrete evidence: one piece, like a CCTV camera footage or a witness, etc, all you’ve got is an accumulation of basically very low-level evidence — coincidences, etc — but when you actually accumulate a large number of these [using] something called a Bayesian analysis, it’s actually more statistically sound to have 100 little arrows pointing towards Lucy and none pointing away from her, and I think that’s how justice was actually reached.”

—Criminologist David Holmes on Sky News, 18 August 2023

Well, to a point. Bayesian analysis starts with a “prior probability” — an initial estimate of the likelihood that “Lucy Letby murdered multiple neonatal infants with no motive, no psychiatric history and no prior tendency” — which is extremely low — and adjusts it to a “posterior probability” on the cumulative effect of the “little arrows” to revise the likelihood of it being true. An accumulation of even weak “little arrows” can increase the “posterior” probability of the hypothesis, but if all the arrows are also consistent with another explanation, their contribution to updating a Bayesian analysis may be modest. There is significant potential for false positives when dealing with rare events and weak evidence. (Compare this with David Bain’s case, where the prior probability that he was the culprit was already high (the event was certainly murder, and he was one of only two plausible suspects), and the circumstantial evidence against him was strong, and Lindy Chamberlain, where the prior probability was very low, and the circumstantial evidence weak).

Prior and posterior probabilities in different cases

Case	There was a Murder		Suspect responsible		Another person responsible
	Prior	Posterior	Prior	Posterior	Prior	Posterior
OJ Simpson	Certain	Unchanged	Very likely	Greatly increased	Fairly unlikely	Unchanged
David Bain	Certain	Unchanged	Fairly likely	Greatly increased	Fairly likely	Greatly decreased
Peter Ellis	Very unlikely	Mildly increased	Extremely unlikely	Mildly increased	Extremely unlikely	Unchanged
Lindy Chamberlain	Very unlikely	Mildly increased	Extremely unlikely	Mildly increased	Extremely unlikely	Unchanged
Lucy Letby	Very unlikely	Mildly increased	Extremely unlikely	Mildly increased	Extremely unlikely	Unchanged

The question, then, is how many of the “little arrows” are inconsistent with another explanation. Here there are two categories of alternative explanation: that someone else was responsible, or that no-one was criminally responsible: the event would have happened anyway.

The prior probability of there being a different murderer on the ward is the same for any other nurse as for Lucy Letby: extremely unlikely. No suggestion was made that any other person was involved, so we can assume two alternatives: either an innocent explanation or Letby was the culprit.

It is worth also looking at the categories of circumstantial evidence in each case and associating it with one or other of those probabilities. Does it make it more likely that There was criminality involved in the deaths, or that, Assuming there was criminality, Letby was the culprit.

Relevance of evidence to probabilities

Evidence	Criminality		Letby was the culprit
	Relevance	Posterior value	Relevance	Posterior value
Ward roster	No	N/A	Yes	Contested
Post-it Note	No	N/A	Yes	Weak
Editing nursing notes to “cover tracks”	Yes	Weak	Yes	Contested
Post-event internet activity	No	N/A	Yes	Weak
“Trophy” handover notes	No	N/A	Yes	Weak
Bubbly personality	No	N/A	No	N/A
Obsession with a married doctor	No	N/A	No	N/A
Unexpected collapse	Yes	Weak	No	N/A
Insulin levels	Yes	Weak	No	N/A
Skin discolouration	Yes	Weak	No	N/A
Liver damage	Yes	Weak	No	N/A
Evidence of air in blood and brain	Yes	Weak	No	N/A

Interestingly, bar for the alleged editing of nursing notes, which case been oddly under-reported, none of the “small arrows” point to both the presence of criminality and Letby’s particular involvement. It is worth reviewing the published pieces of the chief “public prosecutors” who make the case for Letby’s guilt. Among these are the expert witness Dr Dewi Morris, Daily Mail Journalist Liz Hull, BBC Journalist Judith Moritz and the frequently interviewed Criminologist David Holmes. They are emphatic in their dismissal of the “yellow butterfly gang” — in Hull’s words, “diverse band of fanatics and pseudo-scientists” (later upgraded to a “strange band of misfits and ghouls”) coming from all “walks of society: well-to-do pensioners, middle-aged women, and the unemployed” and who, er, “counted scientists, neo-natal nurses, doctors and statisticians among their members” — so I was curious to see what they brought out as their clinchers.

Lizz Hull

Hull, on the New Yorker piece:

I’ve read the article and now the retrial is over I can write about it. And while there’s no doubting the author, who says she obtained full transcripts of the ten-month trial at huge cost, has researched the case thoroughly, it contains errors and cherry-picks evidence, omitting large parts of the prosecution case which was pivotal in reaching a conviction.

For example, it makes no mention of the 250 confidential “trophy” handover notes, blood test results and resuscitation notes relating to the babies police found at Letby’s home; it does not try to explain the Facebook searches that she made for the parents of her victims, years after she harmed their children.

Letby’s abnormal, animated behaviour in front of grieving parents after a baby died and pictures of cards she sent or received from parents of babies she murdered that were stored on her mobile phone, are also ignored, as is her obsession with a married doctor and her deliberate editing of nursing notes to make it seem like a baby was on the verge of collapse to cover her tracks.

In a later article on 24 July 2024 — the first one evidently not having the desired effect — Hull sets out the overlooked evidence that proves the conspiracy theorists (although they are better described as “no conspiracy theorists”) wrong.

Sewage and insulin

• No evidence was presented to show any of the infants contracted bacterial or parasitic infections linked to dirty water caused by drainage problems.
• Though journalists have since queried the suitability of the insulin tests for use in a criminal prosecution, the defence team did not.

Concession that the insulin was deliberate

The Court reporting suggests this was less emphatic than it has been made out to be:

Letby is asked if Child E was poisoned with insulin.
“Yes I agree that he had insulin.”
“Do you believe that somebody gave it to him unlawfully?”
“Yes.”
“Do you believe that someone targeted him?”
“No.”
“It was a random act?”
“Yes...I don't know where the insulin came from.”
“Do you agree [Child L] was poisoned with insulin?”
“From the blood results, yes.”
“Do you agree that someone targeted him specifically?”
“No...I don't know how the insulin got there.”
Letby adds: “I don’t believe that any member of staff on the unit would make a mistake in giving insulin.”

Liver injury

One of the babies suffered significant liver trauma. The post-mortem said the bleed was due to vigorous CPR, but a forensic pathologist from told the jury he’d only ever seen this type of extensive internal injury in children involved in road, trampolines cycling accidents, or who had been deliberately assaulted.

Letby accepted in evidence that the injury took place “on her watch”.

Air in stomachs

The Guardian reported that seven anonymous neonatologists called Dr Evans’ theory about the injection of air into the stomach via nasal feeding tubes “ridiculous”.

Dr Evans admitted to me that injecting air in a nasogastric tube is “utterly bizarre” and something he’d never heard of before. But he added: “That doesn't mean it can’t exist.”

The shift rota

The infamous shift rota chart was not created after the fact, so the “Texas sharpshooter” argument falls over. Dr Evans reviewed all cases bar one were looked at “blind” months, before Letby’s name was disclosed to him.

Dr Evans says Cheshire police did not put together the shift graph until he had identified suspected cases. Only when officers cross-checked those events with staff on duty did the striking pattern of Letby’s presence emerge.

The rash

The argument that prosecution expert witnesses misdiagnosed a rash based on misreading Dr Shoo Lee’s 1989 report on the air embolism phenomenon. Dr Lee told Letby’s appeal he believed the rashes were not diagnostic of the condition.

But Dr Lee did not have access to the medical notes or witness statements when making this assessment and his evidence was ruled inadmissible.

The screaming

Hull describes “harrowing testimony of parents, doctors and nurses” of uncharacteristic “screaming” from several of the premature babies, who likely suffered extreme pain.

Letby, the Prosecution said, had rammed a medical instrument down the boy's throat moments earlier, causing internal bleeding. She later injected him with air to kill him.

Letby’s behaviour

On one occasion Letby told a colleague a baby “looked pale” when no lights were on in the nursery, and her face was obscured by a canopy. That child had stopped breathing but was resuscitated only to die by alleged air injection the next day.

The cards, googling and condolences.

Bayesian probabilities applied to other questions

As Tom Chivers notes in his excellent Everything Is Predictable: How Bayes’ Remarkable Theorem Explains the World, a fellow newly armed with Bayesian techniques is the proverbial “man with a hammer”: once you learn how to do it, it is hard to resist applying it to all kinds of questions not usually seen as the domain of statistics.

For example: miscarriages of justice are, as far as we know, extremely rare: those in the population of murder convicts across history — which surely numbers in the millions — who were justly convicted enormously outweigh those who were unjustly convicted, which we can put in the hundreds or thousands (Wikipedia lists just fifty-four). This might lead to the conclusion that a person who has been convicted by a jury is, ipso facto, highly unlikely to be innocent: that is, after all, the fundamental design goal of the justice system.

But the number convicted of “medical carer serial murders” in history is also small. According to Wikipedia, of nearly 800 serial killers fewer than 60 were medical carers, of whom two-thirds admitted their crimes. Serial murder is rare. Medical carer serial murder is even rarer.

But amongst Healthcare serial murder cases, miscarriages of justice are comparatively common. There are at least five recent examples, all strikingly similar:

• Lucia de Berk: A Dutch nurse wrongly convicted of multiple murders due to statistical errors and misinterpretation of medical evidence. Her conviction was later overturned.
• Susan Nelles: A Canadian nurse accused of murdering infants; charges were dropped due to lack of evidence.
• Ben Geen: A British nurse whose conviction for murdering patients by inducing respiratory arrests was quashed on appeal due to unreliable evidence.
• Colin Norris: A British nurse convicted of murdering patients by insulin injection; his conviction was later overturned due to flawed medical evidence.
• Daniela Poggiali: An Italian nurse accused of murdering patients in a hospital. She was initially convicted but later acquitted on appeal due to a lack of conclusive evidence.
• Jane Bolding: A British nurse accused of murdering patients in her care. She was acquitted after a retrial due to lack of evidence.

The relatively high proportion of miscarriages of justice among “hospital carer” cases raises the “posterior probability” that a given conviction of this type might be wrongful by comparison with other types of murder case where such errors are historically less common.

The multiple modus operandi

An unusual feature, compared with even other hospital carer serial killer cases is the variety of ways by which Letby is alleged to have murdered, or attempted to murder, the children.

• Insulin in intravenous bags
• Injection of air into bloodstream
• Injection of air into stomach via gastric tube
• Dislodging feeding tube
• Liver trauma
• Overfeeding by milk

Two points of significance here: first, serial killers generally develop and stick with a single modus operandi, refining a technique that “works” and avoids leaving evidence or allowing for detection. Leaving no evidence is hard. Second, the more different routes one uses, the more scope there is for evidence or detection.