Talk:Lucy Letby

Alleged Method

• Potassium Chloride: easily available, easy to administer, kills quickly, quickly dissipates and is hard to detect.

Resources

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

Peasant 2:

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.
Bedevere: Does wood sink in water?
Peasant 1: No. It floats! Throw her into the pond!
Bedevere: What also floats in water?
Peasant 1: Bread.
Peasant 2: Apples.
Peasant 3: Very small rocks.
Peasant 4: Cider.
Peasant 5: Cherries.
Peasant 6: Gravy.
Peasant 7: Mud.
Peasant 8: Churches.
Peasant 9: Lead.
Arthur: A duck!
Bedevere: Exactly. So, logically —
Peasant 1: If she weighs the same as a duck, she's made of wood.
Bedevere: And, therefore?

Peasant 1: A witch!
Peasant 1: A witch!

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.

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.

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 medical care 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.