Talk:Lucy Letby

Doubt

Whatever the reason for it, a lack of direct evidence of the defendant’s foul play — of any foul play — means there will always be some doubt. No one saw anything. Inference is needed. The question is whether the inference is justified. Has the prosecution done enough to remove all reasonable doubt?

In some types of crime — burglary, say — we should expect no direct evidence: competent burglars target unmonitored environments where there are no witnesses.

Burglars, we fancy, would steer well clear of the intensive care unit in a neonatal hospital. For there could hardly be a worse environment to get away with crime. Entries and exits are monitored and audited. Medicine is logged, controlled, secured and signed in and out. Medical experts conduct routine rounds and check on patients around the clock. Biochemistry is complex and its signals are delicate. There are specialists at hand with deep expertise and sophisticated machinery who can detect the merest traces of the unusual or sinister.

So the lack of such evidence is a curious feature of the “healthcare serial murder” cases. This one is no exception. No-one saw Ms. Letby doing any harm.

Avoiding eyewitnesses, let alone forensic detection, would require great skill, caution and planning. You would expect a malign perpetrator to refine and perfect a careful technique — a modus operandi — and stick with it.

You would not expect a skilful murderer to make opportunistic attacks, to use multiple, unrelated methods or to improvise on the spot to suit the circumstances.

Certainly not one under active suspicion. The hospital’s lead consultants raised concerns with management about Ms. Letby as early as October 2015.

Yet this is what Ms. Letby is supposed to have done, and still left no implicating evidence. Over 13 months, Ms. Letby is alleged to have variously injected air intravenously, injected it via nasogastric tube, caused blunt force trauma to internal organs (quite how, is not clear), overfed with milk, dislodged breathing tubes, poisoned with insulin, and physically throttled.

Ms Letby was described in the court as premeditated, calculating and cunning, using a number of different methods, thereby misleading clinicians into believing the collapses had a natural cause.

Perhaps — or maybe the collapses did just have a natural cause. There is one other germane feature of an intensive care unit: visitors tend, by unfortunate necessity, to be very, very sick. They have an unusually high probability of dying. If they did not, they would not be there.

Onus

And that is a heavy onus. Between prosecution and defence it is not a straight fight: the prosecution must prove its case beyond reasonable doubt. If it is incumbent on a defendant to prove anything — technically it isn’t, but practically it would be a brave defendant who did not — it is simply that there is some credible doubt.

When a seriously ill patient dies in intensive care, even unexpectedly, and nothing beyond mere presence implicates any perpetrator, there is credible doubt.

For each of the Countess of Chester collapses taken in isolation there is reasonable doubt that the victim was the subject of foul play, let alone that Ms. Letby was responsible for it. Indeed, foul play was not initially suspected in any of them.

How can a series individual cases which have reasonable doubt turn into a collection of cases where there is none?

Probability

Once is happenstance. Twice is coincidence. Three times is enemy action.

—Ian Fleming, Goldfinger

The answer is probability.

It is sometimes said that Ms. Letby was “not tried by statistics”. A case depending on circumstantial evidence is necessarily about probabilities. The “probative value” of circumstantial evidence is: “Does this make it more or less likely that an event, which no one witnessed, happened?”

Statistics are not always an appropriate lens to assess probabilities, especially where data are limited or collected in unusual circumstances. But the shift data are statistics. The Crown may not have framed its arguments about them in those terms, but its arguments were statistical: the shift data have no probative value other than as statistics.

Now: flip a fair coin once and heads is as likely as tails — that’s “happenstance”. Flip it twice and while two heads are less likely there is still a one-in-four chance — that’s “coincidence”.

But flip it twenty-five times and you have a less than one in thirty million chance of getting twenty-five heads. If you get this result, it is most unlikely your coin is “fair”.

This is why the shift data is so important: it is the equivalent of a string of twenty-five coin flips that all came up heads. It can dispel those “credible doubts” in individual cases: okay, one collapse may have been innocent. Two, a coincidence. But twenty five?

If there is a single clinching argument in the evidence presented against Ms. Letby, this was surely it.

But it only holds if the flips really were consecutive: flip a coin fifty times and you would expect to get about twenty-five heads.

And here we come to the statistical problems with the shift data. The shift data presented to the court is a small selection from a much bigger sample of over 700 shifts in the period listing only the events for which Ms. Letby was charged. These all occurred, Q.E.D., while she was on duty. The chart selects just the twenty-five data points that support the prosecution case.

Cue a torrent of criticism from statisticians, much of it summarised in Rachel Aviv’s New Yorker article. For here we run across the “Texas sharpshooter” fallacy. Is this all the incidents? Were there others? What even counts as an “incident”?

The other deaths and incidents

The twenty-five incidents listed in the shift rota represented only those incidents for which Ms. Letby was charged and at which, of course, she was on duty. The chart demonstrates only that “when Ms. Letby was on duty, she was on duty,” and no other nurse was on duty for every shift on which she was on duty.

Whether these really are “consecutive flips of a coin” depends on whether Ms. Letby was rostered on for all unexplained collapses. We know there were ten deaths in the period for which she was not charged. We do not know why. A few commentators have claimed to have seen evidence that Ms. Letby was on duty for every death in 2015-6——but that supporting evidence has not been made public, and nor was it presented at trial.

We do not know whether Ms. Letby’s shifts coincided with these other events. Had prosecutors submitted a list of every shift in the thirteen-month period, and marked every incident in that period, we might have a better story. But they did not.

The prosecution hints blackly that “further charges may be forthcoming” but really? Is nine years not enough to make up your mind? How much longer will they need?

On tonewood and prosecutor’s tunnel vision

Triago: Ho, Ho.
Let not thy witty fool, nor his foolish wit
Besmirch the fruited science of th’ academy.
“A little learning is a dangerous thing” —

Nuncle: Yet not half so dangerous as a lot.

Triago: — So sayeth Pope, you know.

Nuncle: But not the one in Rome:

Queen: Good ser knight: art thou drunk upon the Pierian spring:
A hypoxic draft that suffocates the brain,
So deep no shaft of light can bring it round again?

Triago: My conjecture comports a grain of truth
As pure and true and golden—

Nuncle: — but yet no more roundly causative
Than are the month-past flappings of a Latin papillon
Upon a brewing Filipino typhoon.

JC has, elsewhere waxed long and lyrical about the collection of cognitive biases called prosecutor’s tunnel vision. These biases tend to show up where clinching evidence does not: if there were any clinchers, things would be clinched. Therefore those prosecuting — and, for that matter, defending — start to fixate on finer and finer technical details to win isolated arguments. Once one side goes down a rabbit hole, the other is obliged to follow. Insulin assay tests, entry card swipe data, the significance of skin discolourations — all have been cited as smoking guns for prosecution and defence when they are transparently nothing of the sort.

The fact is, there are very few political, social, and especially personal problems that arise because of insufficient information. Nonetheless, as incomprehensible problems mount, as the concept of progress fades, as meaning itself becomes suspect, the Technopolist stands firm in believing that what the world needs is yet more information.

—Neil Postman

Information is fractal. The more you look at it, the more you can create: it subdivides infinitely — there is no bottom — and the more raw information you create, the more possible arguments you can have about it. This is the implication of information theory: the more data points there are, the more unique patterns you can make from them. If we take it that a theory is simply “a pattern of consistent data drawn from available information from which we can draw a valid inference” then the more information you have, the more plausible alternative theories of the case you can make.

In other words, you cannot win an argument by simply descending further into the weeds. Those who have drunkenly debated evangelical Christians, resolute atheists, real ale connoisseurs, or tonewood freaks — JC has done all of these — will know this. The thing about descending into the oubliette is that as the points atomise, the arguments grow more heated and the less difference they can possibly make.

This is the “tonewood” debate in a nutshell: sure, in theory the harmonic resonance of nitrocellulose varnish could affect the sound of an electric guitar, but not so as a mere human could possibly hear it in perfect conditions let alone in the moshpit at the Roxy on a sweaty night in 1976.

Whatever did make Steve Jones’ Les Paul sound like a screaming chainsaw, that is, it wasn’t the varnish.

Zeroing in to draw further inferences will not help. The only way to do it is by zooming out.

Oh come on ref

It is a common enough trajectory: we start with an instinct that, a popular, diligent, young, female nurse from a stable background is the last person you would expect to be a serial murderer. We might chide ourselves about our unconscious bias in favour of such individuals and remind ourselves that since this kind of intuition is not scientific, let alone evidence, we must set it aside and consider the circumstantial evidence as it accumulates on its merits, and “without prejudice”.

But hold on: if we regard purely circumstantial evidence as “evidence that changes the prior likelihood” of the event: evidence that changes the reasonable inferences we would otherwise draw from the baseline facts — then in as much as a defendant’s background and socialisation and mental health reflects a basic statistical likelihood our intuitions are useful. They are, indeed, circumstantial evidence.

All else being equal, how likely is it that a person selected at random is a serial murderer? Needless to say, extremely unlikely. Serial murderers are already very rare in the general population. Wikipedia records 70 in Britain since 1255. Let’s conservatively put the total number of inhabitants in the UK since 1255 at 100m: this makes the incidence of any (known) serial murderer at a bit less than one in 2 million.

Now: what sort of person is more likely to commit serial murder? Overwhelmingly, male: 61 out of the seventy. Male, criminal history, a history of violence or deprivation and diagnosable psychiatric condition.

We may not be able to assign precise probabilities to them, but we can legitimately ask, where there is no direct evidence of actual wrongdoing, what is the probability that a young female professional with a healthy social life, a stable and affluent background, a good circle of friends and no history of criminality, deprivation, instability or mental illness and no motivation — no “criminal propensity” at all, in other words — will, without warning, transform herself into a calculating serial murderer. We can see this probability is very, very low.

concerning only probabilities, then there is a “mathematical” way of articulating what seem to be “biases” of our own: 

, but has some basis in probabilities. She is the last person you would expect. The prior probability here is about as low as it could possibly be.

Then

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

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!

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.