Lucy Letby, Damn Lies and Statistics

Lucy Letby may not be guilty after all. The case began with and relied on a dodgy statistical association between Letby’s presence and a series of infant deaths and serious incidents. But one aspect that has not been discussed a great deal is whether the cases of twins and triplets on Letby’s charge sheet imply a lesser or greater likelihood of natural causes being the most likely explanation for the series of deaths and incidents.

Like the vast majority of UK news consumers (or news junkies in my case), I believed until recently that Lucy Letby was a serial murderer. I had a sliver of doubt when I saw a friend standing by her – were she indeed guilty, I thought, then surely her friend would know her well enough to understand that she probably was. I’d heard about an article in the New Yorker and vaguely remembered some other articles questioning the verdict, but hadn’t paid the case a great deal of attention until last week.

Then I saw a Twitter ad for Part 3 of a discussion of the case by Private Eye’s “MD”, who I consider to be a reliable authority on medical matters. I rummaged around, found the last few Eye editions amongst my papers, and was soon convinced injustice had been well and truly done in the Letby case.

I was incensed.

For years I and it seems most of the British public had been led to believe that terrible crimes had been committed.

And I really hate being misled.

Especially when the misleading involves emotional manipulation.

There’s a word for that these days – we’ve all been gaslit.

Besides, what’s happened to Letby is nothing short of tragic.

I’ll save more thoughts on the multiple systemic failures of the UK’s “world-beating” medical, policing and judicial systems for another post, but one aspect of the data struck me. The cases Letby was charged with included more than one instance of two or more multiple birth neonatals. E.g. (see this table) babys A (allegedly murdered) and B (“attempted murder”) were twins, and O and P, who both died, were triplets.

I started looking at the data in more detail, but then wondered if someone else had already done a similar exercise. The useful essay at triedbystats.com led me to a Science on Trial case discussion which notes that:

“Another important point to consider is that three sets of twins and one set of triplets are among the neonates in the table and that, regarding these cases, Lucy Letby was found guilty of murder or attempted murder. Where both twins experience adverse health events in a similar timeframe one would assume that such events are due to shared physiological aetiology, thus the two deaths are not statistically independent.”

and goes on to mention the infamous Sally Clark case, where a mother was convicted of causing the deaths of two infants on the basis of the likelihood of sudden infant death syndrome (SIDS) being independent for the two (as argued by the subsequently struck off pediatrician Roy Meadow), whereas, as Science on Trial puts it:

“It was well known from epidemiological data that SIDS tends to run in families, perhaps due to genetic or environmental factors.”

So I decided not to delve further into the detail and instead think about the logic of the situation in the Letby case. Because that’s what I do.

To restate the point, if the deaths and “collapses” (alleged attempted murders) in the Letby case were a result of natural causes, we would expect a positive correlation between the outcomes for babies in the same multiple births. Such babies share the same genes (100% if they are identical twins or triplets etc), the same mother (which implies numerous factors in common, which I’m not qualified to go into) and have experienced very similar environments since birth.

Indeed, there may be a non-random time distribution of fates of babies in a neonatal unit (or patients in any other healthcare setting for that matter) – i.e. clustering of deaths and collapses – as well as the sibling correlation, due to factors such as infections and changes in staffing.

But sticking with the point about twins and triplets, it would be possible to determine whether there is an empirical (and quantifiable) correlation, as well as a theoretical one. That is, in Letby’s neonatal unit at the Countess of Chester Hospital, was a twin or triplet more likely than another baby to die or experience a serious adverse incident if a sibling had already done so? What about among Letby’s patients? Presumably she was responsible for many more babies than those that she was charged with murdering or harming. Was Letby supposedly harming twins or triplets more than unrelated babies?

It would also be very interesting to look at the patterns of deaths at (for example) the 11 hospitals listed on triedbystats.com as having had a greater increase in neonatal deaths from 2014 to 2015 than at Countess of Chester. Though, obviously, discussing those hospitals might not be possible due to sub judice rules, given that they must all surely be the subjects of intensive, if somewhat belated, police homicide investigations.

Let’s suppose that the outcomes for the twins and triplets in the Letby charge sheet is correlated in a way that might be expected if the deaths and collapses were due to natural causes, then how would the prosecution explain that?

Would they argue, perhaps, that Letby was particularly fixated on harming siblings? And that this led to data that just happened to resemble a pattern that might be typical of natural causes?

Or would they perhaps suggest that Letby was aware that siblings might experience similar problems (which she was – I read somewhere [reference to be added if I find it again] that she was worried about baby P, who did subsequently die, because they were an identical triplet to baby O) and harmed them as well to make the data look realistic?

Either way a problem with the entire case against Letby is exacerbated. For her to be guilty we have to suppose that she is a master criminal, able to deploy not just one but a variety of methods to harm babies in her care, all without being observed by colleagues or detected as foul play in post mortems.

If she managed to preferentially harm siblings, then she must also have been able to accomplish this feat at times of her choosing, rather than merely opportunistically.

Letby continues to protest her innocence, so in the increasingly unlikely event that she is actually a murderer, we can presume that not being detected was very important to her. You’d imagine that would have constrained her ability to harm particular babies.

I’d be very interested if someone more expert than I am is able to review the Letby multiple birth data to see whether it does indeed tell us any more about what is looking more and more like a gross miscarriage of justice.