Lucy Letby’s supposed non-randomness
Lucy Letby has been convicted of a series of murders and attempted murders that were clustered in time. If she is guilty why would she draw attention to herself in this way?
The Lucy Letby case perhaps reveals that many well-educated – perhaps “much educated” might be a better term – health, police and legal professionals struggle with statistical concepts.
But when we start to consider the randomness or otherwise of events we’re clearly on a whole new level.
There’s an interesting discussion in a Mephitis blog post of how the deaths in Letby’s neonatal unit at the Countess of Chester Hospital (COCH) may not have been random, even once those Letby was charged with are discounted. Unfortunately, I had issues with the analysis, so can’t yet accept the conclusion. I added a comment but it is not yet approved, let alone responded to:
“Interesting and you may be correct in suggesting that even once the cases attributed to Lucy Letby are excluded the data does imply the likely existence of some other causal factor, though I agree with Stephen Senn’s point that it is invalid to say:
“…there is a 20,844 in 20,845 probability (99.9952%) that the nine did not occur by chance…”
Unlikely events do occur. Some people do win the lottery. Some neonatal nurses are on shift when a relatively large number of deaths occur.
David Liv’s point that:
“Several of the infants/neonates in the LL case were twins or triplets, who might well share health issues reducing (or increasing) survival chances.”
is also valid and complicates any statistical analysis of the data – I’ve written about this at https://timjoslin.org/index.php/2024/09/04/lucy-letby-damn-lies-and-statistics/ .
My question is, is it valid to “calculate the expected number per month… based on the average outside of the nine month period in question (the answer is 0.18 per month)”?
If the null hypothesis is that the deaths are randomly distributed, then surely all deaths should be included to determine the expected number per month, i.e. we need to calculate the average for the entire period, including July 2015 to March 2016.
Not including July 2015 to March 2016 in determining the expected death rate assumes the deaths over that period did not occur by chance, but what we’re trying to establish is the probability that they did occur by chance.
Notwithstanding this quibble, this sort of analysis is very useful.”
Comparing the death rate from July 2015 to March 2016 rather than for a whole year also risks the accusation of cherry-picking. Nevertheless, Mephitis’s point that the data suggest factors other than (allegedly) Letby causing excess deaths at COCH is worth noting. As Mephitis asks, what are the chances of that and a serial killer operating simultaneously?
But following my previous post, I’ve been pondering on the apparent non-randomness of the dates of the murders and attempted murders attributed to Letby:
In the very unlikely event that she was deliberately harming babies why would Letby draw attention to herself by committing crimes very close together in time? The previous post noted that at least some of the alleged victims of these were multiple birth siblings, who might have genetic and/or environmental pathologies in common.
And it was the clusters – both involving siblings – that led to action being taken against Letby: Brearey first raised concerns on 2nd July 2015 and according to the Guardian’s summary the “…’tipping point’ comes following the unexpected deaths of Child O and Child P.”
Again, I would have thought there is some onus on the prosecution to explain why Letby would have a pattern of harming babies in a way that would draw attention to herself, and provoke emotional reactions from (some) colleagues.