Correction to a correction of a statistical error

Dear editor,

This is a response to a recent letter by Dr S. Shuster, ¹ published in the journal, and that takes issue with my work. Firstly, let me express my appreciation to Dr Shuster for taking an interest in this work.

That said, for such a short letter, there are a surprising number of errors. We could begin with my name which is misspelt but, far more importantly, the paper, Suspected Serial Killers and Unsuspected Statistical Blunders is cited in error. There are no calculations of any kind in that paper related to the question of nurse Letby's presence and suspicious events. The only calculations there focus entirely on the issue of the believed spike in the observed death rate. Since none of the calculations deal with the question of the nurse's presence when suspicious events take place, it is quite impossible for Dr Shuster to show, as he claims he does, that those calculations are erroneous. They cannot be erroneous since they do not exist.

We might then find Dr Shuster's claim to be most puzzling, if not for a second paper, also written by myself, called ‘Logical and statistical errors in the investigation and prosecution of suspected serial killer nurses’. Unlike the incorrectly cited first paper, this second paper focuses in some detail on the question of nurse Letby's presence when believed suspicious events took place. We can fairly assume that it is this second paper motivating Dr Shuster's reaction, a paper that was submitted to the same journal but that was rejected as unsuitable for publication.

It would also be fair to assume that Dr Shuster would agree with that editorial decision since not only does he dispute my findings, he takes a very strong position stating that ‘O’Quigley's paper should be withdrawn’. Given Dr Shuster's confusion over the two papers, I see no reason to defend the published paper since it does not seem relevant. Let me simply state that I fully stand by the arguments and conclusions of the published paper. I will however address the points he makes concerning the unpublished manuscript ‘Logical and statistical errors in the investigation and prosecution of suspected serial killer nurses’.

Dr Shuster's first argument is that my paper (not the one he cites) aims to support my belief that the association of Letby's presence and the unanticipated events could have occurred by chance. I have never claimed any such thing, not in any paper nor in any discussion on the topic. Indeed, it is very clear that the opposite is true; the association, which appears to be strong, has nothing at all to do with chance. We do not disagree there. The question – one I do discuss in the paper – is which one of two explanations could be behind that observed association. The first, very superficial, but immediate explanation is that the actions of nurse Letby are behind the observed events. The second explanation, one that is readily demonstrated, is that the association is no more than the direct fruit of cherry picking. Those cases that involved the nurse were the ones that were selected. This is now well established by several authors and not just myself.

Dr Shuster then claims to show that my ‘underlying calculation is erroneous’. Yet he does not show anything to be erroneous and we have simply no idea at all as to which calculation is being referred to. He supports his assertion by mentioning ‘a failure to appreciate biological differences’ but, whatever that may mean, it is not a calculation. And once more, Dr Shuster states that my argument that Letby's supposed presence was due to chance is incorrect due to the singularity of the deaths. Well, two things there. Firstly, as I have already pointed out, I have never said that this supposed presence was due to chance, and at the risk of becoming tedious, it is clear that the opposite is true. I will not repeat the argument of the previous paragraph. Secondly, any death is singular and the deaths that we are describing here would be no exception.

Dr Shuster's reference to a study of some 1516 neonatal deaths and the percentage of them considered unexplained would seem much less relevant than the findings of the two neonatal pathologists in the case itself. They only found one unexplained death and all the rest were evaluated as being through natural causes. Regardless, whether particularly singular or not so singular, none of that is relevant to the issue of Letby's presence and what might be the reason for the observed association. Happily, both Dr Shuster and myself fully agree with the final sentence of his letter, that ‘Letby's presence at the baby deaths could not have been by chance’. He is correct on that: it was due to selection bias, a term used by epidemiologists, in this case, the very strong degree of cherry-picking. There were many deaths and unexplained collapses at which nurse Letby was not present but the nurse's accusers and the police decided to ignore those. Moreover, we are learning through the media and the Thirlwall Inquiry just how reliant Cheshire Police and their lead medical investigator Dr Evans were on the clinicians to select cases to appraise, rather than bringing in an epidemiologist to conduct a thorough, objective investigation of all possibilities and all incidents, whether during the period of elevated mortality or outside of it.

Other assertions in Dr Shuster's letter ‘But the murdered babies didn’t die ordinary deaths: they were in a stable condition, and the deaths were sudden and unexpected’ have been very robustly challenged by a growing number of scientists. The babies were not in a stable condition. And, despite any convictions, the two papers referred to provide yet more support to the belief of several leading neonatologists and statisticians that there was no evidence that any murder ever took place.