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arxiv: 2606.29394 · v1 · pith:KUYPHTANnew · submitted 2026-06-28 · 📊 stat.AP

Critique of "Use of roster charts in the investigation and prosecution of nurses ..." by John O' Quigley

Richard D. Gill This is my paper

Pith reviewed 2026-06-30 02:06 UTC · model grok-4.3

classification 📊 stat.AP
keywords roster chartsstatistical analysisnurse investigationsforensic statisticsmodelling assumptionsLucy Letby caseprosecution evidence
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The pith

The data on 37 nurses strongly disproves the main modelling assumption in O'Quigley's roster chart analysis.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines O'Quigley's hypothesis that statistical information hidden in the roster chart for 37 other nurses can inform investigations of deliberate harm by nurses. It identifies serious errors in the statistical analyses and shows that the actual data strongly disproves the central modelling assumption. The authors agree that the roster chart constitutes fake evidence that should not be presented to jurors. This matters because it questions the reliability of statistical interpretations used in legal proceedings involving medical staff.

Core claim

O'Quigley's paper explores an interesting hypothesis concerning statistical information hidden in the roster chart for the 37 other nurses, but the data actually contains information which strongly disproves his main modelling assumption. Serious errors exist in the statistical analyses. From a forensic statistical point of view, the roster chart is fake evidence which should not have been shown to jurors.

What carries the argument

The main modelling assumption about hidden statistical information in the roster data for the 37 other nurses, which is tested and disproved by the actual roster data.

Load-bearing premise

The roster data for the 37 other nurses provides a valid and sufficient test of the modeling assumption used in the critiqued paper.

What would settle it

Recomputing the statistical tests on the roster data of the 37 nurses and finding consistency with the original modelling assumption instead of strong disproof.

Figures

Figures reproduced from arXiv: 2606.29394 by Richard D. Gill.

Figure 1
Figure 1. Figure 1: A chart believed to show a strong statistical correlation between the presence of nurse 23 and suspicious events. The visual impression that ignores bias is very strong. 2 Medicine, Science and the Law 0(0) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The histogram of the raw data for the presence of the unsuspected nurses. we can easily see the effects of time dependence, as well as another characteristic of the shifts: day shift, or night shift. During the daytime (and especially on weekdays), a number of nurses are doing administrative duties. Day or night, weekend or weekday, roughly the same number of nurses are actually allocated personally to the… view at source ↗
Figure 4
Figure 4. Figure 4: Our next step is straightforward and amounts to sam￾pling a probability of presence from this distribution and then deriving the distribution of presence under a binomial assump￾tion and a sample size of 61.The result is shown in [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 4
Figure 4. Figure 4: Histogram of a sample of size 38 from O’Quigley’s fitted beta distribution, with the estimated density superimposed. The total area of the bars equals the total area under the curve. fairly explicit instructions, something very odd happened: the maximum likelihood fitting algorithm failed to find a solution. The likelihood was apparently maximised at the boundary of the parameter space, where α and β both … view at source ↗
Figure 5
Figure 5. Figure 5: The expected deaths series are derived by combining three data series: a) generic mortality risk by birthweight and gestational age b) CoCH births distribution by birthweight/gestational age assuming in line with general distribution (adjusted in 2013-14, 2015-16 and 2017-22) c) CoCH actual number of births. It is designed to show the high sensitivity of mortality to small shifts in birthweight/gestational… view at source ↗
Figure 6
Figure 6. Figure 6: The present author considers himself also as an [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
read the original abstract

The paper "Use of roster charts in the investigation and prosecution of nurses suspected of inflicting deliberate harm on patients" by Prof. John O'Quigley explores an interesting hypothesis concerning statistical information hidden in the part of the infamous Lucy Letby roster chart pertaining to the 37 other nurses. Unfortunately, we have to point out some serious errors in his statistical analyses. The data actually contains information which strongly disproves his main modelling assumption. We do, however, strongly agree with him that from a forensic statistical point of view, the roster chart is fake evidence which should not have been shown to jurors.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript critiques Prof. John O'Quigley's analysis of roster charts in the Lucy Letby case. It asserts that roster data from the 37 other nurses contains information that strongly disproves O'Quigley's main modeling assumption while agreeing that the roster chart constitutes fake evidence unsuitable for jurors.

Significance. If the claimed disproof of the modeling assumption is valid and the 37-nurse data provides a properly calibrated test, the result would be significant for forensic statistics by demonstrating that roster-based models can be falsified by exchangeable data and by reinforcing warnings against presenting such charts in court. No machine-checked proofs or reproducible code are mentioned.

major comments (1)
  1. [Abstract] Abstract: the central claim that 'the data actually contains information which strongly disproves his main modelling assumption' is load-bearing, yet the manuscript provides no indication that the three conditions required for this inference have been checked: (a) exchangeability of the 37 nurses with the conditions under which the assumption was formulated, (b) attribution of observed deviations to falsity of the assumption rather than differences in shift frequency, patient load, or recording practices, and (c) calibration of the chosen test statistic for the forensic null. Without these verifications the disproof does not follow.
minor comments (1)
  1. [Abstract] The abstract states agreement that the roster chart is 'fake evidence' but does not specify the statistical or legal criteria used to reach this conclusion; a brief clarification would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful and constructive review. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'the data actually contains information which strongly disproves his main modelling assumption' is load-bearing, yet the manuscript provides no indication that the three conditions required for this inference have been checked: (a) exchangeability of the 37 nurses with the conditions under which the assumption was formulated, (b) attribution of observed deviations to falsity of the assumption rather than differences in shift frequency, patient load, or recording practices, and (c) calibration of the chosen test statistic for the forensic null. Without these verifications the disproof does not follow.

    Authors: We agree that the manuscript does not contain an explicit verification subsection for the three conditions. The 37 nurses are taken from the identical hospital roster and observation window as the index case, which supplies exchangeability by construction under the modeling framework. Observed deviations are attributed to the modeling assumption because the nurses share the same shift patterns, patient assignments, and recording protocols; any residual differences in frequency or load are already encoded in the empirical distribution used for the test. The test statistic is calibrated directly against the 37-nurse empirical null, which is the natural forensic calibration. We will add a short subsection in the revised manuscript that spells out these justifications and, where possible, supplies supporting tabulations from the roster data. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claim rests on independent data re-examination

full rationale

The paper asserts that roster data for the 37 other nurses contains information disproving O'Quigley's modeling assumption, presented as an empirical observation from the data rather than a fitted parameter renamed as a prediction or a self-referential definition. No equations or derivations are shown that reduce claims to inputs by construction, and the provided abstract invokes no self-citations as load-bearing support for the disproof. The analysis is therefore self-contained against the external roster data and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the validity of the roster data interpretation and the original modeling assumption; no free parameters, axioms, or invented entities are introduced by this critique paper itself.

pith-pipeline@v0.9.1-grok · 5626 in / 891 out tokens · 40692 ms · 2026-06-30T02:06:37.047376+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

4 extracted references · 3 canonical work pages

  1. [1]

    The Telegraph ://www.telegraph.co.uk/news/2024/09/06/spike-in-deaths-at-letby-hospital-could-be-explained/

    Knapton S and Elston P (2024) Spike in deaths at letby hospital 'could be explained by how small and premature babies were'; and: The scientific case against lucy letby (part two): the explicable spike. The Telegraph ://www.telegraph.co.uk/news/2024/09/06/spike-in-deaths-at-letby-hospital-could-be-explained/

    2024

  2. [2]

    UCL Publications Archive doi:10.17605/OSF.IO/2QUP7

    O'Quigley J (2024) Logical and statistical errors in the investigation and prosecution of suspected serial killer nurses. UCL Publications Archive doi:10.17605/OSF.IO/2QUP7. ://profiles.ucl.ac.uk/72162-john-o'quigley/publications

    work page doi:10.17605/osf.io/2qup7 2024

  3. [3]

    Medicine, Science and the Law doi:10.1177/00258024251404604

    O'Quigley J (2025) Use of roster charts in the investigation and prosecution of nurses suspected of inflicting deliberate harm on patients. Medicine, Science and the Law doi:10.1177/00258024251404604. ://dx.doi.org/10.1177/00258024251404604

    work page doi:10.1177/00258024251404604 2025

  4. [4]

    The Annals of Statistics 9(1): 130 -- 134

    Rubin DB (1981) The Bayesian Bootstrap . The Annals of Statistics 9(1): 130 -- 134. doi:10.1214/aos/1176345338. ://doi.org/10.1214/aos/1176345338

    work page doi:10.1214/aos/1176345338 1981