Independently-Confirmed Lucy Letby data

Post #997

Professor Norman Fenton and a partner (“Mr. Law, Health, and Technology”) analyzed the neonatal death data associated with Lucy Letby, suspected of killing babies.

This is independent analysis that confirms their work, but using other methods. When event counts are low, you can generate Poisson Confidence Intervals which are especially useful for over 15 events. To generate event counts of 16 or more, I combined years to create average neonatal death rates over those years.

The standard errors of the neonatal death rates (all per 1,000 births) were all formed for preliminary comparison. If the ratio of the standard errors of any two rates are less than 2.0, then simultaneous 85.6% confidence intervals around each of the rates have a 0.95 probability of overlap (by chance alone).

Here are the results, with those hospitals with sparse data omitted:

[click image to enlarge]

In cell N3, the two-year average neonatal death rate per 1,000 births shows up for the Countess of Chester Hospital where Lucy Letby worked. Because the highest ratio of standard errors on all of the rates of all the hospitals worked out to 1.63, simultaneous confidence intervals were formed around each rate at a confidence level of 85.6%.

This generates an alpha significance level of 5% for the chance of non-overlap.

Columns P and Q show that even the lowest upper bound (Bedford) was still higher than the lower bound for Countess of Chester Hospital (CoCH), where Lucy Letby worked. The confidence interval around the two-year average rate for CoCH even overlapped the average national rate of England — even at just 85.6% confidence.

Because of how different this analysis is from the first one by Fenton and partner, it is an independent confirmation of their original findings.

Reference

[Simultaneous Confidence Intervals based on the ratio of Standard Errors] — Payton ME, Greenstone MH, Schenker N. Overlapping confidence intervals or standard error intervals: what do they mean in terms of statistical significance? J Insect Sci. 2003;3:34. doi: 10.1093/jis/3.1.34. Epub 2003 Oct 30. PMID: 15841249; PMCID: PMC524673. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC524673/