LL Part 15: Some basic math

I don't math. But when I do...

Following on from our previous Lucy Letby trial post here.

Some people online have unfortunately thought me to be a statistician or mathematician simply because I worked for 7 years for the inimitable Prof. Norman Fenton (Royal Chartered mathematician) and Prof Martin Neil (Statistician). While working in their research group (Risk and Information Management - or RIM) I picked up some useful Bayesian probabilistic math that I employ in making such things as Maternity Outcome Models (see at the end of this article) - but…

I don’t math.

So please bear with me while I lay out some basic math for you, and explain why I am doing so.

Consider the following evidence that I will use in my math:

1. The UK national average for underweight and premature babies is around 6.4% of live births

   

2. For around 18 months (from early 2015 to mid 2016) Countess of Chester Hospital (CoCH) was a Level 2 Local Neonatal Unit (LNU). An LNU can provide care for neonates as tiny as 800 grams, or those as premature as 27 weeks (which is a baby born 13 weeks early). Even smaller babies or those born before 27 weeks at the hospital can also spend up to 6 hours (or more, depending on availability of incubators in nearby Level 3 facilities and NICU ambulance resources to transfer the neonate) being stabilised and prepared to be taken to a higher acuity facility (Arrow Park or Liverpool Women’s Hospital in this case). During this 6 hours quite literally anything can, and will, happen.

   

3. 63% of underweight and very premature babies born at a hospital with a Level 2 LNU neonatal unit will unfortunately die. This, too, is the national average for the UK.

   

4. Many of the babies that died during the period at CoCH were under 1.5kg at birth, with at least one being born right on the Level 2 threshold of 800 grams. Given that a healthy newborn baby will lose 7-10% of their body weight in the first days after birth, this one baby would have breached the protocol minimum weight and been under 800 grams within 24-48 hours and should have been transferred - yet, the testimony shows that doctors decided not to do this. Also note that a Level 2 facility is only supposed to provide intensive care to neonates for up to 48 hours - and that again, protocol dictates that babies needing more than 48 hours intensive care should ideally be transferred to a Level 3 centre. When you look at the demise of each infant described in my articl, ask yourself whether this 48 hour threshold was adhered to in each case.

5. CoCH delivers around 600 live births annually.

6. In each case I will round down in order to take the most positive perspective possible on the final outcome numbers.

The Math

If CoCH delivers 600 live births per year, and 6.4% will be underweight and premature - that means 38 babies annually will be underweight and premature. This is the expected number of underweight and premature babies that would have been born at CoCH in one year:

600 x 0.064 = 38.4

Therefore, for the 18 month period (1.5 years) that CoCH was a Level 2 facility and Lucy is alleged to have caused harm and neonatal deaths, 57 underweight and premature babies would normally have been expected based on the national average. This is the expected number of underweight and premature babies that would have been born at CoCH during an 18 month (1.5 year) period:

38 x 1.5 = 57

The national average for deaths of underweight and premature babies in a Level 2 LNU is 63%. That means 35 babies would have been expected to die based on the national average. This is the number of expected deaths for CoCH in an 18 month (1.5 year) period:

57 x 0.63 = 35.91

Yet, we see from the FOI response that CoCH acknowledge that only 17 deaths occured in the relevant 18 months period on their neonatal unit (this, of course, does not account for babies that were born at CoCH, were stabilised in their Neonatal unit, and were transferred out to other facilities only to subsequently die at those other facilities - as I discuss in my earlier post on The Numbers). Importantly, this means the fatality rate during the 18 month (1.5 year) period on the unit was only 48.5% of expected:

17/35 = 0.485 (48.5%)

Conclusion

That there were fewer deaths than the national average tells us three things:

1. We might have expected that, in the absence of direct evidence such as someone witnessing her actually doing the harm (which we know from testimony was never directly observed), some of the deaths Lucy might have caused would be ‘excess deaths’ - that is, deaths over and above the national average for neonatal deaths in a Level 2 LNU. However, in this case we see that deaths were around 51% below the national average. That simple math shows there were no excess deaths and is, after the absence of direct eye witness evidence of an act of harm, the second nail in the coffin of the alleged “Lucy was an angel of death” hypothesis.

2. That over and above other iatrogenic (treatment), nosocomial (hospital acquired) and reduced resource (low staff) causes, the rise in deaths on the neonatal unit occured because of and can primarily be explained by the uplift from Level 1 SCBU to Level 2 LNU status, and was still well within the rates expected of this new acuity status.

3. That the death rate during the relevant 18 months that CoCH’s Neonatal unit was at Level 2 LNU status being more than 51% below the national average suggests that the unit was actually saving almost half as many more neonates than the national average for all Level 2 LNU units.

Did they have an “angel of death”, or were their nurses actually national heroes?

You decide…

I have done a complete update to this post in my next article - here

Postscript:

As promised in the opening paragraph, here is a diagram of my most recent Maternity Outcomes Bayesian model… which has been trained with the more than 600,000 birth outcomes recorded in the UK during 2021. It can be used to predict outcomes for mothers and babies based on observations of their particular and individual circumstances.