CHAPTER TWENTY. THE STATISTICS OF THE LUCY LETBY CASE.
“There are two kinds of statistics, the kind you look up, and the kind you make up.” – Rex Todhunter Stout.
The Lucy Letby case involved a series of statistical “blunders”. In my opinion, The Police and The Crown Prosecution Service would either have to be dishonest, or stupid, or lazy to perpetrate these statistical “blunders”. In this chapter, I will explain very briefly what these statistical “blunders” were. If you want further verification regarding these statistical “blunders”, including verbatim quotes from highly qualified statisticians, you can go to Appendix. Notes to Chapter 20. Statistics.
ITEM 1. The first, and most important statistical “blunder” concerned the actual number of infant deaths in the unit. The prosecution purported that there were SEVEN infant deaths on the unit (in the relevant time frame). This was the information that was given to the jury. The prosecution claimed that Lucy Letby was present AT ALL SEVEN DEATHS! This looks somewhat incriminating. However, the fact that the jury did NOT hear about was that there were EIGHTEEN DEATHS NOT JUST SEVEN. This hardly looks incriminating at all. There were eighteen deaths, and Lucy Letby was PRESENT AT ONLY SEVEN OF THESE DEATHS. (Various other nurses were also present at least seven deaths.) Now it just looks like the “law of averages”. This was an unfair misrepresentation, an (apparent) attempt to bamboozle the jury. MY source for this information is The Private Eye Special Report – The Lessons of The Lucy Letby Case, by Doctor Phil Hammond, MD. (available on the internet.), Part 13. QUOTE:- “The (Thirwall) enquiry has confirmed that there were 18 neonatal deaths linked to the hospital (in 2015 and 2016), seven of them attributed to Letby”.
This fact is also mentioned in the book – Lucy is Innocent, by Paul Bamford, SECOND EDITION, (I strongly recommend this book!) page 25:- “Ten extra deaths hidden from the jury”. The author continues on page 148:- “And as part confirmation of this lie: Every time the high number of deaths was mentioned in the trial, both the prosecution and the judge used the formula “A significant rise in the deaths compared to previous years,” without specifying whether the total had risen to 7 on the one hand, or 15, 17, or 18.” The author (Paul Bamford) calls this “the prosecutor’s lie of omission”.
A further point that the above book makes (page 82) (which, as far as I know, no other statisticians have picked up on) is that the OTHER TEN deaths (ie:- 17 minus 7 = 10), when Lucy Letby was absent represent a highly improbable statistical anomaly. The average death rate on the unit was (as I understand it) three deaths per year. Now suddenly it spikes to TEN deaths. How improbable is that? Paul Bamford suggests using the Poisson Distribution. I went on the internet to look for Poisson Distribution Calculators. I came across the following web page:-
https://stattrek.com/online-calculator/poisson
I put in the Poisson random variable as 10, and the average rate of success as 3 The result came out as one chance in 1200. Clearly, some OTHER factor is involved besides a hypothetical serial killer. In that case, this OTHER factor could also explain the SEVEN deaths attributed to Lucy Letby.
ITEM 2. The second statistical “blunder” concerns the anomalous “spike” in deaths on the unit. If you consider just this single neonatal unit, a sudden “spike” in deaths seems vastly improbable. However, if you consider all 200 neonatal units in the country, it is almost inevitable that one or two of these units will experience a “spike” in deaths of this magnitude, purely by chance. To clarify this, let me provide an analogy. If I toss a coin six times, and it comes up heads every time, the odds against chance occurrence are one chance in 64. It looks like a “biased” coin. However, if SIXTY-FOUR people each toss a coin six times, then at least one of those people are likely to get six heads in a row. In that case, the “spike” in deaths on the unit was just “law of averages”, or, as a statistician would express it, “not statistically significant”. A Professor of Statistics explains this second “blunder” in more detail in Appendix. Notes to Chapter 20. Statistics, Items 1, 2, 6, and 12.
ITEM 3. The third statistical “blunder” involves what statisticians have called “confounding variables”. The first “confounding variable” is that the unit had just been designated to take on babies OF A GREATER VULNERABILITY than previously – but the unit did not really have the necessary facilities. The unit’s “reach was greater than its grasp”. By a strange coincidence, when Lucy Letby left the unit, the deaths immediately stopped. This appeared to indicate her guilt. However, the ward was downgraded, so as to receive less severe cases AT EXACTLY THE SAME TIME as Lucy Letby was transferred out of the unit. This explains the sudden drop in infant deaths. This did not come out at the trial. This being the case, the coincidence of a sudden drop in infant deaths does NOT indicate her guilt at all! The second “confounding variable” is that there was a problem with the sewage backing up into the sinks on the unit, causing a risk of infection; and there was also pseudomonas bacteria in some of the taps in the unit, which would be lethal to infants. The immune systems of neonates are poorly developed, and unable to withstand infection. These two “confounding variables” make the “spike” in deaths on the unit almost a certainty, rather than it being a vastly improbable statistical anomaly. See Appendix. Notes to Chapter 20. Statistics, Items 3, 25, 31, and 35.
ITEM 4. The fourth statistical “blunder” was as follows:- Even assuming that the “spike” in deaths on the unit was a genuine statistical anomaly (which it was not!), even on this assumption, the presence of Lucy Letby at some of these deaths would not be surprising, for the following three reasons:-
(A). Lucy Letby worked more shifts, and longer shifts. Therefore she was at greater “risk” of being present at a collapse or death. See Appendix. Notes to Chapter 20. Statistics, Items 7, 11, 27, 31, and 37.
(B). Lucy Letby worked a lot of night shifts, when there were less doctors available on the unit to deal with emergencies. These night shifts put Lucy Letby at greater “risk” of being present at a collapse or death. In fact, 14 out of 40 collapses of infants on the unit occurred at night. See Appendix. Notes to Chapter 20. Statistics, Items 27, 35, and 38.
(C). Lucy Letby was one of the more skilled nurses on the unit, and therefore was put in charge of the more vulnerable babies. Therefore she was at greater “risk” of being present at a collapse or death. See Appendix. Notes to Chapter 20. Statistics, Items 10, 27, and 33.
When you factor in these three “risk factors” that Lucy Letby “suffered”, her presence at various deaths and collapses was almost inevitable, and was no way improbable.
ITEM 5. The fifth statistical “blunder” involves the following issue:- Lucy Letby is ALLEGED to have been present at various deaths and collapses on the unit. The problem is that it is by no means certain that she actually WAS present at any specific time. The entries and exits to the unit were recorded by “door swipe data”. However, the “door swipe data” was faulty and inaccurate. I go into this issue in greater detail in Chapter 16.
ITEM 6. The sixth statistical “blunder” involves the classification of deaths and collapses on the unit into two separate categories – “suspicious” and “NOT suspicious”. The chief prosecution witness, Doctor Dewi Evans, was tasked with arranging this classification, having read the medical notes for each baby. He should have carried out this task “blind”, ie:- NOT knowing the names of the nurses involved with any particular baby. However, he DID know the names of the nurses involved with each baby. He designated deaths and collapses as “suspicious” ONLY if he saw that Lucy Letby was present. He designated deaths and collapses as “NOT suspicious” ONLY if she was NOT present. One statistician has called this “a completely circular argument”. It is obvious that Lucy Letby would be present at “suspicious” deaths or collapses, because it was her presence that automatically placed these events into the “suspicious” category in the first place!
For example, one baby died of asphyxiation, which suggests deliberate “smothering” – but this baby was placed in the NOT “suspicious” category by Doctor Dewi Evans, simply because Lucy Letby was NOT present! To verify that this incredible statistical “blunder” really did occur, go to Appendix. Notes to Chapter 20. Statistics, where you can see verbatim quotes from highly qualified statisticians (Items 5, 6, 8, 16, 24, 37, and 42.)
ITEM 7. Here are some quotes from various highly qualified statisticians regarding the statistics used in The Lucy Letby trial:-
A “statistical abomination.” Statistician Peter Elston calls the statistical evidence given during Letby’s trial “a scientific fake.”
“Her guilt was assumed by some very strange statistical arguments”.
“The statistical analysis of the Letby case does not hold water”.
The Letby trial involved “a massive problem of selection bias”.
“She argued that the analysis of these records appeared to be influenced by hindsight bias - - - interpreting normal medical events as SUSPICIOUS BECAUSE THEY WERE LINKED TO LETBY” (My capitals and highlighting.)
To verify the sources of these quotes, and to see further similar quotes, go to Appendix. Notes to Chapter 20. Statistics.
Also, in Appendix. Notes to Chapter 20. Statistics, I provide some quotes from qualified statisticians stating that statistics is a very tricky subject, and that people who are not qualified in statistics can very easily make terrible statistical “blunders” of the sort made in the Lucy Letby case.