Based on recent work on three notable cases: Lucia de Berk, Ben Geen, Daniela Poggiali

1. StatisticalissuesinSerial
KillerNursecases
NSG Semin
a
r
Rich
a
rd Gill, M
a
rch 22, 2022
(*) aka “Accused”
(*)

2. What I had hoped
to discuss today
In preparation
Members of the working party
(58 pp.)

3. • Bev Allitt, 1991 (*)
• [Harold Shipman, 1998]
• Lucia de Berk, 2001
• Ben Geen, 2004
• Daniela Poggiali, 2014
• Lucy Letby, 2016
Myfocus:nurses
It was only following the death of […] that medical staff became suspicious of the number of cardiac arrests on the
children's ward and police were called in. It was found that Allitt was the only nurse on duty for all the attacks on the
children and she also had access to the drugs
(*) In all these cases, the indicated year is the year in which the alleged killing spree ended through the arrest
of the health care professional; it is also the year of the incident which was the “trigger case”
The Shipman enquiry reports 3 and 4 were published in 2003 and 2004,
fi
nding major
fl
aws in the
processes of death registration, prescription of drugs and monitoring of doctors.

4. • Francesco Dotto, RDG, Julia Mortera (2022), Statistical Analyses in the case of
an Italian nurse accused of murdering patients, https://arxiv.org/abs/2202.08895
• Norman Fenton, RDG, David Lagnado (2022), Statistical issues in Serial Killer
Nurse cases, https://arxiv.org/abs/2106.00758
• Healthcare Serial Killer or Coincidence? In preparation. RSS Statistics and the
Law section
• https://en.wikipedia.org/wiki/Angel_of_mercy_(criminology)
• https://en.wikipedia.org/wiki/
List_of_serial_killers_by_number_of_victims#Medical_professionals_and_pseudo-
medical_professionals
• https://www.netflix.com/au/title/80185622 “Nurses who kill”
Selectedreferences

5. • A disturbing incident is associated with a particular nurse and brought to the attention of
hospital management
• Often, there had already been suspicion of the nurse in question and gossip shared between
nurses, doctors, and administrators [Lucia de B, Ben Geen, Daniela Poggiali]
• The nurse in question stood out in the crowd through striking personality and sharp tongue
• Hospital management including key specialists go into crisis mode, gather dossiers, write
summary evaluations of “suspicious cases”, call in the police, giving them a big collection of
possible murders, murder attempts, attempts to harm
• The trigger case is re-classi
f
ied as an unnatural event and reported to the health authorities
• The hospital puts out a press release, leading to intense media interest
• Sometimes there is pretty hard evidence against the nurse and in such cases often also a
confession
• Often, enough medical evidence can be marshalled against the nurse in one or two of the cases
in order for triers of fact to conclude that the nurse certainly did murder a few particular
patients. The statistical evidence of a surplus of “suspicious/unexplained” deaths and other
incidents when the suspect was present supports conviction with a maximal sentence
Atypicalhistory

6. • In most serial murder cases, it is pretty clear that one or two particular persons actually
were murdered. The main unknown is: who was the perpetrator. But in our cases, the
court has to decide whether or not there was any unlawful doing at all; only then, if so,
by whom
• The evidence is largely gathered by hospital administrators and doctors, and needs to
be interpreted by medical experts
• The hospital community is hierarchically organised; the medical profession too
• Judges and medical specialists both come from the highest echelons of society
• Most deaths in hospital are actually caused by medical errors, and very many of those
errors are not admitted. There is a tendency to blame the lowest in the hierarchy
• Defence lawyers and defence experts do not have access to inside information about
the hospital
• The base rate is very, very low
• Result: the error rate seems to be very, very high
Thesecasesareveryrare
(
a
nd often rem
a
in disputed)

7. • Experts from criminology and from forensic psychology agree
that about 1 in 2 million nurses kill patients on more than one
occasion per year
• Alternative explanations for a cluster of events to apparently
concentrate in the shifts of a particular nurse are hard to come
up with
Thebaserate; alternativeexplanations
Toronto children hospital deaths: new plastics used in arti
f
icial rubber components of feeding tubes
A hospital in the UK: a new supplier of baby milk formula
Lucia de B: secret change in hospital policy concerning transfer of seriously ill babies (genetic abnormalities)
from intensive care to medium care (so that they could die at home rather than in the hospital)
Lucia de B: change of name of ward allowed hospital director to state under oath that the number of deaths in the last year on Lucia’s ward
was much larger than ever before
Ben Geen: change in classi
f
ication of events (cardiac/respiratory/hypoglycaemic, fainting
f
it) creates a cluster
NL: ca. 200 000 nurses employed in care sector
About 1 case per 10 years?

8. Theunknownunknowns
Bec
a
use the ch
a
nce of unknown unknowns being the
a
ctu
a
l c
a
use
of the coincidence is so l
a
rge,
a
bsence of h
a
rd evidence
a
g
a
inst
the nurse under suspicion c
a
n be strong evidence of innocence
I will illustrate this with a simple graphical model:
this little DAG, + 4 sets of possible values of variables/nodes S, U, E, C,
+ plus four conditional probability tables

9. Marginal probabilities of each node, together with simultaneous of nodes S, U
No evidence has been incorporated! (No nodes have been observed)

10. The conditional probability tables of the four variables S, U, E, C
Each takes values in the set {“YES”, “NO”}

11. Conditional probability table of S + U : S, U
(Just a trick to also see some “marginal joint probabilities” of special interest)

12. Marginal probabilities of each node, together with simultaneous of nodes S, U
No evidence has been incorporated! (No nodes have been observed)

13. Marginal probabilities of each node, conditional on
observation of: Cluster of Events = “YES”

14. Marginal probabilities of each node, conditional on
observation of: Cluster of Events = “YES”, and Strong Evidence of one murder = “YES”

15. Marginal probabilities of each node, conditional on
observation of: Cluster of Events = “YES”, and Strong Evidence of one murder = “NO”

16. Everythingcanbeautomated,
andusingfreesoftwareonly(R;GeNIe)
library(Rgraphviz)
library(gRain)
yn <- c("yes", "no")
S <- cptable(~SerialKiller, values=c(1, 999999), levels = yn)
U <- cptable(~UnknownCause, values=c(1, 99), levels = yn)
E.S <- cptable(~EvidenceOneMurder:SerialKiller, values = c(99, 1, 1, 999), levels = yn)
C.SU <- cptable(~ClusterofEvents:SerialKiller:UnknownCause, values = c(999, 1, 1, 99, 999, 1, 1, 99999),
levels = yn)
killerNurse <- compileCPT(S, U, C.SU, E.S)
killerNurse
In fact all formulas of interest could be written out explicitly as simple functions of four parameters,
standing for the four distinct “small probabilities” 1 / 100, 1 / 1 000, 1 / 100 000, 1 / 1 000 000 in my model.
Alternative software: Python; Hugin, AgenaRisk, …

17. • Daniela Poggiali tended to arrive for work well before the beginning of her shift,
tended to leave well after the end
• Deaths are registered administratively by a doctor signing a death certi
f
icate,
on which he also writes the time and date that he performs this task
• This administrative work is mainly done at the hand-over between shifts, and at
midnight (the date of death has very large legal and administrative signi
f
icance)
• Hence the apparent rate of deaths when Daniela was at work was much larger
than when she was not at work
• The p-value of 10 to the minus a huge number meant according to Tagliaro and
Micciolo (*) that Daniela’s presence de
f
initely caused 60 excess deaths. They are
careful to add that they do not conclude that she deliberately caused the
deaths (they know that that is for the court to decide)
Howtoliewithstatistics
(*) It
a
ly’s foremost forensic p
a
thologist prof. T
a
gli
a
ro
a
nd
his regul
a
r st
a
tistici
a
n coll
a
bor
a
tor prof. Micciolo

18. Howtoliewithstatistics(continued)
Some ex
a
mples from the Ben Geen c
a
se
The following data was never seen in court
(with the exception of the
f
irst plot, seen by all consulted experts in advance)

19. Key statistical graphic
From report on SUI 219 submitted to Crown Prosecution Service
by the Clinical Risk Management Committee,
Oxford Radcli
ff
e Hospitals Trust, September 2004
Admissions to critical care from the emergency department, with a diagnosis
of cardio−respiratory arrest and/or hypoglycaemia, data: Head Nurse Brock
Dec
−02
Jan
−03
Feb
−03
Mar
−03
Apr
−03
May
−03
Jun
−03
Jul
−03
Aug
−03
Sep
−03
Oct
−03
Nov
−03
Dec
−03
Jan
−04
Feb
−04
0
2
4
6
8
????
Ben’s last
workday:
6 Feb

20. Key statistical graphic
reconstructed (data: FOI)
Data from FOI requests, 2014 (RDG hired by defence for CCRC application)
Admissions to critical care from the emergency department, with a diagnosis
of cardio−respiratory arrest and/or hypoglycaemia, data: FOI
Dec
−02
Jan
−03
Feb
−03
Mar
−03
Apr
−03
May
−03
Jun
−03
Jul
−03
Aug
−03
Sep
−03
Oct
−03
Nov
−03
Dec
−03
Jan
−04
Feb
−04
0
2
4
6
8
ORHT (FOI)
Full
month
of Feb

21. Key statistical graphic
0
1
2
3
4
5
6
7
Admissions to critical care from the emergency department, with a diagnosis
of cardio−respiratory arrest and/or hypoglycaemia, data: FOI
Dec
−02
Jan
−03
Feb
−03
Mar
−03
Apr
−03
May
−03
Jun
−03
Jul
−03
Aug
−03
Sep
−03
Oct
−03
Nov
−03
Dec
−03
Jan
−04
Feb
−04
0
2
4
6
8
0
1
2
3
4
5
6
7
Brock
FOI
????
2004
2014
2004, SUI crisis team; 2014, FOI requests
6 days
of Feb/
Full
month
of Feb

22. Key statistical graphic
Admissions to CC from ED with CR, Hypo or Resp arrest, FOI data:
Cardio−respiratory (blue), hypoglycaemic (green), respiratory (red)
Dec
−02
Jan
−03
Feb
−03
Mar
−03
Apr
−03
May
−03
Jun
−03
Jul
−03
Aug
−03
Sep
−03
Oct
−03
Nov
−03
Dec
−03
Jan
−04
Feb
−04
0
2
4
6
8
Prepared by RDG, data (2014) from FOI requests in 2013
Full
month
of Feb

23. STL LOESS (Cleveland et al., 1990) R function “stl”
Monthly total admissions to ED
400
500
600
700
data
−40
−20
0
20
seasonal
400
500
600
trend
−60
−20
20
60
2000 2002 2004 2006 2008 2010
remainder
time

24. Transfers / 100 admissions
From ER to CC with CR or Hypo arrest
2000 2002 2004 2006 2008 2010
0.0
0.2
0.4
0.6
0.8
1.0

25. Shifting meanings, example:
Categories of event (Ben Geen case)
• Respiratory arrest vs. resp/cardiac/hypoglycaemic vs.
patient faints (psychological reaction/medication/ …)
• Any vs. unexplained only
• Total # various arrests in winter 2003-4 same as in
previous year!

26. Raw counts versus normalised rates
Ben Geen case
• The total stream of patients entering A&E almost doubled
in size over a period of a year culminating in the crisis of
Feb 2004, then plummeted [Never mentioned in court]
• Did the number of nurses grow? Did the number of
specialists grow? [Nobody knows, nobody asked]
• Ben complained about the lack of su
ffi
cient nurses in A&E
but this complaint was threatening (threatened survival of
his hospital, HGH)

27. • Serial killer nurse cases are very rare
• Error rates are very large: these cases are a big challenge to all legal
systems
• All parties involved in them should learn of the many speci
f
ic dangers of
such cases
• Both error rates could go down if better use is made of the available
information, especially the statistical information – read the RSS report!
• Academics, esp. in the UK: study, and publish on, the Ben Geen
case!
Conclusions
And: watch the movie based on the case of Lucia de B!
https://en.wikipedia.org/wiki/Accused_(2014_
f
ilm)