Healthcare serial killer or coincidence Statistical issues in investigation of suspected medical misconduct

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Healthcare serial killer or coincidence?

Statistical issues in investigation of suspected

medical misconduct

P.J. Green∗

, R.D. Gill†

, N. Mackenzie‡

, J. Mortera§

, W.C. Thompson¶

27 September, 2022

Abstract

Justice systems are sometimes called upon to evaluate cases in which

healthcare professionals are suspected of killing their patients illegally.

These cases are diﬃcult to evaluate because they involve at least two levels

of uncertainty. Commonly in a murder case it is clear that a homicide

has occurred, and investigators must resolve uncertainty about who is

responsible. In the cases we examine here there is also uncertainty about

whether homicide has occurred. Investigators need to consider whether

the deaths that prompted the investigation could plausibly have occurred

for reasons other than homicide, in addition to considering whether, if

homicide was indeed the cause, the person under suspicion is responsible.

In this report (commissioned by the Section on Forensic Statistics of the

Royal Statistical Society, London) we provide advice and guidance on

the investigation and evaluation of such cases. Our work was prompted

by concerns about the statistical challenges such cases pose for the legal

system.

Contents

1 Overview 2

2 “This could not have been a coincidence!” 5

2.a Seemingly unlikely coincidences can and do occur . . . . . . . . . 8

2.b The importance of avoiding illogical inferences from p-values . . 9

3 Competing theories 11

4 Investigative bias 15

4.a Unconscious bias throughout society . . . . . . . . . . . . . . . . 16

4.b Anatomy of a biased investigation . . . . . . . . . . . . . . . . . 18

∗University of Bristol,UK

†Leiden University, Netherlands; email: gill@math.leidenuniv.nl

‡Arnot Manderson Advocates, Edinburgh

§Universit´a Roma Tre

¶University of California, Irvine

arXiv:2210.00962v1 [stat.AP] 3 Oct 2022

4.c “Suspicious deaths” . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.d Access and opportunity . . . . . . . . . . . . . . . . . . . . . . . 20

4.e Similar circumstances . . . . . . . . . . . . . . . . . . . . . . . . 21

4.f Theroleofchance .......................... 22

5 Advice on investigative procedures 23

5.a Identifying all potential causal factors . . . . . . . . . . . . . . . 24

5.b Minimisingbias............................ 25

5.c The role for statistics in other specialist evidence . . . . . . . . . 27

6 Advice for evidence evaluation and case presentation 28

6.a Thelawyer’srole ........................... 28

6.b Evaluating event clusters . . . . . . . . . . . . . . . . . . . . . . . 30

6.c Recognising the consequences of investigative bias . . . . . . . . 31

6.d Avoiding fallacious interpretations of statistical ﬁndings . . . . . 34

7 Conclusions and summary of recommendations 34

8 References 37

A Appendices 42

A.1 Probability and odds . . . . . . . . . . . . . . . . . . . . . . . . . 42

A.2 Statistical signiﬁcance, eﬀect size and risk . . . . . . . . . . . . . 43

A.3 Sensitivity and speciﬁcity . . . . . . . . . . . . . . . . . . . . . . 45

A.4 Bayes’rule .............................. 45

A.5 Cumulative eﬀects of bias: two worked numerical examples . . . 48

A.5.1 Example1........................... 49

A.5.2 Example2........................... 50

A.6 Patterns of occurrence of adverse events . . . . . . . . . . . . . . 51

A.7 Usual practice in medical statistics and epidemiology. . . . . . . 54

A.8 Annotated code and output . . . . . . . . . . . . . . . . . . . . . 56

A.9 Members of the working party drawing up this report . . . . . . 63

1 Overview

Justice systems are sometimes called upon to evaluate cases in which health-

care professionals are suspected of killing their patients illegally. These cases

are diﬃcult to evaluate because they involve at least two levels of uncertainty.

Commonly in a murder case it is clear that a homicide has occurred, and in-

vestigators must resolve uncertainty about who is responsible. In the cases we

examine here there is also uncertainty about whether homicide has occurred.

Investigators need to consider whether the deaths that prompted the investiga-

tion could plausibly have occurred for reasons other than homicide, in addition

to considering whether, if homicide was indeed the cause, the person under

suspicion is responsible.

In this report, the RSS provides advice and guidance on the investigation

and evaluation of such cases. This report was prompted by concerns about

the statistical challenges such cases pose for the legal system. The cases often

turn, in part, on statistical evidence that is diﬃcult for lay people and even

legal professionals to evaluate. Furthermore, the statistical evidence may be

distorted by biases, hidden or apparent, in the investigative process that render

it misleading. In providing advice on how to conduct investigations in such

cases, this report particularly focuses on minimising the kinds of biases that

could distort statistical evidence arising from the investigation. This report

also provides guidance on how to recognise and take account of such biases

when evaluating statistical evidence and more broadly on how to understand

the strengths and limitations of such evidence and give it proper weight.

This report is designed speciﬁcally to help all professionals involved in in-

vestigating such cases and those who evaluate such cases in the legal system,

including expert witnesses. It will also be of interest to scholars and legal profes-

sionals who are interested in the role of statistics in evidentiary proof, and more

generally to anyone interested in improving criminal investigations. With such

a wide range of audiences, it is inevitable that for some readers certain sections

may seem more relevant, and some less so, but we believe it is important not

to aim particular sections at particular kinds of reader. We want, for example,

the barrister to see what advice we give to the expert statistical witness – and

we hope understand it, at least in broad terms – and vice versa; we believe that

is important in helping all parties to appreciate the contributions of others in

reaching just outcomes.

Because suspicions about medical murder often arise due to a surprising

or unexpected series of events, such as an unusual number of deaths among

patients under the care of a particular professional, this report will begin (in

Section 2) with a discussion of the statistical challenge of distinguishing event

clusters that arise from criminal acts from those that arise coincidentally from

other causes. This analysis will show that seemingly improbable patterns of

events (eg apparent clusters, rising trends, etc.) can often arise without criminal

behaviour and may therefore have less probative value than people assume for

distinguishing criminality from coincidence.

Section 3 of this report will focus on the competing theories that are of-

ten advanced by the prosecution and defence when a medical professional faces

criminal charges for killing patients. The prosecution’s theory is typically that a

medical professional, previously trusted to perform critical life-saving functions,

has unexpectedly (and sometimes inexplicably), chosen to murder patients in

his or her care. While history has shown that humans are capable of such be-

haviour, and there have indeed been cases in which, for example, physicians

have murdered multiple patients, nevertheless proven instances are thankfully

extraordinarily rare – a mere handful of documented cases, perhaps a dozen or

so per year, among the many millions of healthcare professionals worldwide. So

the prosecution’s theory in such cases is often one that appears, a priori, to

be improbable. Alternative theories – ie, that some unknown factors, or mere

chance, caused deaths to occur in apparently extraordinary numbers among pa-

tients under the care of a particular professional – often also appear improbable.

So the assessment of the case invariably turns, at least in part, on a weighing or

balancing of the probabilities of seemingly extraordinary events. Such assess-

ments are challenging under the best of circumstances but become especially

diﬃcult when the evidence adduced to distinguish between the competing the-

ories may be biased or presented in a misleading manner.

Section 4 of this report discusses the kinds of investigative biases that can

arise in these cases. Our focus is on ways that investigators’ desires and expec-

tations may unintentionally and even unconsciously inﬂuence what they

look for, how they characterise and classify what they ﬁnd, what they deem to

be relevant and irrelevant, and what they choose to disclose. Examiner bias is a

well-known phenomenon in both scientiﬁc and forensic investigations. It arises

in large part from what are known as observer eﬀects, a tendency for human

beings to look for data conﬁrming their expectations (conﬁrmation bias) and

to interpret data in ways that are subtly (and often unconsciously) inﬂuenced

by their expectations and desires. Statisticians have long studied the ways in

which examiner bias can distort statistical evidence emerging from scientiﬁc

and forensic investigations. In Section 4, we apply insights from this scientiﬁc

literature to an analysis of the investigative process in the types of cases dis-

cussed in this report. We also draw examples from investigations of actual cases

that illustrate what we believe to have been biased investigative processes and

discuss how such biases can generate misleading statistical ﬁndings. It bears

repeating that our focus in this section is on processes that can unintentionally

and unconsciously inﬂuence the investigative process. We are not questioning

the general honesty, integrity or good intentions of those involved in investigat-

ing such cases. We focus instead on investigative procedures that can distort

statistical ﬁndings in ways that, while entirely unintentional, may nevertheless

be important.

Section 5 of this report provides advice on how to improve investigative

procedures in order to minimise investigative biases. While it is impossible to

eliminate all human biases from a criminal investigation, there are a number of

procedures that can reduce bias and thereby improve the quality and objectivity

of the evidence emerging from the types of investigations we discuss here. We

focus particularly on the advantages of blinding and masking procedures, which

involve temporarily withholding potentially biasing facts from some of those

involved in the investigation. We go on to discuss ways to reduce “tunnel vision”

in which the investigation becomes a search for evidence conﬁrming a particular

investigative theory while ignoring or dismissing evidence inconsistent with that

theory. We provide and explain advice on appropriate correct analyses of data,

and discuss two worked examples.

Section 6 provides advice on evidence evaluation and fact-ﬁnding in these

cases. We expect this report to be relevant and useful anywhere such cases may

arise; hence we do not limit our discussion to the needs of a particular legal

system, and expect our advice to be useful both in inquisitorial and adversarial

legal processes. We believe the statistical issues in these cases pose challenges to

legal fact-ﬁnders in every jurisdiction, whether they are professional judges or lay

jurors, and are challenging for lawyers as well. Our advice focuses on identifying

and appreciating ways in which statistical evidence may be misleading, and

assuring (to the extent possible) that presentations of evidence are balanced in

order to help triers-of-fact appreciate both the strengths and limitations of the

evidence, and give it only the weight it deserves. We will provide examples of

presentations and arguments that we consider to be misleading or inappropriate.

We will discuss cautionary instructions that may be helpful to lay fact-ﬁnders.

Ultimately, we hope our comments will help lawyers and judges, and statisticians

and other experts, reﬁne their presentation and evaluation of evidence in these

diﬃcult cases in order to better serve the interests of justice.

Finally, we draw together our main conclusions, and present a summary of

our most important recommendations in Section 7.

2 “This could not have been a coincidence!”

The challenge of drawing conclusions from suspicious clusters of deaths

(or other adverse outcomes)

In some cases suspicions against medical professionals arise for the very rea-

son that an apparently unusual number of deaths occurs among their patients.

In other cases suspicions arise for unrelated reasons and this prompts an ex-

amination of cases where a certain medical professional was on duty and this

reveals an apparently unusual number of deaths. There is a statistical chal-

lenge of distinguishing event clusters that arise from criminal acts from those

that arise coincidentally from other factors. Seemingly improbable clusters of

events can often arise by chance without criminal behaviour and may therefore

have less probative value than people assume for distinguishing criminality from

coincidence.

Lucy and Aitken published an analysis of evidence used to prosecute medical

professionals accused of harming their patients1. They found (see p. 152) that

“evidence of attendance” was “by far the most frequently occurring” yet was also

“the most diﬃcult type of evidence, both from a legal and epistemological point

of view”. While other types of evidence may be presented, such as evidence

of a criminal intent (mens rea) and the means to carry it out, or eyewitness

accounts, these tend to be less than deﬁnitive for a variety of reasons, such as

the diﬃculty of ascertaining retrospectively the exact cause of death and the

uncertainty inherent in assessing human motives and behaviour. Statistics on

the relative rate of deaths when a particular professional was “in attendance”

may, by contrast, seem more objective and scientiﬁc, making statistical evidence

the lynchpin of these cases.

Drawing causal conclusions from a statistically improbable cluster of events

is often challenging, however.2A criminal investigation is analogous to a ret-

rospective observational study. In such a study, it is possible to ascertain cor-

relations between variables. The study might establish, for example, that the

death rate was higher when a particular medical professional was present on a

hospital ward. However, one of the fundamental principles of logical inference

is that correlation does not prove causation. The increase in death rate cannot,

in itself, prove that the professional in question was engaging in misconduct

that caused the increase in deaths because other factors, known as confounding

variables, might oﬀer alternative explanations.3Competent investigators are

attentive to the possibility of confounding variables and may attempt to take

them into account. Even if all known confounding variables are taken into ac-

count, however, there might be additional confounders, unknown, unmeasured,

unmeasurable, or otherwise inadequately dealt with, that aﬀect mortality rates

when a given medical professional is on duty. For example, there may be changes

in the circumstances and characteristics of the hospital for reasons that are not

measured, or even not observable at all. So ﬁnding an association of a particular

professional with high mortality rates cannot per se have a causal interpretation.

1Lucy and Aitken (2002).

2Wartenberg, 2001.

3A confounder is a variable, not of prime concern in a study, that is associated with both

the ‘exposure’ (eg presence of a particular nurse) and the ‘outcome’ (eg unexpected death

of a patient). Neglect or inadequate attention to confounders typically leads to misleading

conclusions about the causal eﬀect of the exposure.

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Healthcareserialkillerorcoincidence?StatisticalissuesininvestigationofsuspectedmedicalmisconductP.J.Green*,R.D.Gill,N.Mackenzie,J.Mortera§,W.C.Thompson¶27September,2022AbstractJusticesystemsaresometimescalledupontoevaluatecasesinwhichhealthcareprofessionalsaresuspectedofkillingtheirpatientsillegal...

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