Systematic Review/Meta-analysis
Estimating the Risk of Cardiac Mortality After Exposure to
Conducted Energy Weapons
Ben Rich, PhD, and James M. Brophy, MD, PhD
Department of Medicine, McGill University Health Center, and Department of Epidemiology and Biostatistics, McGill University, Montreal, Quebec, Canada
ABSTRACT
Background: Conducted energy weapons (CEWs), commonly known as
Tasers, are a reputed nonlethal law enforcement weapon. Nevertheless
high profile cases have suggested a causal association with cardiac
death but the magnitude of any putative risk is unclear.
Methods: An electronic systematic review of all real world, cohort
studies of consecutive CEW cases was performed. “Pessimistic” and
“optimistic” previous beliefs about CEW mortality were derived from an
unbounded internet search, including case series but excluding the
previously identified cohort publications. A Bayesian analysis updated
these previous beliefs with the published objective cohort data.
Results: Pessimistic and optimist previous beliefs with modes of
1/700 and 1/7000, respectively, and upper limits (< 2.5% probability)
of 1/100 and 1/1000, respectively, were constructed. Three cohort
studies formed the objective data source and their combined mortality
was 1 in 2728 cases or 3.67/10,000 (95% confidence interval,
RESUME
Introduction : Les armes à impulsions (AI), communement connues
sous le nom de Taser, sont des armes reputees non mortelles par les
forces de l’ordre. Neanmoins, des cas très mediatises ont suggere un
lien de causalite entre le Taser et la mort cardiaque, mais l’ampleur de
tout risque putatif n’est pas elucidee.
Methodes : Une revue systematique electronique de toutes les etudes
de cohortes reelles de cas consecutifs d’AI a ete realisee. Les croyances «
pessimistes » et « optimistes » precedentes sur la mortalite liee à l’AI
provenaient d’une immense recherche dans internet, y compris les series
de cas, mais à l’exclusion des publications de cohortes precedemment
identifiees. Une analyse bayesienne a actualise ces croyances
precedentes par la publication de donnees de cohortes objectives.
Resultats : Les croyances pessimistes et optimistes precedentes par
valeurs dominantes de 1/700 et de 1/7000, respectivement, et limites
superieures (probabilite < 2,5 %) de 1/100 et de 1/1000, respectivement,
Conducted energy weapons (CEWs) are one of several options
along the use-of-force continuum used by law enforcement
officials to facilitate arrests of uncooperative, violent individuals.
These devices use electrical energy to inflict pain,
immobilize, and ultimately incapacitate human subjects.
Online video examples of CEW use associated with nonlethal
and lethal outcomes have gone “viral.”1,2
Despite their purported
design as nonlethal weapons, considerable debate is
ongoing not only in the popular press/media but also in the
medical literature3-6
concerning the potential danger of CEWs
to precipitate sudden cardiac arrest/death.
In 2008, Amnesty International summarized many incustody
deaths that were proximate to CEW exposure.7
Recently, 8 cases of sudden cardiac arrest/cardiac death after
CEW exposure have been reported in a high-impact cardiovascular
subspecialty journal,3
although any link to causality
has been vigorously contested.8
Based on these data and animal
studies, it has been opined that CEW stimulation can
cause cardiac electrical capture and provoke cardiac arrest
resulting from malignant ventricular arrhythmias.3
This
interpretation of these recent and past cases has been called
into dispute by noting underlying health issues in some of the
victims and the lack of evidence for induced arrhythmias in
numerous volunteer and epidemiologic studies.4-6
In response
to this debate, there has been a call “to transform the argument”
from if CEW-induced mortality can occur to how
often it occurs.9
The goal of this report was to quantify the
CEW mortality risk, as best possible, using probability models
and to explicitly acknowledge the effect of previous beliefs in
light of the paucity of quality objective data.
Methods
An electronic systematic review of all clinical studies was
executed using the PUBMED, EMBASE, and Cochrane databases.
The PUBMED query string used was: (((conducted
OR conductive) AND (energy OR electric* OR electronic)
AND (weapon* OR device*)) OR ((electric* OR electronic)
AND (control OR discharge) AND (weapon* OR device*))
OR “stun gun” OR taser* OR “Conducted Energy Weapon
Canadian Journal of Cardiology 31 (2015) 1439e1446
Received for publication December 1, 2014. Accepted February 9, 2015.
Corresponding author: Dr James M. Brophy, McGill University Health
Center, Royal Victoria Hospital, 687 Pine Ave West, Ross 4.12, Montreal,
Quebec H3A 1A1, Canada. Tel.: þ1-514-934-1934 Â36771; fax: þ1-514-
843-1493.
E-mail: james.brophy@mcgill.ca
See page 1445 for disclosure information.
http://dx.doi.org/10.1016/j.cjca.2015.02.006
0828-282X/Ó 2015 Canadian Cardiovascular Society. Published by Elsevier Inc. All rights reserved.
Injuries”[Mesh]) AND (“Law Enforcement”[Mesh] OR
“Police”[Mesh]) AND (“Retrospective Studies”[Mesh] OR
“Prospective Studies”[Mesh] OR “Review”[pt] OR “MetaAnalysis”[pt]).
Because consecutive real world (not volunteer)
cohort studies represented the highest quality real world safety
evidence available (no randomized trials having been conducted),
only such studies in adults that also measured mortality
were retained and formed the objective database.
Specifically, animal, volunteer, modelling, case series, pediatric,
and duplicate studies were excluded. Data were abstracted
and validated by both authors. Only mortalities and total
number of exposed individuals in the retained articles were
abstracted. Mortalities in these studies were represented by
binomial distributions, which are parameterized by the
number of successes (deaths) in a sequence of independent
yes/no experiments.
Direct probability statements can only be made if the
objective data are conditioned on previous beliefs. This is the
correlate of clinical decision-making in which test results are
only sensibly interpreted in a clinical context. To determine
the final (posterior) probability that CEWs are associated with
mortality these objective data (likelihood) must be combined
with previous beliefs about CEWs according to the following
equation:
Posterior distribution ¼
Likelihood of data  previous distribution
Normalizing constant
Although Bayes’ Theorem as expressed in the preceding
formula follows the formal rules of probability in an uncontested
and irrefutable mathematical manner, the difficulty
becomes in choosing a previous distribution. One approach to
this difficulty is to accept that no single previous belief will
reflect everyone’s beliefs. Therefore “pessimistic” (belief in
high CEW mortality risk) and “optimistic” (belief in low
CEW mortality risk) previous beliefs for putative CEW
mortality might be established.10
For example, a “pessimist”
might believe the risk of CEW-related mortality is far from
rare because of the many incidents reported in the media and
the “optimist” might believe that the safety information
supplied by the manufacturer concerning volunteer and
animal studies is reassuring. Medical electronic and unbounded
internet searches were also performed to find all
reports, excluding the objective cohort studies already
mentioned for the likelihood of CEW-associated mortality
and this was used to derive transparent explicit previous
probabilities for CEW mortality.
Although a large range of potential previous beliefs is to be
expected initially, as more objective data accumulate, the effect
of the previous beliefs will reduce and the posterior beliefs
(distributions) of the “optimist and “pessimist” will converge.
These previous distributions can be fully characterized by
specifying 2 parameters; the mode and a measure of the spread
or variation, typically an estimate of an upper limit delineating
the point at which there is a less than 2.5% probability that
the result would fall. For the mathematical convenience of
simple closed-form calculations for the posterior distribution,
we used Beta prior distributions, the conjugate family for the
binomial likelihood. A Bayesian analysis is thus essentially an
updating of the “pessimistic” and “optimistic” previous beliefs
with the best objective data available.
To determine the effect of future studies on the estimate of
CEW mortality and to assess how quickly our subjective
previous estimates become dominated by newly observed
high-quality prospective data, we performed an additional
analysis that assumed that a new cohort with 4 times the
currently available data were to become available.
Computations were done using the R software.11
Results
The objective data
The literature search identified 41 studies via PubMed,
105 from EMBASE, and none in the Cochrane library. From
this sample only 3 large high-quality independent multicentre
cohort studies that recruited consecutive patients were
retained. The first study reported no CEW-attributed deaths
in 1201 consecutive cases of CEW deployment.12
There were
in fact 2 fatalities that were judged by medical examiners not
to be causally related to the CEW. However, 1 fatality
occurred within 5 minutes of CEW deployment and we will
1/107,751 - 1/490). The maximum a posteriori estimated risks of
CEW mortality for the pessimistic and optimistic prior distributions
were 5.3 and 2.2 deaths per 10,000 exposures, respectively. The upper
limits (< 1% probability of occurrence) of the posterior distribution
were 1 death per 408 and 982 CEW exposures for the pessimistic and
optimistic previous beliefs, respectively.
Conclusions: Limited available evidence can be used to construct
approximate boundaries for CEW mortality risk and suggests that the
population risk of CEW mortality is likely small but not negligible. More
high quality data are required to refine these estimates and extreme
caution must be exercised before applying these population risks to
individual cases.
ont ete elaborees. Trois etudes de cohortes formaient la source
objective de donnees et leur mortalite combinee etait de 1 sur 2728
cas ou 3,67/10 000 (intervalle de confiance à 95 %, 1/107 751 - 1/
490). Les risques estimes a posteriori maximaux de la mortalite liee à
l’AI des distributions pessimistes et optimistes precedentes etaient de
5,3 et de 2,2 morts par 10 000 expositions, respectivement. Les
limites superieures (probabilite de survenue < 1 %) de la distribution
posterieure etaient respectivement de 1 mort par 408 et de 982 expositions
à l’AI pour les croyances pessimistes et optimistes
precedentes.
Conclusions : Les rares donnees probantes disponibles peuvent être
utilisees pour etablir les limites approximatives du risque de mortalite
liee à l’AI et montrent que le risque de mortalite liee à l’AI de la
population est possiblement faible, mais non negligeable. Plus de
donnees de haute qualite sont necessaires pour affiner ces estimations.
Il faut egalement faire preuve d’une grande prudence avant
d’appliquer ces risques pour la population à des cas individuels.
1440 Canadian Journal of Cardiology
Volume 31 2015
assume, contrary to the study event adjudicator, that the
CEW was causally responsible for the death. Another cohort
study,13
conducted from 2001 to 2006, also reported no
deaths in 1101 consecutive CEW uses. A third study14
reported
426 consecutive CEW deployments from November
2004 to January 2006, and a single death that occurred 12
hours after CEW deployment, which again was deemed not to
have been caused by the CEW, but by other factors (hyperthermia,
severe cocaine intoxication). Based on these 3 cohort
studies combined, the estimated risk of CEW death is
therefore 1/2728 or 3.67/10,000. A 95% confidence interval,
computed using an ‘exact’ binomial method, ranged from
0.093 to 20.4 per 10,000, indicating that based on these data
alone one cannot exclude the possibility that the risk of death
might be as low as 1 in 107,751, or as high as 1 in 490. If
both deaths in the first cohort study12
were attributed to
CEWs then the risk could be as high as 26 per 10,000, and if
the death from the third study was also assumed to be caused
by CEWs then the risk could be as high as 32 per 10,000 (see
Fig. 1). Conversely, if the original adjudication of no deaths
causally related to CEWs is accepted then the mortality risk
estimated from these cohort studies is likely < 14 per 10,000.
Previous beliefs
As mentioned previously, these objective data can only be
sensibly interpreted in the context of previous beliefs about
the safety of CEWs. There is no single definitive previous
belief and these might range from a “pessimistic” to an
“optimistic” view. The “pessimist” might believe the risk of
CEW-related mortality is far from rare because many incidents
have been reported in the media. For example, Amnesty
International7
reported 334 deaths after CEW use in the
United States from June 2001 to August 31, 2008. Another
Internet site (http://electronicvillage.blogspot.ca/2009/05/
taser-related-deaths-in-united-states.html) claims that in the
United States 351 people died in the period 2000-2008 and
186 in the period 2009-2012 after CEW exposure. Specific
yearly death rates are not provided in either case. Although it
is perhaps highly unlikely that all of these in-custody deaths
were causally related to CEWs, for the “pessimistic” viewpoint
we will nevertheless assume that all of the approximate 100
in-custody deaths reported in the 2005-2008 timeframe were
indeed caused by CEWs. Unfortunately, the exact number of
annual CEW deployments is unknown. The worldwide estimate
of CEW deployments that occurred during the period
2005-2008 is approximately 300,00015
but no information is
provided about how this number was derived. Therefore, we
have conservatively estimated the number of deployments in
the United States using indirect evidence. In a US populationbased
publication on use of force injuries, it was reported
that in 2005-2008 approximately 35,000 emergency room
(ER) visits occurred because of nonfatal CEW injuries.16
Although the percentage of CEW exposures that led to
these hospital visits is unknown, it was reported to be 17% in
one large cohort study.12
If, instead of this 17% ER visit event
rate that one assumes, again pessimistically, that 1 of every 2
CEW exposures (50%) would cause a nonfatal injury leading
to an ER visit, the most likely pessimistic previous mortality
risk belief becomes 100 deaths per 70,000 exposures or 1
death per 700. To fully describe the “pessimist” previous
distribution, we require some measure of its spread. The
pessimist might argue that because of unreported events the
risk might be much higher, perhaps even as high as 1/100. We
have assumed that most “pessimists” would accept that there
is only a small probability (2.5%) that the mortality risk is > 1
per 100 CEW exposures. This upper boundary seems
empirically justified because it represents a signal to noise ratio
(the inverse of the coefficient of variation) < 0.3. Moreover,
this choice of spread for the previous distribution seems
intuitively justified when it is recalled that previous information
can also be expressed as an “effective number” of previously
observed events. In this case, the parameter choices
correspond to 0.72 deaths in 505 exposures (corresponding to
a b [1.72-505] prior). Because of the limited amount of
objective data, a much stronger previous belief would be
difficult to justify for most reasonable people.
For the “enthusiast” or “optimist” previous belief we
apply the same logic. The “optimist” might believe that
because of claims of theoretically safe waveforms, to negative
animal, volunteer, and computer simulation studies, and to
the manufacturer’s claims of absence of definitive proof
regarding the CEW’s ability to induce ventricular fibrillation
in humans that the previous risk of CEW-induced mortality
is very low.15,17
Apparently, the manufacturer, who would
surely be judged an “optimist,” has quoted mortality rates in
the vicinity of 1 in 100,0009
and, although it is impossible
to accord an exact “optimistic” probability, this is likely
much lower than most reasonable people would be
comfortable with. A more cautious “optimistic” opinion of
the previous mortality risk might be in the order of 1 in
7000 or 1/10 the risk of the “pessimist’s” previous belief.
The “optimist” might also believe that the upper limit of risk
(< 2.5% probability) is 1/1000. As previously mentioned,
an equivalent way to think about this previous belief is to
think in terms of the number of events as a representation of
the quantity of information contained in the prior belief.
This assumption about the “optimist’s” previous belief
translates to 0.72 deaths in 5050 exposures (corresponding
to a b [1.72-5050] prior). Notice that the “pessimist” and
“optimist” previous beliefs are quite vague, as reflected in the
low number of “effective” cases they contribute. In this case,
this appears appropriate because the objective data are also
Figure 1. Likelihood function expressed on the scale of deaths per
10,000 conducted energy weapon (CEW) exposures based on 3
cohort studies of consecutive individuals.12-14
Rich and Brophy 1441
Tasers and Cardiac Mortality
sparse and would otherwise be totally dominated by the
perhaps not unreasonable, but nevertheless subjective, previous
beliefs.
Posterior beliefs
For the “enthusiast” or “optimist”, using Bayes’ Theorem,
the best estimate of the posterior probability of CEWassociated
mortality after updating their previous belief with
available objective evidence from the published literature is
2.2/10,000 with minimal chance (< 1% probability), that
this would exceed 1 death per 982 exposures. In contrast, the
“skeptic” or “pessimist” should believe, after updating his
previous beliefs with the best available objective data,11-13
that
the most likely CEW mortality risk is 5.3 deaths per 10,000
exposures with a very small probability (< 1%) that this
would exceed 1 death per 408 exposures. These distributions
are displayed in Figure 2.
Because the estimates of CEW mortality vary depending
on somewhat subjective previous beliefs, further research is
needed. It would be interesting to investigate the effect of a
large multicentre prospective cohort study on these posterior
estimates. Suppose a new registry or previously unpublished
study was identified with 4 immediate deaths likely causally
related to CEWs in 10,000 exposures. Our previous posterior
distributions in Figure 2 could now serve as our previous
beliefs and the incorporation of these new data would result in
the new posterior distributions shown in Figure 3. Figure 3
demonstrates that as more objective data accumulate the
importance of the original subjective pessimistic and optimistic
previous beliefs dissipate and the posterior distributions
become similar. With this hypothetical data the pessimistic
and optimistic modes have quite quickly equalized to
approximately 4 deaths per 10,000 CEW exposures. This
rapid equalization speaks to the vague nature and low power
we assigned to both initial previous beliefs and their dominance
by the accumulating evidence.
Of course, other outcomes for the hypothetical study
might be considered; outcomes closer to the largest or
smallest mortality estimate bounds. An outcome of 2 deaths
in 10,000 exposures would shift both posterior much farther
to the left (Fig. 4), and an outcome of 8 deaths in 10,000
exposures would shift both to the right (Fig. 5), again confirming
the vague nature of the initial previous beliefs.
Notice that again in both cases as more objective data
accumulate the importance of the original pessimistic and
Figure 2. Prior and posterior distributions of the risk of death from conducted energy weapons (CEWs) expressed on the scale of deaths per 10,000
CEW exposures for 2 prior beliefs (optimistic and pessimistic) of CEW-associated mortality.
1442 Canadian Journal of Cardiology
Volume 31 2015
optimistic previous beliefs dissipate and the posterior distributions
become similar.
Discussion
In this report, we have quantified the mortality risk after
CEW exposure, as best possible, using explicit probability
models and all available data sources and evidence. This
analysis recognizes that the, at least partially subjective but not
unreasonable, differing previous beliefs and especially the
paucity of quality objective data will obviously leave some
residual uncertainty in these estimates. Nevertheless, these
results suggest that with a high degree of certainty the CEW
mortality risk is < 1 death per 408 exposures (0.25%) and
possibly < 1 death in 982 exposures (0.10%). This current
analysis provides a more precise estimate of CEW mortality
than a previous review article reporting a very wide mortality
range from 0.0% to 1.4%.18
The present analysis takes no position on the appropriateness
of CEW use as this would seem best decided by law
enforcement agencies and their governing bodies. Rather, in
this analysis we tried to present in a transparent and
mathematically sound manner the risks of CEW mortality
while acknowledging differing but reasonable previous beliefs.
Although the results of this analysis suggest that the risk of
CEW mortality is likely small it should not be concluded that
it is inconsequential. Results of our analysis suggest that the
risk is possibly several orders of magnitude larger than what
has been suggested by the manufacturer.9
In absolute terms, it
has been estimated that between 100 and 300 people per
million US adults are exposed annually to CEWs.15
Although
we appreciate a possibly large amplification of errors in
extrapolation to a population level, our analyses, if correct,
suggests that between 30 to 60 individuals (based on the
“optimist” and “pessimistic” previous beliefs, respectively)
might possibly die annually because of this “less than lethal”
technology.
The present analysis does show how indirect and incomplete
evidence can be used to provide approximate boundaries
as to the risk of mortality after CEW exposure. Clearly, more
high-quality data are required to refine these estimates and
remains a desirable goal. As more objective data become
available the probability distribution functions will narrow
and the previous beliefs will become less important and the
Figure 3. New (updated) posterior distributions of the risk of death from conducted energy weapons (CEWs) expressed on the scale of deaths per
10,000 CEW exposures after the accumulation of data from a new hypothetical study with an outcome of 4 deaths in 10,000 CEW exposures using
the previous optimistic and pessimistic posterior distributions from Figure 2 as the new prior distributions. Notice that as more objective data
accumulate the importance of the original pessimistic and optimistic previous beliefs dissipates and the posterior distributions become similar.
Rich and Brophy 1443
Tasers and Cardiac Mortality
“optimist” and “pessimist” posterior opinions will converge.
We demonstrate that this rapid convergence occurs with only
4 additional deaths from a hypothetical new study of 10,000
CEW exposures. Perhaps this demonstrated benefit of future
studies might serve as an added impetus to collect more systematic
high-quality data in a timely manner so as to improve
our CEW mortality estimates.
A strength of the present study is its transparency in stating
the range of previous beliefs. Current debate has been clouded
by accusations on both sides of the debate concerning conflicts
of interest and potential bias.4-6,9
Our main limitation
rests with the paucity and quality of the objective data. It
should be noted that the literature does not permit an estimate
of CEW mortality for each shock applied but rather for each
CEW encounter, which might entail several shocks for some
individuals. Also we have not considered other serious but
nonfatal injuries. We have also made no estimate of possible
injuries avoided by the avoidance of lethal weapons. Although
CEWs are believed to reduce lethal weapon injuries to suspects
and officer injuries, the evidence to support this seems
fragile.19
Further, no consideration has been given to the risk
of other competing causes of death.
Finally, we have provided only an estimate of the overall
marginal risk of CEW mortality. Extreme caution should be
exercised in applying these population risks to individual cases
because potential competing causes and mediators of mortality
including location of the CEW darts with a likely higher risk
for chest “hits,” number of CEW deployments, underlying
individual cardiac pathology, concomitant use of physical and
chemical restraints, drug intoxications, and their potential
interactions with CEWs need to be considered. This is not
dissimilar to the judgement required in attempts to extrapolate
the overall results from a clinical trial and apply them to individual
patients.
Funding Sources
Dr Brophy receives salary support from the FRQS (Fonds
de recherche du Quebec - Sante), a nonprofit provincial
funding agency.
Figure 4. New (updated) posterior distributions of the risk of death from conducted energy weapons (CEWs) expressed on the scale of deaths per
10,000 CEW exposures after the accumulation of data from a new hypothetical study with an outcome of 2 deaths in 10,000 CEW exposures using
the previous optimistic and pessimistic posterior distributions from Figure 2 as the new prior distributions. Notice that as more objective data
accumulate the importance of the original pessimistic and optimistic previous beliefs dissipate and the posterior distributions become similar.
1444 Canadian Journal of Cardiology
Volume 31 2015
Disclosures
The authors have no conflicts of interest to disclose.
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Figure 5. New (updated) posterior distributions of the risk of death from conducted energy weapons (CEWs) expressed on the scale of deaths per
10,000 CEW exposures after the accumulation of data from a new hypothetical study with an outcome of 8 deaths in 10,000 CEW exposures using
the previous optimistic and pessimistic posterior distributions from Figure 2 as the new prior distributions. Notice that as more objective data
accumulate the importance of the original pessimistic and optimistic previous beliefs dissipates and the posterior distributions become similar.
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Volume 31 2015