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Technical Note
Medical Decision Making
1–8
ÓThe Author(s) 2021
Article reuse guidelines:
sagepub.com/journals-permissions
DOI: 10.1177/0272989X211021603
journals.sagepub.com/home/mdm
Maximizing the Efficiency of Active Case
Finding for SARS-CoV-2 Using Bandit
Algorithms
Gregg S. Gonsalves , J. Tyler Copple, A. David Paltiel, Eli P. Fenichel,
Jude Bayham, Mark Abraham, David Kline, Sam Malloy, Michael F. Rayo,
Net Zhang, Daria Faulkner, Dane A. Morey, Frank Wu, Thomas Thornhill,
Suzan Iloglu , and Joshua L. Warren
Even as vaccination for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) expands in the United
States, cases will linger among unvaccinated individuals for at least the next year, allowing the spread of the corona-
virus to continue in communities across the country. Detecting these infections, particularly asymptomatic ones, is
critical to stemming further transmission of the virus in the months ahead. This will require active surveillance efforts
in which these undetected cases are proactively sought out rather than waiting for individuals to present to testing
sites for diagnosis. However, finding these pockets of asymptomatic cases (i.e., hotspots) is akin to searching for nee-
dles in a haystack as choosing where and when to test within communities is hampered by a lack of epidemiological
information to guide decision makers’ allocation of these resources. Making sequential decisions with partial infor-
mation is a classic problem in decision science, the explore v. exploit dilemma. Using methods—bandit algorithms—
similar to those used to search for other kinds of lost or hidden objects, from downed aircraft or underground oil
deposits, we can address the explore v. exploit tradeoff facing active surveillance efforts and optimize the deployment
of mobile testing resources to maximize the yield of new SARS-CoV-2 diagnoses. These bandit algorithms can be
implemented easily as a guide to active case finding for SARS-CoV-2. A simple Thompson sampling algorithm and
an extension of it to integrate spatial correlation in the data are now embedded in a fully functional prototype of a
web app to allow policymakers to use either of these algorithms to target SARS-CoV-2 testing. In this instance,
potential testing locations were identified by using mobility data from UberMedia to target high-frequency venues in
Columbus, Ohio, as part of a planned feasibility study of the algorithms in the field. However, it is easily adaptable
to other jurisdictions, requiring only a set of candidate test locations with point-to-point distances between all loca-
tions, whether or not mobility data are integrated into decision making in choosing places to test.
Keywords
bandit algorithms, reinforcement learning, SARS-CoV-2, surveillance, testing
Date received: December 31, 2020; accepted: May 10, 2021
Even as vaccinations against severe acute respiratory
syndrome coronavirus 2 (SARS-CoV-2) roll out in the
United States, new infections continue to mount across
the country.
1
However, while new infections will decrease
as more people are immunized, lingering cases of the cor-
onavirus will still exist in communities across the United
States, frustrating attempts to fully suppress transmission
and end the pandemic.
2
Even though multiple sites for
testing for SARS-COV-2 are available in many
Corresponding Author
Gregg S. Gonsalves, Department of Epidemiology of Microbial Dis-
eases, Yale School of Public Health, Public Health Modeling Unit, 350
George Street, 3rd Floor, New Haven, CT 06511, USA
(gregg.gonsalves@yale.edu).
communities, tracking down and detecting many cases of
the virus will require active surveillance, in which public
health workers seek out infections rather than waiting
for individuals to present for diagnosis.
3
While active surveillance efforts, particularly tied to
contact tracing, were stymied by the scale of the epidemic
in 2020 in the United States, other countries, particularly,
China, South Korea, Hong Kong, Singapore, Taiwan,
Australia, Vietnam, and New Zealand, achieved low
community transmission levels through robust control
measures that include extensive surveillance efforts.
4,5
In
fact, relying on presentation to health care facilities for
diagnosis cannot contain the pandemic, and community-
based surveillance and contact tracing are vital to early
detection of new cases and prevention of the resurgence
of the disease.
5,6
Community-based surveillance efforts in the United
States are now widespread and have taken SARS-CoV-2
testing out of the health care setting. There are different
types of off-site testing designs, retrofitting existing struc-
tures (e.g., a sporting venue) and using tents for pop-up
clinics and vans to take SARS-CoV-2 testing fully
mobile.
7
Our efforts are directed toward the last two
design choices, in which SARS-CoV-2 testing does not
depend on individuals seeking out a fixed site but can be
moved to seek out places in the community at higher risk
for transmission than others and reach vulnerable popu-
lations that may not be able to reach other venues at a
distance from their homes (e.g., the elderly, those with-
out transport).
These kinds of mobile testing opportunities have been
successful in increasing uptake of human immunodefi-
ciency virus (HIV) testing in the United States and
abroad, particularly targeting high-risk populations that
otherwise may not come forward for screening.
8–10
This
targeted testing among high-risk communities is now
also happening in the context of coronavirus disease
2019 (COVID-19).
11
Combining these types of testing
interventions with geospatial and phylogenetic data,
information on social and sexual networks has also been
proposed as a way to home in on hotspots of HIV,
increasing the yield of testing.
12
However, even with
these kinds of efforts, approximately 14% of Americans
living with HIV remain unaware of their HIV serostatus,
leaving the detection of undiagnosed infections as the
‘‘holy grail’’ of HIV control efforts, indicating additional
approaches are necessary to reach these individuals.
13
A
similar situation may persist with SARS-CoV-2 in the
United States, with many undiagnosed infections still
undetected across the country.
14
As happened with HIV infection, new platforms for
SARS-CoV-2 testing are emerging quickly, from at-
home tests to rapid antigen assays to supplement stan-
dard laboratory-based polymerase chain reaction (PCR)
diagnostics, with saliva-based alternatives to invasive
nasopharyngeal swabs for the comfort and convenience
of patients.
15
But these technologies cannot address the
simple question that underlies active surveillance efforts:
where can we find lingering cases of SARS-COV-2?
Identifying most, if not all, infections in the United
States through active case finding, contact tracing, isola-
tion of infected individuals, and quarantine of their con-
tacts is the ideal route to containing SARS-CoV-2.
16–18
Universal testing, contact tracing, and isolation strate-
gies for SARS-CoV-2 deployed in places like Wuhan,
China, and akin to the universal test-and-treat efforts for
HIV in some countries are expensive, are resource inten-
sive, and, in the context of SARS-CoV-2 control in
Wuhan, have raised human rights concerns.
19,20
If uni-
versal testing, contact tracing, and isolation are infeasible
for the United States, how can we maximize the yield of
new cases detected? While we might target pop-up or
mobile testing to places where we believe the prevalence
of undetected infection to be very high (e.g., apartment
buildings, nursing homes, police stations) in many cities
and towns, choosing between these venues may be diffi-
cult both in terms of their epidemiological value (i.e., the
Department of Epidemiology of Microbial Diseases, Yale School of
Public Health, New Haven, CT, USA (GSG, JTC, FW, TT, SI);
Department of Health Policy and Management, Yale School of Public
Health, New Haven, CT, USA (ADP); Yale School of the Environ-
ment, New Haven, CT, USA (EPF); Department of Agricultural and
Resource Economics, Colorado State University, Fort Collins, CO,
USA (JB); DataHaven, New Haven, CT, USA (MA); Center for Bios-
tatistics, Department of Biomedical Informatics, The Ohio State Uni-
versity, Columbus, OH, USA (DK); Battelle Center for Science,
Engineering, and Public Policy, John Glenn College of Public Affairs,
The Ohio State University, Columbus, OH, USA (SM, NZ); Integrated
Systems Engineering, The Ohio State University, Columbus, OH, USA
(MFR, DAM); College of Public Health, The Ohio State University,
Columbus, OH, USA (DF); Department of Biostatistics, Yale School
of Public Health, New Haven, CT, USA (JLW); Public Health Model-
ing Unit, Yale School of Public Health, New Haven, CT, USA (GSG,
JTC, ADP, FW, TT, SI). The author(s) declared no potential conflicts
of interest with respect to the research, authorship, and/or publication
of this article. The author(s) disclosed receipt of the following financial
support for the research, authorship, and/or publication of this article:
Financial support for this study was provided entirely by grants from
the National Institute on Drug Abuse DP2 (DA049282 to GSG), R37
(DA15612 to GSG and ADP), the National Institute of Allergy and
Infectious Diseases R01 (AI137093 to JLW), the National Science
Foundation Northeast Big Data Innovation Hub Subaward 4
(GG01486-02) PTE Federal Award (No. OAC-19165850) (EPF), Yale-
AWS Enterprise Agreement (EPF), and the Tobin Center for Economic
Policy at Yale University (EPF). The funding agreement ensured the
authors’ independence in designing the study, interpreting the data,
writing, and publishing the report.
2Medical Decision Making 00(0)
underlying prevalence at a site) and the willingness of
people passing through these locations to volunteer for
testing.
The elements of the predicament for screening for
SARS-CoV-2 in the United States are clear: many people
remain undiagnosed with SARS-CoV-2, and the pros-
pects of universal testing of entire communities are slim.
Thus, we want to maximize the number of cases detected
with the limited resources we do have while cognizant
that we also have imperfect information about where
these undetected infections are to be found. Policy-
makers have choices about how to address this problem.
In deciding where to deploy their testing resources, pol-
icymakers must choose between making the best possible
choice based on their current understanding of the evi-
dence and investing in improving their understanding of
the evidence in the hope that it will lead to even better
choices in subsequent periods. That is, policymakers can
go with what they know and target testing at places they
assume are high risk (e.g., nursing homes), but the kinds
and numbers of high-risk venues, which might yield the
most cases, may be large and diverse and shift over
time.
21
In addition, SARS-CoV-2 is an overdispersed
pathogen tending to spread in clusters with heterogeneity
and stochasticity in transmission, and targeting locations
based on simple assumptions about risk environments
may turn up to be dead-ends.
22
Beyond universal testing,
the alternative is to test randomly across a community,
with the hopes of finding ‘‘hotspots’’ but facing the pros-
pect that the number of positive diagnoses may wane at
promising locations as testing uncovers most of the
undiagnosed cases there or the epidemic moves on to
new places in a community. Both of these choices open
to policymakers present an iterative series of questions:
where do we test today, how long do we stay in that
location, when do we move on, and where do we go
next? How can policymakers best make these compli-
cated decisions between the choices open to them for
venues to test for SARS-CoV-2 on an ongoing basis and
in an evidence-based fashion? Here we describe how a
set of tools we have modified and adapted from the
sequential decision making field—namely, bandit
algorithms—may help solve the conundrum of SARS-
CoV-2 testing in the context of limited resources.
The Explore v. Exploit Dilemma
and Bandit Algorithms
The ‘‘explore v. exploit dilemma’’ is a classic problem,
where a limited resource must be deployed across alter-
native targets in a way that maximizes overall gain, when
the critical attribute of each target is only partially
known at the time of deployment but may become better
understood as a result of the deployment decision. This
is a problem that has been studied in depth in the fields
of operations research and decision science. How do you
mine your best current prospects (‘‘exploit’’) while keep-
ing your eye open to better opportunities (‘‘explore’’)?
The tools that are used to address this dilemma are
called bandit algorithms.
23
They are widely used to guide
sequential decisions under uncertainty in a range of set-
tings, from commercial applications (e.g., oil explora-
tion) to military efforts (e.g., searching for downed
airplanes).
24
We have previously studied the use of bandit algo-
rithms for HIV testing—to identify undiagnosed HIV
infection using mobile testing units—for several
years.
24,25
Using model-based simulation studies, we
have shown that bandit algorithms outperform more tra-
ditional approaches for deploying HIV testing resources,
including going this year where you found the most HIV
cases last year or sampling a large number of candidate
locations before settling down on the best place to
test.
24,25
The basic bandit algorithm—known as Thomp-
son sampling—outperforms these other methods.
26
Thompson sampling is an adaptive Bayesian approach.
First, it makes an inventory of all possible target settings.
Second, a policymaker offers an initial assessment of the
prevalence of undetected infection in each target setting.
This takes the form of a probability distribution and is,
by design, a subjective exercise that permits the policy-
maker to be as definitive or tentative as their prior infor-
mation directs them to be. These prior probability
distributions are updated as new information arrives.
Third, the decision to deploy testing resources on the
first day is made via a random selection from the various
prior distributions assigned to each candidate setting.
Fourth, on each day, a record is maintained in every
active testing setting of the total tests performed and the
number of positive cases detected. This information is
used to update the prior distribution for that site. Then,
the decision to deploy testing resources on the next day
is repeated via a random selection using the updated
priors (i.e., posteriors) and the process repeats.
At the outset, this strategy assigns greatest priority to
settings based entirely on the policymaker’s initial assess-
ment, which is based on the data available at the
moment. But as the testing campaign proceeds, this
strategy provides new information about the probability
of finding a case among the available locations by using
the daily test results (positive and negative) at each site
selected to refine the understanding of the prevalence at
each location. Over time, this continuous process of
Gonsalves et al. 3
‘‘learning while doing’’ homes in on the places with
highest potential yield of finding new cases faster than
other strategies. In addition, if the situation changes—
for instance, if one has saturated a given location and
depleted the number of undetected cases in that
location—the posterior distribution associated with that
location will reflect those shifts as well, making it less
likely that the site will be chosen in the future. The algo-
rithm is flexible in its accommodation of the time-value
of information. If, for example, there is reason to believe
that information acquired in previous rounds should
have diminishing influence over time (e.g., the site has
not been visited in a month) or some exogenous factor
has changed the underlying environment (e.g., emergence
of new viral strains or variants), one can apply a ‘‘dis-
count factor’’ that assigns less and less weight to prior
observations as time goes by. Alternatively, if there is
reason to privilege initial assumptions and to make deci-
sions increasingly resistant to new observations, one can
apply a different discount factor that assigns decreasing
weight to newer data.
27
In practical terms, this strategy
is meant on an ongoing basis to guide and draw those
performing testing in the field to the sites where more
people are willing to test and with a premium on loca-
tions with a higher prevalence of undetected infection.
That is, the goal is to maximize yield of positive cases,
not to estimate local prevalence of disease. The details
of the Thompson sampling strategy are described in
Table 1.
We have also developed a variation on Thompson
sampling to account for spatial correlation in the
prevalence of undetected infections between adjacent
geographical areas using a hierarchical Bayesian spatial
modeling framework employing an intrinsic conditional
autoregressive (ICAR) prior distribution for the spatial
random effects and exchangeable, normally distributed
random effects to account for nonspatial heterogene-
ity.
25,28
The details of the spatial algorithm are shown in
Table 2.
Adapting the Bandit Algorithm to SARS-CoV-2
Bandit algorithms, including Thompson sampling and
those that model spatial correlation, can be implemented
easily as a guide to active case finding and screening for
SARS-CoV-2. To provide priors to initialize the algo-
rithms for use with SARS-CoV-2, we defined a set of
highly trafficked candidate locations for daily testing.
For Columbus, Ohio, we used raw data from the Uber-
Media COVID-19 recovery data set (https://covid19.ub
ermedia.com/covid-19-recovery-insights/), which con-
tains pairs of individual smart devices within 5 meters of
each other within a 5-minute window. These data were
cleaned for obvious geolocation errors and to remove
contacts on roadways using the Census Tiger Lines.
These data were then spatially joined with Loveland
Landgrid (https://landgrid.com/) parcel data. We pro-
duced indices of contacts and unique contacts per parcel,
and we also rarified the window of the contact definition.
These various indices generally produced consistent
rankings. We chose highly trafficked locations as these
venues create more opportunities for casual encounters
for testing but also because these bandit algorithms are
sensitive to testing volume, and a low number of volun-
teers could hamper the effectiveness of this approach. In
fact, in our studies of bandit algorithms in the context of
HIV infection, at fewer than 10 tests per day, bandit
algorithms performed poorly.
24
Before deploying these
algorithms in field testing, establishing a floor for daily
testing volume at potential locations through simulation
using best estimates of local epidemiology of SARS-
CoV-2 will be an important operational consideration,
and performing more tests at fewer sites may be a trade-
off to weigh for those using these algorithms in practice.
We supplemented this list of highly trafficked locations
with residential settings (e.g., apartment buildings),
where close contacts are numerous and frequent and
where adherence to social distancing and other infection
control measures may be more difficult. These are likely
to be potential hotspots for disease transmission and
Table 1 Thompson Sampling Strategy for Identifying Testing Sites for Severe Acute Respiratory Syndrome Coronavirus 2.
Algorithm 1 Thompson sampling strategy
For each potential testing site i=1...,nset X
i
(0) =0, Y
i
(0) =0.
for each t=1,2...t
max
,do
For each testing site i=1...,n, sample p
i
(t– 1) from the Beta(a
i
+X
i
(t–1), b
i
+Y
i
(t–1)) distribution.
Select testing site j = argmax
i
p
i
(t– 1).
Perform mBernoulli trials in testing site jand observe x
j
successes and (m–x
j
) failures.
Let X
j
(t)=X
j
(t–1)+x
j
and Y
j
(t)=Y
j
(t–1)+(m–x
j
).
For all testing sites i6¼ j, let X
i
(t)=X
i
(t– 1) and Y
i
(t)=Y
i
(t– 1).
End
4Medical Decision Making 00(0)
could be important places to search for new cases, partic-
ularly in census tracts with no public locations for test-
ing. Because we are assessing the yield of testing at point
locations rather than areal zones, we use the Euclidean
distance between locations rather than map adjacencies
when defining spatial proximity. However, distances
between locations can be defined in other ways given
topographical considerations and local contexts. We set
prior distributions for the prevalences in these locations
with a Beta(0.50,0.50) distribution (i.e., Jeffreys prior),
indicating our lack of knowledge of SARS-CoV-2
prevalence in any of these areas in Columbus. With more
data on the epidemiology of SARS-CoV-2, these prior
distributions could be crafted to reflect more knowledge
of local epidemics. Potential testing sites can also be
determined in other ways beyond the use of cell phone
and epidemiological data. For instance, targeting indus-
tries that are low-work-from-home and demand high
physical proximity for workplace testing could be con-
sidered potential targeting sites where social gatherings
regularly still take place even in the context of the pan-
demic (e.g., houses of worship).
29,30
Table 2 Hierarchical Bayesian Spatial Strategy for Identifying Testing Sites for SARS-CoV-2.
Algorithm 2 BYM strategy
For each potential testing site i = 1, . . ., n set X
i
(0) =0, Y
i
(0) =0.
do while the number of unique potential testing sites is \10:
For each testing site i=1,2,...,n, sample p
i
(t– 1) from the Beta(a
i
+X
i
(t– 1), b
i
+Y
i
(t– 1)) distribution.
Select testing site j = argmax
i
p
i
(t– 1).
Perform mBernoulli trials in testing site jand observe x
j
successes and (m–x
j
) failures.
Let X
j
(t)=X
j
(t–1)+x
j
and Y
j
(t)=Y
j
(t–1)+(m–x
j
).
For all testing sites i6¼ j, let X
i
(t)=X
i
(t– 1) and Y
i
(t)=Y
i
(t– 1).
do while the number of unique visited zones is 10:
Fit the hierarchical Bayesian spatial logistic regression model to the complete set of data:
Xit1ðÞjpi;Binomial Yit1ðÞ+Xit1ðÞ,pi
ðÞ;
logit pi
ðÞ=b0+fi+ui
where Xit1ðÞis the total number of identified severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) cases in testing
site iup to time t–1,Yit1ðÞ+Xit1ðÞis the total number of administered tests in testing site iup to time t–1,pirepresents
the true but unobserved prevalence in testing site i,b0is an intercept parameter, fiis a spatial random effect that follows the
ICAR distribution, and uiis an exchangeable random effect (independent and normally distributed with variance
parameter, s2
u). Note that only previously sampled zones contribute data to the fitting of this model.
The intrinsic conditional autoregressive (ICAR) random effects are defined conditionally as
fijfi,s2
f;Normal Pn
j=1wijfj
Pn
j=1wij
,s2
f
Pn
j=1wij
where fi=f1,...,fi1,fi+1,...,fn
ðÞ
Tand wij describes the spatial proximity between spatial zones iand j(e.g., touching
borders, inverse distance weights) with wii =0for all i.
After fitting the model, we obtain posterior samples from f(pijXt1ðÞ,Yt1ðÞ) for each testing site (even those that have not
been visited yet) where Xt1
ðÞ
and Yt1
ðÞ
are the complete set of data from all zones (Xt1
ðÞ
=X1t1
ðÞ
,...,Xnt1
ðÞðÞ
T;
Yt1ðÞdefined similarly). We then randomly select a posterior sample from each testing site and define it as p
i
(t– 1).
Select testing site j = argmax
i
p
i
(t– 1).
Perform mBernoulli trials in testing site jand observe x
j
successes and (m–x
j
) failures.
Let X
j
(t)=X
j
(t–1)+x
j
and Y
j
(t)=Y
j
(t–1)+(m–x
j
).
For all zones i6¼ j, let X
i
(t)=X
i
(t– 1) and Y
i
(t)=Y
i
(t– 1).
End
Prior specifications:
b0;Normal 0,2:85ðÞ; results in ’Uniform(0,1) prior probabilities for each testing site a priori assuming no excess
variability in the data.
s2
f(variance parameter for the ICAR random effect) ;Inverse Gamma 3:00,2:00ðÞ.
s2
u(variance parameter for the exchangeable random effect) ;Inverse Gamma 3:00,2:00ðÞ.
Gonsalves et al. 5
We have now set up a fully functional prototype of a
web app to allow policymakers in Columbus to use
Thompson sampling to target SARS-CoV-2 testing in
the city (Figure 1).
It is straightforward to adapt the algorithm to other
jurisdictions, requiring only a set of candidate test loca-
tions with point-to-point distances between all locations.
Finally, the only inputs required for these bandit algo-
rithms between testing forays are the number of tests
performed on a given day in each location and the num-
ber of positive tests obtained on that day in that loca-
tion. This makes the algorithm easy to use by local
public health departments. The algorithm is simple
enough that it can make virtually instantaneous use of
new data to inform the deployment of testing units for
the next day’s effort. This would make this approach
best suited for rapid diagnostic tests, particularly rapid
lateral-flow antigen-based assays, which, although with
lower sensitivity than standard PCR, are well positioned
to detect individuals with high titers of SARS-CoV-2
and most likely to transmit in a given settings.
7
In fact,
while a pilot in Columbus, Ohio, is still in the planning
stage, we intend to use the BinaxNOW COVID-19 Ag
Card provided through our collaboration with the Ohio
Department of Health.
31
However, even with standard
PCR-based assays and the delays in reporting of SARS-
CoV-2 results in practice, these tools can be useful. In
this case, the updating of prior distributions for testing
locations will be lagged, so the allocation of new testing
assignments will only benefit from additional informa-
tion about potential yield of new diagnoses among loca-
tions as testing results from previous days become
available. Furthermore, bandit algorithms complement
test pooling strategies and can help to concentrate
Figure 1 Home page of the web app for targeting severe acute respiratory syndrome coronavirus 2 testing with mobile units
(https://netzissou.shinyapps.io/BanditDemo/).
6Medical Decision Making 00(0)
positives within pools to minimize the number of
second-round tests needed. Finally, although these algo-
rithms are simple to set up and run, the practical consid-
erations of deploying testing teams to multiple locations,
often shifting teams at least initially from day to day,
require the support and engagement of local public
health officials, the resources to mount and maintain a
mobile testing program over time, and a seamless inte-
gration of the algorithms into the normal workflow of
testing sites. In the context of SARS-CoV-2, ensuring
safety of those getting tested as well as staff at a given
testing location is also paramount.
7
Bandit algorithms could provide a useful, simple tool
to find needles in a haystack—the tens of thousands of
undiagnosed infections from coast to coast—when one
cannot test everyone, everywhere. As discussed above,
bandit algorithms are widely used to successfully address
the explore v. exploit dilemma in several other fields.
Deployment of bandit algorithms for SARS-CoV-2 may
provide useful answers, enable more cost-effective test-
ing, and offer a lifeline to policymakers trying to figure
out where to test next for SARS-CoV-2.
ORCID iDs
Gregg S. Gonsalves https://orcid.org/0000-0002-5789-9841
Suzan Iloglu https://orcid.org/0000-0003-1611-9850
Research Data
All code and data associated with the web app are available at
https://github.com/NetZissou/Bandit. The web app itself is
available at https://netzissou.shinyapps.io/BanditDemo/.
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