HPTN 071 (PopART): A Cluster-Randomized Trial of the
Population Impact of an HIV Combination Prevention
Intervention Including Universal Testing and Treatment:
Mathematical Model
Anne Cori1, Helen Ayles2,3, Nulda Beyers4, Ab Schaap2,5, Sian Floyd5, Kalpana Sabapathy5,
Jeffrey W. Eaton1, Katharina Hauck6, Peter Smith6, Sam Griffith7, Ayana Moore7, Deborah Donnell8,
Sten H. Vermund9, Sarah Fidler10, Richard Hayes5, Christophe Fraser1*, HPTN 071 (PopART) study team"
1 MRC Centre for Outbreak Analysis and Modelling, Department of Infectious Disease Epidemiology, Imperial College London, London, United Kingdom, 2 ZAMBART,
University of Zambia, School of Medicine, Ridgeway Campus, Lusaka, Zambia, 3 Department of Clinical Research, London School of Hygiene and Tropical Medicine,
London, United Kingdom, 4 Desmond Tutu TB Centre, Department of Paediatrics and Child Health, Stellenbosch University, Stellenbosch, South Africa, 5 Department of
Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, United Kingdom, 6 Business School, Imperial College London, South
Kensington, London, United Kingdom, 7 FHI 360, Research Triangle Park, North Carolina, United States of America, 8 Vaccine and Infectious Disease Division, Fred
Hutchinson Cancer Research Center, Seattle, Washington, United States of America, 9 Vanderbilt Institute for Global Health and Department of Pediatrics, Vanderbilt
University, Nashville, Tennessee, United States of America, 10 Department of Medicine, Imperial College London, London, United Kingdom
Abstract
Background: The HPTN 052 trial confirmed that antiretroviral therapy (ART) can nearly eliminate HIV transmission from
successfully treated HIV-infected individuals within couples. Here, we present the mathematical modeling used to inform
the design and monitoring of a new trial aiming to test whether widespread provision of ART is feasible and can
substantially reduce population-level HIV incidence.
Methods and Findings: The HPTN 071 (PopART) trial is a three-arm cluster-randomized trial of 21 large population clusters
in Zambia and South Africa, starting in 2013. A combination prevention package including home-based voluntary testing
and counseling, and ART for HIV positive individuals, will be delivered in arms A and B, with ART offered universally in arm A
and according to national guidelines in arm B. Arm C will be the control arm. The primary endpoint is the cumulative threeyear HIV incidence. We developed a mathematical model of heterosexual HIV transmission, informed by recent data on
HIV-1 natural history. We focused on realistically modeling the intervention package. Parameters were calibrated to data
previously collected in these communities and national surveillance data. We predict that, if targets are reached, HIV
incidence over three years will drop by .60% in arm A and .25% in arm B, relative to arm C. The considerable uncertainty
in the predicted reduction in incidence justifies the need for a trial. The main drivers of this uncertainty are possible
community-level behavioral changes associated with the intervention, uptake of testing and treatment, as well as ART
retention and adherence.
Conclusions: The HPTN 071 (PopART) trial intervention could reduce HIV population-level incidence by .60% over three
years. This intervention could serve as a paradigm for national or supra-national implementation. Our analysis highlights the
role mathematical modeling can play in trial development and monitoring, and more widely in evaluating the impact of
treatment as prevention.
Citation: Cori A, Ayles H, Beyers N, Schaap A, Floyd S, et al. (2014) HPTN 071 (PopART): A Cluster-Randomized Trial of the Population Impact of an HIV
Combination Prevention Intervention Including Universal Testing and Treatment: Mathematical Model. PLoS ONE 9(1): e84511. doi:10.1371/journal.pone.0084511
Editor: Michael Alan Polis, National Institute of Allergy and Infectious Diseases, United States of America
Received July 29, 2013; Accepted November 20, 2013; Published January 15, 2014
Copyright: ß 2014 Cori et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted
use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: HPTN 071 is sponsored by the National Institute of Allergy and Infectious Diseases (NIAID) under Cooperative Agreements UM1-AI068619, UM1AI068617, and UM1-AI068613, with funding from the U.S. President’s Emergency Plan for AIDS Relief (PEPFAR). Additional funding is provided through NIAID, the
National Institute of Mental Health (NIMH), the National Institute on Drug Abuse (NIDA), and the International Initiative for Impact Evaluation (3ie) with support
from the Bill & Melinda Gates Foundation. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIAID,
NIMH, NIDA, PEPFAR, 3ie, or the Bill & Melinda Gates Foundation. The study sponsor (DAIDS/NIH) contributed to the study design and review of the manuscript
but had no role in the data collection and analysis or decision to publish. Other study funders contributed to none of the aforementioned activities.
Competing Interests: The authors declare that co-author Sten Vermund is a PLOS ONE Editorial Board member. This does not alter the authors’ adherence to all
the PLOS ONE policies on sharing data and materials.
* E-mail: c.fraser@imperial.ac.uk
" Membership of the HPTN 071 (PopART) study team is provided in the Acknowledgments.
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HPTN 071 (PopART) Trial: Mathematical Model
Mathematical modeling was a key part of designing the HPTN
071 (PopART) trial: we developed a deterministic compartmental
model of HIV transmission specifically conceived to assist the trial
design. We focused on realistically describing the intervention
package to be delivered during the trial. Model parameters were
calibrated based on data collected during previous studies in the
study communities as well as routine national surveillance data.
In the following, we describe this mathematical model and
present the predicted impact of the intervention package that will
be delivered during the trial. Most importantly, we present an
extensive uncertainty and sensitivity analysis to quantify the
influence of process variables (such as the uptake of testing) on the
relative reduction in population level cumulative incidence in the
intervention arms compared to the control arm. This analysis
pinpoints the key variables that drive the magnitude of the
reduction in incidence, and could therefore affect success or failure
of this intervention package. Monitoring those variables during the
trial will enhance evaluation of its progress, as will feeding values
back into the model to obtain revised interim predictions.
Introduction
In 2011, the HPTN 052 trial (HPTN: HIV Prevention Trials
Network) reported that early antiretroviral therapy (ART) reduces
HIV-1 transmission amongst serodiscordant couples by 96% [1].
This finding, obtained in a closely monitored individuallyrandomized trial, corroborated the results of earlier studies [2,3]
and opened new and exciting perspectives for HIV prevention and
control: expanding HIV testing and treatment could reduce sexual
transmission of HIV close to zero [4]. A recent observational study
in South Africa demonstrated that in fact, the ART coverage in
the population immediately surrounding an individual was highly
predictive of his/her risk of HIV acquisition [5]. In this context,
several trials have been designed in order to test the feasibility of
large scale HIV combination prevention strategies including
universal HIV testing with immediate antiretroviral treatment
for HIV-positive persons, and to measure their impact at the
population level [6–10].
HPTN 071 (PopART, Population effects of Antiretroviral
Therapy to reduce HIV transmission) is the largest of these trials,
co-funded by the Office of the US Global AIDS Coordinator
(OGAC), the US National Institutes of Health, and the Bill and
Melinda Gates Foundation. It is planned to start in 2013, with
annual follow-up until 2016, and analyses and results reported in
2017 [11–14].
In brief, it is a cluster-randomized trial consisting of 21
communities in Zambia and South Africa, covering approximately
1.2 million people. Each community, delimited as the catchment
population of a health facility delivering ART, will be randomized
to one of three arms. Interventions in arms A and B will include
home-based voluntary testing (HBT) and counseling, male
circumcision, prevention of mother to child transmission
(PMTCT) services, treatment of sexually transmitted infections
(STIs), condom distribution, and ART for HIV positive individuals. ART will be offered universally (regardless of CD4 count) in
arm A and according to national guidelines (currently CD4,350
cell count per mL of peripheral blood) in arm B. Arm C will serve
as a control arm with health system strengthening activities to
ensure that standard of care services (voluntary testing and
counseling, male circumcision, PMTCT, treatment of STIs, and
ART for HIV positive individuals) are delivered according to
national guidelines. The inclusion of three arms will allow separate
assessment of the benefit of enhanced home-based voluntary
testing, counseling and linkage to care, under national guidelines
for treatment, and the additional prevention benefit of treatment
regardless of CD4 count. The primary end-point will be
cumulative HIV incidence over 3 years, measured in cohorts of
2,500 adults randomly selected in each of the 21 communities
(total cohort size 52,500).
Mathematical modeling is an essential tool to assess the impact
of interventions on HIV epidemics [15] because of the indirect
benefit to members of the population not receiving the intervention. Also, mathematical modeling allows analyzing in a single
framework the effect of multiple interventions, and thus takes into
account synergistic (or interfering) effects between components of a
combination prevention package. Therefore, over the last years,
mathematical models have been increasingly used to provide
insights in the potential long-term impacts of different interventions [4,16,17] and to assist with the post-hoc interpretation of
trials and observational studies [18,19]. It has also become clear
that mathematical modeling could be used more extensively within
clinical trials, to assist trial design, to inform monitoring and
evaluation as a trial progresses, and finally to interpret and
extrapolate the trial results [8].
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Materials and Methods
Model structure
The model was designed with the intention to be simple but
capable of representing different scenarios explored in trial design,
and to represent a relative consensus of existing approaches to
modelling the dynamics of generalised HIV epidemics. Its
structure was particularly inspired by the models of Granich et
al. [4], Hallett et al. [20], and Bezemer et al. [21,22]. The model
describes the generalised HIV epidemics in Zambia and South
Africa, the two countries where the HPTN 071 (PopART) trial will
take place.
The model is a deterministic compartmental model describing
heterosexual transmission of HIV in the population aged 15 and
over, specified by ordinary differential equations for the timeevolution of the number of individuals in different states. Our
model is not age-structured and we therefore do not distinguish
between the intervention, which is universal, and the measurement
of incidence, which is in a cohort of adults aged 18 to 44. Our
choice of age group was motivated by the availability of national
prevalence estimates to which we calibrate our model.
A full description of the model structure, equations and
parameterization, is presented in the supporting information (see
in particular Figures S1 and S2 in File S1 and Tables S1, S2, S3
and S4 in File S1 for model structure and Tables S5, S6, S7, S8
and S9 in File S1 for definitions and values of model parameters).
Individuals are classified by sex (female/male), infection status
(susceptible/infected), and sexual risk propensity (high/medium/
low). The susceptible and infected stages are further stratified to
represent the clinical progression of HIV and the intervention
delivered in each arm of the trial. The model includes temporal
delays between different steps of the intervention (such as testing
and treatment). Susceptible males are classified as uncircumcised,
uncircumcised planning circumcision (following a negative HIV
test), circumcised in the wound healing period, and circumcised
(see Figure 1A). Infected individuals are classified as untreated,
untreated waiting for treatment (following a positive test), treated
but not virally suppressed, and treated and virally suppressed.
Infected individuals who are untreated are further classified in one
of five disease stages: acute/early HIV, followed by four stages
defined by the CD4 count (stage 1 corresponds to CD4$500 cells/
mL peripheral blood, stage 2 to 350#CD4,500, stage 3 to 200#
CD4,350, and stage 4 to CD4,200, see Figure 1B). Upon ART
initiation, infected individuals enter an ART category correspond2
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HPTN 071 (PopART) Trial: Mathematical Model
Figure 1. Model structure for susceptible men. A. Flow diagram of the model. Arrows depict the different flow rates between compartments.
Men can be circumcised during childhood (i.e., before the age of 15). If they are not, they can be circumcised following a negative HIV test. Upon
testing, some HIV negative men decide to get circumcised. They then enter a ‘‘waiting’’ stage, which encompasses the time from testing to them
actually visiting the clinic for circumcision. After circumcision, they go through a healing period, before being circumcised and healed. B. Relative
susceptibility and infectivity in the different stages, relative to an uncircumcised man. Relative susceptibility and infectivity of circumcised men in
healing period incorporate both biological increases in susceptibility and infectivity and reduction in sexual activity during the healing period (see
main text).
doi:10.1371/journal.pone.0084511.g001
scheduled to last 6 months: here we model these taking place from
1st July to 31st December, from 2013 to 2015. Both the schedule
and start date are subject to adjustment, with a likely 4 to 5-month
delay from this modelled schedule. These annual rounds of testing
were modelled by a constant number of tests offered each day by
CHiPs. Following testing by CHiPs (which, when offered, is only
accepted by a proportion of individuals), a fraction of men testing
negative will decide to get circumcised and a fraction of individuals
testing positive will decide to link to care (and start ART if
eligible). Those individuals will go through the ‘‘waiting’’ stages
(awaiting circumcision or awaiting treatment) before becoming
circumcised or initiating treatment. Those stages were modelled to
account for delays from the time that elapses between HIV testing
and presentation at the health facility for circumcision or
treatment initiation.
ing to the CD4 count level at which they initiated treatment, such
that persons initiating treatment at higher CD4 levels have a better
prognosis. A schematic description of the model for infected
individuals is presented in Figure 2A.
Modelling testing, treatment, and circumcision
We separately modelled a background level of HIV-related care
for adults in all arms that would be presumed to occur in the
absence of the trial activities, and an additional process, specific to
interventions implemented in arms A and B during the trial.
Background testing, treatment and circumcision
Background HIV testing was not modelled explicitly. Instead,
we modelled the rate at which individuals initiate ART,
encompassing both testing and successful linkage to care. We
assume that only individuals with CD4,350 could initiate
treatment. The rate at which they do so was modelled as a
smooth function gradually ramping up from 2004 onwards, with a
greater rate for individuals with CD4,200.
We assumed that, in all arms and both countries, a certain
proportion of males are circumcised prior to entry into the
modelled population at age 15. We assume these are fully
circumcised. We did not model any adult circumcision outside of
that offered as part of the intervention package in arms A and B.
Treatment failure and drop-out
Individuals on ART were assumed to stop receiving treatment
(e.g. due to dropping out or treatment failure) at a rate of 10% per
year (an assumption varied in sensitivity analysis). They were then
assumed to go back to the ‘‘untreated’’ stage. They may then be
re-started on treatment at a later time at the same rate as
treatment-naı̈ve persons.
Clinical progression on and off treatment
Additional testing, treatment and circumcision in arms A
and B during the trial
Upon becoming infected, all persons first enter a period of acute
HIV infection lasting for a mean of 2.9 months, after which
infected persons may enter any of the CD4 cell count categories.
The proportion entering each category and the rate of progression
to the next lower CD4 count category were calibrated to recent
During the trial, community HIV care providers teams (CHiPs)
will offer, in arms A and B, home-based testing in annual rounds
in all intervention communities. These intervention rounds are
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Figure 2. Model structure for infected individuals. A. Flow diagram of the model. The model describes progression through different stages of
natural history and treatment. Arrows depict the different flow rates between compartments. Once infected, individuals enter an early/acute infection
stage and then progress to death through 4 stages of infection shown in b. At any stage after acute infection, individuals can get HIV tested,
following which a proportion of individuals will decide to seek care. Those individuals then enter the ‘‘treatment pending’’ stage, during which they
visit the clinic and get assessed towards ART eligibility. Once assessed, all those eligible initiate treatment. Once on treatment, individuals go through
a first phase during which viral load is not fully suppressed, before becoming successfully treated, that is, having a negligible viral load. Individuals on
ART can drop out of or fail treatment; they then go back to the pre-test stages. B. Flow diagram of the four stages of infection following acute
infection and leading to death. Those stages are defined by the level of CD4 in cells/mm3. Individuals can only move from a higher to a lower CD4
count. The rate of progressing through those stages is different for treated and untreated individuals (see File S1). C. Relative infectivity (on the log
scale) of the different stages, compared to an undiagnosed individual with CD4$350, not in acute infection. Individuals in acute infection and stage 4
(CD4,200) have an increased infectivity. Individuals on ART have a decreased infectivity.
doi:10.1371/journal.pone.0084511.g002
of viral suppression and CD4 reconstitution [29] could be
important for capturing long-term predictions of epidemiological
impacts, costs, and clinical benefits. Interpretation of current
clinical data from generalised epidemics in sub-Saharan Africa has
proven difficult because of the confounding of mortality and loss to
follow up [30]; improving these estimates will be an important
feature of the analysis of trial outcomes in HPTN 071 (PopART),
albeit with a relatively short time horizon.
clinical cohort data from the large multinational CASCADE
collaboration [23] (see File S1). Compared to previous models,
which assumed all individuals start with a post-seroconversion
CD4 count $500 and progress through each CD4 stage, the new
model better captures heterogeneity between individuals observed
in the clinical seroconverter data.
Upon treatment initiation, following the approach of Granich et
al. [4], individuals enter a ‘treatment’ compartment mirroring the
CD4 stage from which they initiate treatment. They then progress
through stages of treatment half as fast as untreated patients. This
simple model allows capturing the improved prognosis for patients
initiating treatment at higher CD4 cell counts [24–28]. Sensitivity
analyses show that the short-term predicted epidemiological
impact is not strongly dependent on assumptions about the rate
of progression of individuals on treatment (see supplementary
material in File S1). However, a more mechanistic representation
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Contact patterns, relative susceptibility and relative
infectivity
We use a model of assortative heterosexual sexual mixing
between three sexual risk groups. Individuals in our model form
partnerships at different rates according to their risk group. We
assume that individuals in the low and middle risk groups have on
average one new partner every ten years and one partner every
4
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Table 1. Sensitivity analysis: range of parameter values considered and influence on the relative reduction in 3-year cumulative incidence in arms A and B compared to arm C in
each country.
Parameter
Name
Most pessimistic
Optimistic
*
Central target target
Most optimistic Parameters of the linear regression
ArmA
Arm B
Zambia
South Africa
Zambia
South Africa
(The range of values defined by the most pessimistic and most
optimistic targets was uniformly explored)
Slope
%var**
Slope
%var**
Slope
%var**
Slope
%var**
5
-
-
-
-
-
0.42
-
0.47
-
0.54
-
0.62
-
Relative infectivity due to behavioural
changes at the community level
ibc
1.33
1.0
1.0
0.67
20.32
33%
20.32
34%
20.54
81%
20.58
86%
Relative infectivity of individuals under
ART during the intervention, principally
determined by adherence to ART
iART
0.2
0.1
0.05
0.01
21.1
34%
21.1
35%
20.60
8.4%
20.68
8.9%
Probability of accepting HIV test when offered
by CHiPs
ptest
0.6
0.837
0.867
0.95
0.43
17%
0.41
16%
0.22
3.7%
0.20
2.7%
Probability of going to get treatment
given a positive HIV test delivered by CHiPs
pART
0.7
0.837
0.867
0.95
0.35
6.2%
0.35
6.5%
0.10
0.57%
0.15
0.89%
Proportion of sex acts with individuals from
neighbouring areas
p
0.1
0.05
0.05
0.0
20.71
3.7%
20.70
3.6%
20.19
0.21%
20.27
0.27%
Annual drop-out rate after intervention has
started
QUTT
0.2
0.1
0.1
0.01
20.26
1.7%
20.29
1.9%
20.11
0.27%
20.15
0.24%
Probability of getting circumcised given
negative HIV test delivered by CHiPs
pcirc
0.25
0.5
0.5
0.75
0.096
1.5%
0.028
0.27%
0.17
4.4%
0.057
0.39%
Mean time between positive test and actual
start of treatment (year)
uwait
2/13 (8 weeks)
1/13 (4 weeks)
3/52 (3
weeks)
8/365 (8 days)
20.016
0.098%
20.028
0.035%
20.014
0.16%
20.027
0.054%
Relative susceptibility of individuals waiting
circumcision
spcirc
1
1
1
0.8
20.0050
0.040%
20.0050
0.013%
20.0075
0.005%
0.0027
0.0095%
Average Rate of getting circumcised once
decision to get circumcised has been made
(year21)
tcirc
6 (average delay from
test to circumcision 2
months)
26 (average
delay 2 weeks)
52 (average 182.5 (average
delay 2 days)
delay
1 week)
0.00000016
0.084%
0.000022
0.040%
0.00000069 0.022%
Relative infectivity of individuals waiting
treatment
ipART
1
1
1
20.0037
0.059%
0.0095
0.025%
20.0011
0.060%
0.8
20.000011 0.033%
20.017
0.014%
*Regression exploring the linear dependence of the relative reduction in 3-year cumulative incidence in arms A and B compared to arm C (on the linear-scale) on process parameters (see File S1 for detail).
**%var: proportion of variance in the reduction in 3-year cumulative incidence explained by each predictor (see File S1 for detail).
doi:10.1371/journal.pone.0084511.t001
HPTN 071 (PopART) Trial: Mathematical Model
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Intercept
HPTN 071 (PopART) Trial: Mathematical Model
year, respectively. The average number of partners per year for
individuals in the high risk group is calibrated to fit national HIV
prevalence estimates. We assume partnerships are made preferentially within the same risk group, with a level of assortativity
which is calibrated by fitting the model to national HIV
prevalence estimates. We also assumed that 5% of partnerships
are formed with partners from outside the study community,
thereby allowing for ‘‘contamination’’ of the intervention communities. We further assume that within a partnership, unprotected sexual acts occur at an instantaneous rate which depends on
the risk groups of the two individuals: it is the same for all
partnerships between individuals of different risk groups, as well as
partnerships between two mid-risk individuals; it is twice as high
for partnerships between two high-risk individuals and twice as low
for partnerships between two low-risk individuals.
During the trial, we aim to collect data for better parameterisation of this component of the model.
We assumed that circumcision decreases male susceptibility by
60% [31–34]. We assume infectiousness is greater during acute/
early and late stage infection, and reduced for individuals on ART
(see Figure 1B, Figure 2C and Table S7 in File S1). Men in the
wound healing period following circumcision are assumed to have
decreased sexual activity, but an increased susceptibility and
infectiousness per sex act, in balance leading to an overall reduced
susceptibility and infectiousness during the same period than had
they not undergone circumcision [35,36]. We assume no
difference in infectiousness for circumcised and healed infected
males and uncircumcised infected males.
In a sensitivity analysis, we also investigate potential consequences of reductions in unprotected sexual activity (modelled as
lower susceptibility and infectivity levels) for individuals in the
‘‘waiting’’ stages due to the HIV counselling and condom
distribution.
obtain a neighbour parameter set with an improved fit to HIV
prevalence. Because we were using a local optimisation algorithm,
this did not converge on the global optimum. We compared the
predicted reduction in incidence under these 9 final parameter sets
to the original best-fit parameter combination.
Influence of process parameters
To explore the influence of process parameters that could
potentially be controlled during the intervention implementation,
we defined four scenarios ranging from best to worst case (most
optimistic, optimistic, central and most pessimistic), with corresponding parameters shown in Table 1. For each country, we
generated, using a Latin hypercube sampling scheme [40], a set of
1000 parameters drawn uniformly within the range defined by the
worst and best cases, and examined the resulting variability in the
predicted 3-year cumulative HIV incidence in each arm. In order
to assess the main drivers of this variability, we used a linear model
exploring the relationship between the reduction in 3-year
cumulative HIV incidence in intervention arms and the process
parameters. The relative impact of each process parameter on the
reduction in incidence was assessed by examining the proportion
of the variance explained by each predictor (see File S1).
Results
The projected HIV prevalence and incidence for each country
and in each arm are shown in Figure 3, demonstrating a good fit to
the UNAIDS national prevalence estimates used for calibration.
The saw-tooth pattern in incidence in the intervention arms
projections reflects the six-monthly rounds of the intervention. In a
sensitivity analysis, we found that rounds of 6 months for the
CHiPs intervention would be preferable to rounds of 9 or 12
months, as they would lead to a greater reduction in HIV
incidence over 3 years (see supporting information, in particular
Figure S7 in File S1). The predicted relative reductions in HIV
incidence for both countries are shown in Table 2. Under the
central target, we estimated a reduction in 3-year cumulative
incidence of 61% (Zambia) and 62% (South Africa) in arm A and
25% (Zambia) and 26% (South Africa) in arm B respectively,
compared to standard of care (arm C), with an effect increasing
from one year to the next.
These results were based on parameter values that yielded HIV
epidemics most closely matching UNAIDS prevalence estimates.
Exploring a variety of parameter sets which fitted those relatively
well, we found that very different combinations of parameter
values relating to the contact structure in the population could
match the prevalence data (see Figures S3 to S5 in File S1). This
suggests that these data alone are not very informative about the
structure of contacts between the three risk groups, or the
characteristics of those groups.
Despite those differences, we found that the predicted reduction
in HIV incidence over three years was relatively stable regardless
of the parameter set chosen (see Figure S6 in File S1).
However, the reduction in 3-year cumulative incidence was
highly dependent on the value of process parameters such as the
uptake of circumcision or testing, as illustrated in Figure 4. We
found a very strong linear dependence of the relative reduction in
3-year cumulative HIV incidence on process parameters (adjusted
R-squared .97% in both arms and both countries). The
coefficients of the regression were strikingly similar between
countries, although interestingly, a stronger influence of parameters related to circumcision was found in Zambia, where we
assumed only 13% of men are circumcised during adolescence,
than in South Africa, where we assumed 76% of men are
Model calibration
The non HIV-related death rate was calculated dynamically to
constrain the population size and the birth rate to match national
demographics data since 1978 (see File S1).
The HIV epidemic was calibrated to match HIV prevalence
estimates reported by UNAIDS [37] by varying the basic
transmission rate (l0, the rate at which an untreated infected
individual with CD4$350 not in acute infection transmits to a
partner, assuming they are both in the mid-risk group), the time of
seeding of the epidemic, the proportion of individuals in each risk
group, the rate of sexual contacts in the high risk group, and the
assortativity. The background rate of ART initiation was modelled
as a Hill function increasing from 2004 onwards to achieve the
ART coverage data reported during the ZAMSTAR trial [38,39].
Uncertainty and sensitivity analysis
Uncertainty and sensitivity analyses were conducted to assess
whether the predicted reduction in HIV incidence in the
intervention arms was strongly influenced by the parameter values
chosen to best fit the UNAIDS national prevalence estimates, and
to analyse the impact that the ‘‘process’’ parameters, such as the
uptake of circumcision during the intervention, would have on the
estimated reduction in HIV incidence.
Influence of parameters calibrated to prevalence curves
For each country, we used a Latin hypercube sampling scheme
[40] to simulate epidemics for range of values for the parameters
described in Table 1, and selected the 9 parameter sets (out of
9000) with best fits to the prevalence. For each of these, we then
ran an optimization routine, starting from this parameter set, to
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Figure 3. Model fit and projections under central target scenario for Zambia (top row) and South Africa (bottom row). Left panels
show HIV prevalence and right panels show annualized HIV incidence over time. The red, blue and black lines correspond to arms A, B and C
respectively. The grey dots and error bars are the UNAIDS HIV prevalence estimates [37].
doi:10.1371/journal.pone.0084511.g003
community, not to specific responses in individuals following
ART. While this behavior is an overall modifier that affects all
individuals, it will be balanced by counseling and treatment in
those aware of their status. Therefore the principal manner in
which this community change affects incidence is through changed
risk behaviors in individuals who do not know their serostatus. In
particular, changes towards more risky behaviors could jeopardize
the success of the trial and lead to an increase in incidence in
intervention arms compared to the control arm. On the other
hand, protective changes in sexual behavior resulting from the trial
activities could increase the reduction in incidence beyond that
directly associated with the home-based testing, active linkage to
care, ART and circumcision interventions. However, based on
previous experience, we do not expect major changes in risk
behavior during this trial, and our baseline scenarios reflect this
assumption [41–43].
The second driver of the variability in the reduction in
cumulative incidence was the relative infectivity of individuals
under ART, which accounted for 34% (Zambia) and 35% (South
Africa) of the variance in cumulative incidence in arm A, and
approximately 8% in arm B in both countries. In fact, in arm A,
the relative infectivity of individuals on ART was as important as
the community-level changes in sexual risk behavior in response to
the intervention activities, which accounted for 33% (Zambia) and
34% (South Africa) of the variability in cumulative incidence.
Other important drivers included the uptake of testing and
ART, the proportion of sex acts with partners from outside of the
community and the rate of drop-out from ART. The uptake of
circumcision was found to have little influence on the outcome in
South Africa, but a larger influence in Zambia, especially in arm
B.
Although the intervention is planned to run for a 3-year
duration, we looked at the impact of an intervention extended to a
circumcised during adolescence, as measured in ZAMSTAR
[38,39] (see Table 1).
Unsurprisingly, the major driver of the variability in the
reduction in incidence was the magnitude of community-level
changes in sexual risk behavior in response to the intervention
activities (ibc), especially in arm B, where over 80% of the variance
in the outcome is explained by ibc. We emphasize that in the
model, behavior change refers to an overall response in the
Table 2. Projected impact of the intervention on HIV
incidence in Arms A and B compared with Arm C for central
and optimistic target scenarios (specific parameter values for
each scenario defined in Table S10 in File S1).
Country
Relative reduction in…
Central
target
Optimistic
target
Arm A Arm B Arm A Arm B
Zambia
3-year cumulative incidence 61%
25%
63%
27%
2-year cumulative incidence 58%
24%
61%
25%
First year incidence
51%
20%
54%
21%
Second year incidence
65%
27%
67%
28%
Third year incidence
67%
29%
68%
30%
South Africa 3-year cumulative incidence 62%
26%
64%
27%
2-year cumulative incidence 59%
25%
61%
26%
First year incidence
52%
22%
55%
23%
Second year incidence
65%
28%
67%
29%
Third year incidence
68%
29%
69%
30%
doi:10.1371/journal.pone.0084511.t002
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HPTN 071 (PopART) Trial: Mathematical Model
Figure 4. Uncertainty on the trial outcome in Zambia (top panels) and South Africa (bottom panels). The red and blue histograms show
the relative reduction in 3-year cumulative incidence in arms A and B respectively when parameters vary within ranges shown in Table 1. The left
panels show results obtained when all parameters are varied, and the right panels when assuming no population-level behavioural changes
associated with the intervention.
doi:10.1371/journal.pone.0084511.g004
10-year horizon under the central target. We found a reduction in
10-year cumulative incidence of 63% and 29% in arms A and B
respectively in Zambia, and 64% and 29% in South Africa,
compared to standard of care (arm C). The relative reduction in
incidence for year 10 only would be 61% and 30% for arms A and
B respectively in Zambia, and 64% and 31% in South Africa.
trials, should be enough to assess its progress in real time and to
increase targeted efforts if needed.
Unsurprisingly, we found that important threats to the trial
success would be increases in risky sexual behaviors at the
population level in response to the trial activities and secondarily
the uptake of testing and ART as well as non-adherence to
treatment. We hypothesize that continued counseling, facilitated
by the annual visits of the CHiP teams in all households will be
important to prevent increased risk behaviors and promote
adherence.
The uptake of circumcision appeared to be a relatively
important factor in determining changes in incidence in Zambia,
where the current circumcision levels are low, but less so in the
South African trial sites, located in the Western Cape region where
circumcision is more common.
We found that once uptake of the intervention and adherence
are ensured, minimizing delays in linkage to care would favor the
trial success, but might not be as crucial as could have been
anticipated, if those delays do not greatly exceed those we have
explored here.
Importantly, 10-year model projections suggested that in the
long term, prolonged interventions similar to those proposed in
arms A and B would allow to maintain HIV incidence at lower
levels, but not achieve elimination. This result is different to that of
Granich et al. [4] who found that annual incidence could be
reduced below 1 per thousand per year within only a few years.
However, that model made much more optimistic assumptions
about the reduction in infectiousness for persons on ART (99%
versus 90% in our central target scenario) as well as uptake of
universal testing and treatment (92% of untreated persons per year
versus 70% in our central target scenario), which we showed were
important determinants of the reduction in HIV incidence. Our
model predictions had previously been compared to predictions of
eleven other models, in a study designed to assess the influence of
assumptions regarding HIV epidemiology on the predicted impact
of ART on HIV incidence [16]. Although long-term predictions
Discussion
We developed a deterministic compartmental model to predict
the potential impact of the intervention activities that will be
undertaken in the HPTN 071 (PopART) trial, designed to explore
the potential population effect of universal home-based testing (in
arm B) and universal testing and treating (in arm A) on HIV
incidence in large communities in Zambia and South Africa. Our
pre-trial modeling analysis predicts that if intervention targets are
reached, HIV incidence will decrease dramatically in both
intervention arms, with a 3-year cumulative reduction of 61 to
62% in arm A and 25 to 26% in arm B, relative to standard of care
(arm C), in both countries. Our model predicts that the reduction
in cumulative HIV incidence associated with home-based HIV
testing (.25% over 3 years in arm B) will be much greater than
that effected by community-based HIV testing in a recent trial in
sub-Saharan Africa and Thailand (14% over 3 years, not
statistically significant) [44].
In addition to projecting the overall impact of the complex
intervention package for the purposes of designing and ensuring
adequate power in the trial, understanding, in this pre-trial phase,
the modifiable factors affecting the reduction in incidence is
crucial to prioritize allocation of human and financial resources to
areas where the success of the intervention could be threatened.
We showed that the reduction in 3-year cumulative incidence in
the intervention arms compared to the control arm is almost
linearly determined by a handful of process parameters. This
linear dependency suggests that monitoring a few parameters
during the course of the HPTN 071 (PopART), and other similar
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HPTN 071 (PopART) Trial: Mathematical Model
varied substantially across models, our model was generally
consistent with others, and rather conservative with regards to
the long-term reductions in incidence due to ART. Epidemiologic
and service uptake data collected during the trial, in conjunction
with mathematical modelling, should improve the accuracy and
precision of future model projections and allow re-evaluation of
the effort required to achieve HIV elimination.
In the uncertainty analysis, we found that the relative reduction
in incidence over the three years of the trial was largely insensitive
to input parameters (such as structure of the sexual mixing matrix),
despite great uncertainty on some of these parameters. However,
such uncertainty can affect the long term projections of
interventions, as illustrated by the variability in the predicted
reduction in cumulative 10-year incidence in Arm A in South
Africa (see Figure S6 in File S1) when assuming that the
intervention were extended to a 10-year horizon. Similarly,
improving the mechanistic representation of viral suppression,
CD4 cell dynamics, and survival on ART, would probably affect
the long-term projections, although unlikely to change the shortterm ones. Data collected during the trial, in particular through
the questionnaires administered in the population cohort and in
planned case-control studies, will help quantify some of those
parameters directly, notably the parameters describing the
structure of contacts between and within risk groups. The prospect
of combining these granular survey and biomarker data with novel
phylogenetic methods for associating clusters of transmissions
provides a unique opportunity to answer long-standing epidemiological questions, such as the amount of transmission occurring
during primary HIV infection [45], patterns of sexual mixing, the
geographic patterns of infection [46,47] or the importance of core
groups of highly transmissible or particularly at-risk individuals.
This will be crucial when trying to generalize the trial results to
wider spatial and temporal scales.
Indeed, the HPTN 071 (PopART) trial will be performed at an
unusually large scale, with approximately 1.2 million individuals
across all clusters and trial arms [11,14]. Therefore this
intervention could serve as a paradigm for routine implementation
of universal testing and treatment on a provincial or even national
scale. The economic analysis of HPTN 071 will provide guidance
on whether routine implementation is a valuable investment in the
health of populations, and is therefore an integral part of the trial.
It will help policymakers assess the costs and benefits of universal
testing and treatment, in comparison to alternative strategies. In a
collaborative effort to estimate the cost-effectiveness of earlier
ART eligibility and expanded access to ART in low- and middleincome settings, both the population-level health-benefits and
particularly the implementation costs of earlier ART eligibility and
achieving high levels of access to early ART were identified as key
uncertainties and sources for caution in policy setting; the HPTN
071 trial is ideally placed to answer these questions. Many
expected benefits of HPTN 071, including saved future healthcare
costs due to secondary infections averted, will occur after the trial.
It is therefore crucial to integrate the projected outcomes from the
epidemiological model into an economic model, with the objective
of calculating the cost-effectiveness of HPTN 071 over different
time horizons.
The model used in this analysis relies on simplified representations of the complex dynamics of HIV infection and the
determinants of the spread of HIV. Data collected during the trial
will allow assessing the extent to which simplifications we have
made, such as omitting age structure, considering only heterosexual sex, disregarding the nature of sex, assuming similar
distribution of men and women amongst risk groups, or assuming
independence between risk group and propensity to have sexual
PLOS ONE | www.plosone.org
contacts outside of the community, are reasonable. The model also
does not include selection and transmission of drug resistant strains
of virus. A more detailed model, informed by those data, will be
developed during the trial and used to help interpreting the trial
results. This future model will also be able to account for how
potential changes in the national treatment guidelines in Zambia
and South Africa and other secular changes in the epidemic and
the response to the epidemic affect the outcomes of the trial and
the course of these severe HIV epidemics.
Our analysis highlights the role that mathematical modeling can
play in trial development and monitoring, and more widely in
evaluating the impact of treatment as prevention. In the case of the
HPTN 071 (PopART) trial, we showed that a reduction in 3-year
cumulative incidence by over 60% could be expected, but would
require careful real-time monitoring of the intervention uptake to
ensure adequate program coverage.
Supporting Information
File S1 Combined supporting information. This file
contains a detailed description of the model structure and
parameterization as well as sensitivity analyses.
(PDF)
Acknowledgments
The members of the HPTN 071 (PopART) study team are (in addition to
named authors): Yaw Agyei (Department of Pathology, Johns Hopkins
University School of Medicine, Baltimore, Maryland, USA), Megan
Baldwin, (Vaccine and Infectious Disease Division, Fred Hutchinson
Cancer Research Center, Seattle, Washington, USA), Mark Barnes (Ropes
& Gray LLP, Boston, Massachusetts, USA), Peter Bock (Desmond Tutu
TB Centre, Stellenbosch University, South Africa), Virginia Bond (London
School of Hygiene and Tropical Medicine, London, UK and ZAMBART,
University of Zambia, School of Medicine, Ridgeway Campus, Lusaka,
Zambia), David Burns (Division of AIDS, National Institute of Allergy and
Infectious Diseases, U.S. National Institutes of Health, Bethesda,
Maryland, USA), Nathaniel Chishinga (ZAMBART, University of
Zambia, School of Medicine, Ridgeway Campus, Lusaka, Zambia),
Vanessa Cummings (Department of Pathology, Johns Hopkins University
School of Medicine, Baltimore, Maryland, USA), Lynda Emel (Vaccine
and Infectious Disease Division, Fred Hutchinson Cancer Research
Center, Seattle, Washington, USA), Susan Eshleman (Department of
Pathology, Johns Hopkins University School of Medicine, Baltimore,
Maryland, USA), Peter Godfrey-Faussett (London School of Hygiene &
Tropical Medicine, London UK), Elizabeth Greene (FHI 360, Durham,
North Carolina, USA), James Hargreaves (Department of Infectious
Disease Epidemiology, London School of Hygiene & Tropical Medicine,
London, UK), Tanette Headen (FHI 360, Durham, North Carolina, USA),
Lyn Horn (Desmond Tutu TB Centre, Stellenbosch University, South
Africa), Peter Kim (Division of AIDS, National Institute of Allergy and
Infectious Diseases, U.S. National Institutes of Health, Bethesda,
Maryland, USA), Estelle Piwowar-Manning (Department of Pathology,
Johns Hopkins University School of Medicine, Baltimore, Maryland,
USA), Katie McCarthy (FHI 360, Durham, North Carolina, USA),
Maurice Musheke (ZAMBART, University of Zambia, School of
Medicine, Ridgeway Campus, Lusaka, Zambia), Albert Mwango (ZAMBART, University of Zambia, School of Medicine, Ridgeway Campus,
Lusaka, Zambia), Alwyn Mwinga (ZAMBART, University of Zambia,
School of Medicine, Ridgeway Campus, Lusaka, Zambia), Monde
Muyoyeta (ZAMBART, University of Zambia, School of Medicine,
Ridgeway Campus, Lusaka, Zambia), Musonda Simwinga (ZAMBART,
University of Zambia, School of Medicine, Ridgeway Campus, Lusaka,
Zambia), Kwame Shanaube (ZAMBART, University of Zambia, School of
Medicine, Ridgeway Campus, Lusaka, Zambia), Deborah Watson-Jones
(Department of Clinical Research, London School of Hygiene & Tropical
Medicine, London, UK and Mwanza Intervention Trials Unit, Mwanza,
Tanzania), Shauna Wolf (Department of Pathology, Johns Hopkins
University School of Medicine, Baltimore, Maryland, USA), Rhonda
White (FHI 360, Durham, North Carolina, USA).
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January 2014 | Volume 9 | Issue 1 | e84511
HPTN 071 (PopART) Trial: Mathematical Model
materials/analysis tools: AC JWE CF. Wrote the paper: AC JWE CF.
Contributed to revising the manuscript and approved the final version: AC,
HA, NB, AS, S. Floyd, KS, JWE, KH, PS, SG, AM, DD, SHV, S. Fidler,
RH, CF.
Author Contributions
Conceived and designed the experiments: AC, HA, NB, AS, S. Floyd, KS,
KH, PS, SG, AM, DD, SHV, S. Fidler, RH, CF. Performed the
experiments: AC. Analyzed the data: AC CF. Contributed reagents/
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