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Cost-effectiveness of alternative strategies for provision of HIV preexposure prophylaxis for people who inject drugs

Fu, Ruia; Owens, Douglas, K.b,c; Brandeau, Margaret, L.a

doi: 10.1097/QAD.0000000000001747
Epidemiology and Social

Background: Oral HIV preexposure prophylaxis (PrEP) has been recommended as a means of HIV prevention among people who inject drugs (PWIDs) but, at current prices, is unlikely to be cost-effective for all PWID.

Objective: To determine the cost-effectiveness of alternative strategies for enrolling PWID in PrEP.

Design: Dynamic network model that captures HIV transmission and progression among PWID in a representative US urban center.

Outcome measures: HIV infections averted, discounted costs and quality-adjusted life-years (QALYs), and incremental cost-effectiveness ratios.

Intervention: We assume 25% PrEP coverage and investigate four strategies: first, random PWID are enrolled (Unselected Enrollment); second, individuals are randomly selected and enrolled together with their partners (Enroll Partners); third, individuals with the highest number of sexual and needle-sharing partnerships are enrolled (Most Partners); fourth, individuals with the greatest number of infected partners are enrolled (Most Positive Partners).

Results: PrEP can achieve significant health benefits: compared with the status quo of no PrEP, the strategies gain 1114 QALYs (Unselected Enrollment), 2194 QALYs (Enroll Partners), 2481 QALYs (Most Partners), and 3046 QALYs (Most Positive Partners) over 20 years in a population of approximately 8500 people. The incremental cost-effectiveness ratio of each strategy compared with the status quo (cost per QALY gained) is $272 000 (Unselected Enrollment), $158 000 (Enroll Partners), $124 000 (Most Partners), and $101 000 (Most Positive Partners). All strategies except Unselected Enrollment are cost-effective according to WHO criteria.

Conclusion: Selection of high-risk PWID for PrEP can improve the cost-effectiveness of PrEP for PWID.

aDepartment of Management Science and Engineering, Stanford University, Stanford

bVA Palo Alto Health Care System, Palo Alto

cStanford Health Policy, Centers for Health Policy and Primary Care and Outcomes Research, Stanford University, Stanford, California, USA.

Correspondence to Rui Fu, Department of Management Science and Engineering, Huang Engineering Center, Stanford University, 475 Via Ortega, Stanford, CA 94305-4026, USA. Tel: +1 650 575 9161; fax: +1 650 723 1919; e-mail:

Received 23 August, 2017

Revised 13 December, 2017

Accepted 22 December, 2017

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HIV causes a substantial health burden in the United States, with a disproportionate impact among people who inject drugs (PWID). HIV prevalence among US PWID is approximately 25 times that of the general population [1]. Enhancing HIV prevention programs to reach PWID may greatly reduce morbidity and mortality, thus protecting the health of a vulnerable population [2].

A number of interventions have been proposed for controlling drug injection and its associated harms, including oral HIV preexposure prophylaxis (PrEP). The Centers for Disease Control and Prevention (CDC) recommend PrEP use for uninfected adults who report injection of unprescribed drugs in past 6 months, and in addition have shared injection equipment, enrolled in a drug treatment program, or had risk of sexual HIV acquisition [3]. In prior work, we found that PrEP for PWID in the United States is not cost-effective at current prices and would likely be unaffordable in terms of aggregate expenditures (including the cost of the drug and ongoing care and monitoring) [4]. We also found that PrEP is not likely to be cost effective as part of a portfolio of preventive interventions that includes opioid agonist therapy (OAT), needle and syringe exchange, and intensive testing and treatment for HIV [5].

In this study, we evaluate the cost-effectiveness of various strategies for selecting high-risk PWID for PrEP. We adopt a healthcare sector perspective [6] and, for each strategy, we estimate costs, quality-adjusted life-years (QALYs) gained, incremental cost per QALY gained and HIV infections averted compared with the status quo of no PrEP.

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We model the PWID population in a representative US urban center (i.e. a city with a relatively high population density and approximately 10% HIV prevalence among PWID), using a model of the form developed by Fu et al.[7] (Fig. 1). We capture two types of risky contacts – sexual and needle-sharing – that are the primary routes of HIV transmission among PWID. We use a network model to represent sexual and needle-sharing partnerships [7]. The model is instantiated to reflect sexual and needle-sharing data of enrollees in a needle/syringe program operated by Community Outreach Intervention Projects (COIP) at the University of Illinois at Chicago [8]. The mean age of participants in that study was 40 years old. We obtained the joint sexual and needle-sharing partner distribution for male and female PWIDs in the population, and we simulated a network reflecting this distribution. The contact network evolves dynamically over time as individuals initiate or quit injection drug use, and partnerships form or dissolve. We assumed a constant population size and a steady partnership distribution over time.

Fig. 1

Fig. 1

Disease transmission is restricted by the contact network, and disease progression is simulated separately for each individual in the model. Our model includes HIV testing, antiretroviral therapy (ART) and OAT (e.g. methadone or buprenorphine maintenance) to reflect the current scale of HIV prevention programs targeted to PWID. Table 1 lists values and sources for key model parameters, as well as ranges considered in sensitivity analysis; Table S1, shows values and sources for all parameters. We calibrate the model to the proportion of the population who know they are HIV-infected (infection awareness), ART enrollment, and HIV prevalence trends [1,9,24]. We simulate the model over a 20-year time horizon in monthly time steps and calculate all healthcare costs incurred and QALYs experienced.

Table 1

Table 1

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Our model follows the drug injecting population in a representative US urban center. Reflecting data from COIP [8], we model a population of 5000 male and 3503 female PWID [7]. We assume 9.8% baseline HIV prevalence [1]. We assume an open population: individuals enter the population at a monthly rate of 0.1%, and exit following non-HIV or HIV-related mortality.

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Network model

The network model captures sexual and needle-sharing contacts. We divide sexual partnerships into two types – regular and casual – as they differ significantly in terms of duration, frequency of sexual acts, and consistency of condom use. Similarly, we divide needle-sharing partnerships into long-term and one-time partnerships. Long-term partners share injection equipment on a regular basis, whereas one-time partners share once. It is worth noting that the sexual and needle-sharing networks are correlated, as sexual partners are likely to share needles, and vice versa [8].

To generate a simulated network that reflects the joint degree distribution of the COIP PWID network, we use behavioral data collected by COIP to infer values for the parameters that govern network structure: we obtained data on the proportion of PWID having a regular sex partner, the concurrent sexual partnership distribution, and the distribution of long-term needle-sharing partnerships [8]. We adjust these values in model calibration to account for the fact that PWID who enroll in a needle/syringe exchange program (such as that in COIP) are potentially more risk-aware and less prone to risky behaviors than those who do not [7]. We account for the dynamics of the contact network: each existing partnership dissolves at a rate reciprocal to the average duration of that particular type of partnership. We compute the rates at which new partnerships form, so that the joint degree distribution of the network remains steady over time [7].

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HIV progression and treatment

Upon acquiring HIV, an individual enters an acute phase marked by high viral load and high infectivity, and then progresses through an asymptomatic phase (CD4+ cell count 500–1200 cells/μl), a symptomatic phase (200–500 cells/μl) and finally AIDS (≤200 cells/μl). ART suppresses the HIV virus and slows the progression of HIV disease, leading to decreased infectivity and prolonged average duration of the symptomatic and AIDS stages.

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HIV transmission

The network model captures the two key routes of HIV transmission among PWID – sexual contact and injection equipment sharing. This allows us to model disease acquisition on an individual basis over time. Each sexual partnership is associated with a frequency of sexual behavior and a binary variable indicating consistency of condom use. These two parameters, together with the HIV stage and ART status of the infected partner, and possible PrEP use by the uninfected partner, determine the HIV transmission risk in each sexual partnership. Transmission risks are not constant over time: for example, if the infected partner progresses from asymptomatic to symptomatic HIV infection, his or her viral load rises, thereby increasing the risk of transmission to the uninfected partner.

Each needle-sharing partnership is associated with a frequency of sharing behavior. We assumed three levels of needle-sharing frequency with long-term partners: once per month (in 38% of long-term needle-sharing partnerships), once per week (45% of partnerships), and once per day (17%) [14]. We assume that needle-sharing partners are equally likely to inject with a used needle (receptive sharing); that is, if two partners are sharing a clean needle, there is an equal likelihood of each person being the first to use the needle (a clean needle) or the second to use the needle (a used needle). Transmission risk via each needle-sharing partnership is determined by the number of times a needle is shared with the uninfected partner, the HIV stage and ART status of the infected partner, as well as the uninfected partner's use of PrEP.

At each time step, we simulate disease transmission for every sero-discordant partnership in the network. A susceptible person becomes infected if HIV transmission occurs via any of his or her risky relationships.

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Awareness of HIV status

Infected individuals become aware of their status through HIV testing. We assume that 69.9% of HIV-infected PWID are aware of their infection [1,9]. Unaware patients receive testing at a rate that depends on their disease stage (e.g., individuals with AIDS are more likely to be diagnosed than those with asymptomatic HIV) and OAT status (individuals are screened for HIV upon enrollment in OAT), and whether they are on PrEP (in which case they are screened every 3 months). We calibrate the screening rates for individuals not on PrEP so that at any given time, approximately 69.9% of HIV-infected PWID are aware of their status.

Following a positive diagnosis, some PWID immediately initiate ART and adhere to the treatment for life. This probability of ART uptake is higher for individuals in later HIV stages as they have greater need for sustained medical care and is calibrated to reflect the current ART enrollment level. Awareness of disease status leads to reduced needle-sharing (to a lower level of the three assumed frequencies, if not already at the once per month sharing level) and increased condom use.

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Opioid agonist therapy

OAT reduces the number of risky injections and the overdose mortality risk. In our base-case analysis, we assume that 25% of PWID receive OAT, and the annual entrance and exit rates are balanced to maintain a steady OAT enrollment level. We also assume that PWID who quit OAT resume their risk behavior at the level prior to receiving treatment [25].

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Preexposure prophylaxis strategies

A recent analysis [26] showed that PrEP is most effective when accompanied by a package of clinical care that includes HIV screening every 3 months and increased provision of ART given a positive diagnosis, as recommended by the CDC [4]. We assume a similar program (25% PrEP coverage, HIV screening every 3 months for those enrolled in PrEP, and access to ART for 50% of newly diagnosed PWID) and consider different strategies for enrolling PWID at high risk of HIV acquisition with the hope of improving the cost-effectiveness of the program. We investigate four strategies: first, random PWID are enrolled (Unselected Enrollment); second, individuals are randomly selected and enrolled together with their partners (Enroll Partners); third, individuals with the highest number of sexual and needle-sharing partnerships are enrolled (Most Partners); fourth, individuals with the greatest number of infected partners are enrolled (Most Positive Partners). The last three strategies depend on information about sexual and needle-sharing partnerships: the Enroll Partners strategy relies on the partnership information possessed by each individual, whereas the Most Partners and Most Positive Partners strategies are idealized strategies that require knowledge of every individual's number of risky contacts and, for the Most Positive Partners strategy, the infection status of every individual in the drug injecting population. Located partners who are found to be HIV-infected receive ART at rates consistent with the rest of PWID population.

To initialize the model, we select a group of PWID according to our enrollment strategy and screen them for HIV infection. Individuals with a negative test result are enrolled in PrEP, whereas those who are found to have HIV become aware of their infection and receive ART with a given probability depending on HIV stage [4]. We repeat this process until 25% of PWID are enrolled. As the simulation progresses, some enrollees die from non-HIV causes. In addition, some enrollees become HIV infected as PrEP does not completely eliminate the chance of HIV acquisition; these individuals continue on PrEP until they are diagnosed by screening that accompanies PrEP. New enrollees are selected every 6 months to sustain the 25% enrollment level.

Given the evolution of the contact network as well as the disease status of PWID over time, the high-risk groups reached by the three network-based enrollment strategies also vary over time. To address this variation, we reselect PWID according to our enrollment strategy every 6 simulated months. PWID who are no longer enrolled are assumed to stop PrEP intake.

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Health outcomes and costs

We adopted QALY and cost frameworks from previous HIV studies [19,26,27]. Each simulated month, QALYs and costs accrue to individuals depending on their HIV disease stage, treatment status, and enrollment in OAT and PrEP programs. We also included future health benefits and costs of individuals still alive at the end of the 20-year time horizon using estimates from published literature [4]. We discounted all values to the present at 3% annually [28]. Using WHO criteria, a strategy is considered to be very cost-effective with an incremental cost-effectiveness ratio (ICER) less than the national annual gross domestic product (GDP) per capita ($57, 466 in 2016), and cost-effective with an ICER less than three times the per capita GDP [29]. Thus, the cost-effectiveness threshold adopted for this study is $170 000 (an approximation of $172 398) per QALY gained.

For the Unselected Enrollment strategy, we assume no additional cost to identify and enroll PWID in PrEP; this assumption is natural as PWID are assumed to be randomly recruited and any one-time enrollment costs are negligible compared with the drug cost of $10 000 per year [19–22].

For the Most Partners and Most Positive Partners strategies, obtaining the partnership information of the entire PWID population incurs extra cost. Estimation of such cost is difficult, as it depends on the size of the population, the accessibility of PWID (due to the illicit nature of drug use, PWID may be difficult to reach), the amount of information possessed by each individual (a person may be unaware of the disease status of his/her risky contacts), and a variety of other factors. In our baseline analysis, we assumed no enrollment cost; in sensitivity analysis, we calculated the maximal cost we would be willing to spend on collecting information to make these two strategies still cost-effective.

The Enroll Partners strategy requires health workers to elicit identifying information on the sexual or needle-sharing partners of enrolled PWID, then seek to locate these partners and enroll them in the PrEP program. The cost of contact tracing depends on the cost of collecting and managing identifying information, the cost of physically tracking the identified partners, and the level of incentive offered. The success rate of locating and enrolling partners also affects the cost-effectiveness of such programs. We obtained estimates of the cost and success rate for contact tracing from the Santa Clara County (California) Public Health Department which operates an HIV partner notification service using a team of social workers. They estimate that the cost to track a partner is $400, and that 30% of those they attempt to track can be located [18]. Thus, we assumed in the baseline analysis that the contact tracing cost for the Enroll Partners strategy would be $400 per person, with a 30% success rate. We varied these values widely in sensitivity analysis.

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Model calibration

We calibrated the model so that projected HIV prevalence matches observed trends, and the proportion of HIV-infected PWID aware of infection/receiving treatment as well as OAT enrollment levels remain steady.

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Sensitivity analyses

We performed sensitivity analysis on parameters relating to PrEP program cost, efficacy, and coverage, as well as OAT coverage (ranges in Table 1). As we calibrated the model to match data from the COIP program [8], we did not vary demographic, behavioral, and epidemiological parameters in sensitivity analysis.

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Baseline results

Baseline results are shown in Fig. 2 and Table 2. The least effective strategy is the Unselected Enrollment strategy which, over 20 years, averts 207 new HIV infections and gains 1114 QALYs compared with the status quo. The next most effective strategy, Enroll Partners, averts 435 HIV infections and gains 2087 QALYs compared with the status quo, followed by the Most Partners strategy, which averts 476 HIV infections and gains 2481 QALYs. The most effective strategy, Most Positive Partners, averts 581 HIV infections and gains 3046 QALYs. Costs of the four strategies over the 20-year time horizon are very similar, ranging from $303 million for the Unselected Enrollment strategy to $331 million for the Enroll Partners strategy.

Fig. 2

Fig. 2

Table 2

Table 2

The Most Positive Partners strategy is the most cost effective and dominates all other strategies. (The Most Positive Partners strategy strongly dominates the Most Partners strategy and the Enroll Partners strategy, as it costs less yet accrues more QALYs. It weakly dominates the Unselected Enrollment strategy as it has an ICER that is less than that of Unselected Enrollment strategy). However, as all strategies may not be realistic in some settings, we also present the cost effectiveness of each strategy compared with no PrEP (Table 2). The Unselected Enrollment strategy costs $272 000 per QALY gained compared with the status quo of no PrEP and is thus not likely to be considered cost-effective. The ICER for the Enroll Partners strategy is approximately half as much, at $158 000 per QALY gained compared with the status quo. This shows that even simple targeting can significantly improve the cost-effectiveness of PrEP. The ICER for the Most Partners strategy is further improved, at $124 000 per QALY gained compared with the status quo. The ICER for the Most Positive Partners strategy is lowest, at $101 000 per QALY gained compared with the status quo. All strategies, except the Unselected Enrollment strategy, are cost-effective.

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Results of sensitivity analysis

Cost and success rate of tracking partners

The base case assumed that the cost to track a partner is $400, with a 30% success rate in identifying and enrolling partners. We evaluated the Enroll Partners strategy over a wide range of costs and success rates (Fig. 3), finding that the Enroll Partners strategy is still more favorable than Unselected Enrollment even if the cost per partner traced is $1000 and the success rate in locating partners is 10%. PrEP costs less than $170 000/QALY gained when the contact tracing cost is no more than $600 per partner traced and the success rate in locating and enrolling partners is at least 20%. The ICER did not change much as the contact tracing cost and success rate varied (Fig. 3). This can be explained by the fact that the cost to track partners is much smaller than cost of PrEP itself.

Fig. 3

Fig. 3

Some contact tracing programs may consider paying small incentives to partners who enroll in PrEP. The value of such incentives under different assumptions about success in enrolling partners who receive an incentive can be assessed using the information in Fig. 3.

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Cost of partnership information

Our baseline analysis assumes no cost for obtaining information about the number of (infected) partners that each person has for the Most (Positive) Partners strategy. In sensitivity analysis, we calculated the maximum amount of expenditure per person receiving PrEP to obtain network information such that the enrollment strategies that employ network information are at least as cost-effective as the Enroll Partners strategy. The Most Partners strategy is at least as cost-effective as the Enroll Partners strategy if the cost to obtain information about the number of partners of each individual is no more than $251 per person in the population. The Most Positive Partners strategy is at least as cost-effective as the Enroll Partners strategy if the cost to obtain information about the number of infected partners of each individual is no more than $518 per person in the population.

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Cost of preexposure prophylaxis

We varied PrEP cost from $4000 to $10 000. Figure 4 shows that drug cost critically determines cost-effectiveness. At current drug prices, the cost per QALY gained is below $170 000 for all enrollment strategies except Unselected Enrollment. At a 60% price reduction, the Unselected Enrollment strategy becomes cost-effective, and the Most Partners and Most Positive Partners strategy very cost-effective.

Fig. 4

Fig. 4

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Preexposure prophylaxis efficacy

Previous studies suggest that PrEP's efficacy in reducing HIV acquisition depends strongly on adherence [30]. The Bangkok Tenofovir Study estimated a 49% reduction in risk of HIV acquisition [95% confidence interval (CI): 9.6–72.2], and a 74% risk reduction among high adherers (95% CI: 16.6–94.0) [17]. It is unclear what level of adherence would be achieved if 25% of PWID in the United States received PrEP. To assess this uncertainty, we varied PrEP efficacy from 10 to 90%. Figure 4 shows that cost-effectiveness decreases significantly as efficacy (adherence) decreases, especially for the Unselected Enrollment strategy. When efficacy is below 20%, the cost per QALY gained remains above $170 000 regardless of enrollment strategy. This suggests that insufficient adherence undermines the value of a PrEP program even if it reaches high-risk PWID.

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Preexposure prophylaxis coverage

The baseline analysis assumes 25% PrEP coverage. In sensitivity analysis, we varied coverage from 5 to 50% (Fig. 4), and observed that cost per QALY gained increases as coverage increases, suggesting that PrEP delivers less marginal health benefit as coverage increases. This is probably because in our network model, which reflects data from a PWID network, a high proportion of uninfected PWID have no HIV-infected contacts; a higher coverage level means enrolling individuals who are not at risk of acquiring HIV, driving down the cost-effectiveness of the intervention. This might not be the case for well connected PWID communities (with sexual and needle-sharing contacts between many individuals) or for PWID communities with high HIV prevalence.

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Opioid agonist therapy coverage

We evaluated the influence of the level of OAT coverage on cost-effectiveness of PrEP program by varying it within the range of 25–60%. Figure 4 shows that scaling up OAT reduces the ICERs of Unselected Enrollment, Enroll Partners, and Most Partners strategy, although the reduction of ICERs is in a diminishing manner. For the Most Positive Partners strategy, expanding OAT coverage increases the ICER. This suggests that the marginal health benefit provided by expansion of OAT decreases as the PrEP enrollment strategy reaches individuals at higher risk of acquiring HIV infection.

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Although PrEP for all PWID is likely not cost-effective at current drug prices [4], PrEP programs that can reach PWID who are at substantially higher than average risk of acquiring HIV infection may be cost-effective. We estimate that with Unselected Enrollment, PrEP for PWID would cost $272 000/QALY compared with no PrEP; this is similar to the cost of $253 000/QALY gained estimated in a recent study [4]. A program that enrolls random PWID and then their sexual and needle-sharing partners would be significantly more cost-effective, at $158 000 per QALY gained relative to no PrEP. Although likely not feasible in practice, an idealized strategy that could enroll PWID who have the greatest number of HIV-infected sexual and needle-sharing partners would cost $101 000 per QALY gained relative to no PrEP.

Although the Most Positive Partners enrollment strategy significantly improves the cost-effectiveness of PrEP, the knowledge of the entire contact network that would enable such a strategy is generally unavailable. In contrast, the Enroll Partners strategy is likely to be feasible in a real-world setting. The idea is to start with unselected PWID, then enroll the sexual/needle-sharing partners of these PWID (first wave), then the risky contacts of those individuals (second wave), and so forth until program capacity is reached. Although not as cost-effective as the Most Positive Partners strategy, the Enroll Partners strategy nonetheless provides a significant improvement in cost-effectiveness compared with the Unselected Enrollment strategy, reducing the ICER to $158 000/QALY gained. Our analysis highlights the value of targeting PrEP to PWID who are at increased risk of acquiring HIV.

Although we have shown that PrEP delivers greater population-level health benefits when delivered to PWID at highest HIV risk, we emphasize that other PWID who wish to enroll in PrEP should not be excluded.

Our study has several limitations. We exclude the non-PWID population even though PWID can spread the infection to their non-PWID sexual partners. This exclusion may lead to an underestimate of the cost-effectiveness of PrEP programs. For example, we estimate that the Unselected Enrollment strategy would cost $272 000 per QALY gained compared with the status quo of no PrEP, whereas a study that also included non-PWID estimated that such a program would cost $252 000 per QALY gained [4]. However, inclusion of only PWID in our network model does not undermine the conclusion of our study that targeted PrEP is more cost-effective; inclusion of non-PWID would make PrEP look even more favorable. In addition, we do not include MSM or sex workers in our model though they constitute a nonnegligible proportion of the PWID population [9]. They are often centrally located in the contact network, and selecting this population might make PrEP more cost-effective.

Our model makes several simplifying assumptions regarding needle sharing behavior. We assumed that, in a needle-sharing partnership, each partner is equally likely to inject with a used needle (receptive sharing). A previous study shows that PWID with fewer resources to share are more often engaged in receptive sharing than distributive sharing [31]. Extending our model to assign a specific probability to each needle-sharing partnership of one partner injecting before another would require identifying the socioeconomic status of every PWID in the population and then estimating the probability of receptive and distributive sharing as a function of the difference between the socioeconomic status of two partners. We assumed that awareness of HIV disease status leads to reduced frequency of needle-sharing, but the likelihood of receptive sharing is unaffected by the HIV status of the partners. Some studies report the rate of disclosure of HIV-positive serostatus to injecting partners to be around 33–49%, and some PWID may adopt strategies to manage the risk, such as asking others to wash used equipment, and limiting the number of injecting partners [32–36]. We were unable to find studies that investigate the behavioral change of PWID who become aware of the HIV-positive serostatus of their injecting partners. We also assumed that sharing behavior is unaffected by hepatitis C virus (HCV) status. In a serosurvey of out-of-treatment PWID, those who reported awareness of HCV infection engaged in fewer risky behaviors compared with those who were unaware [37]. Other studies, however, suggest that HCV awareness is insufficient to change injection risk behaviors [38,39] and may even increase needle sharing [40].

Finally, although we performed extensive sensitivity analysis on factors such as PrEP efficacy and cost, and found that the relative cost-effectiveness of PrEP enrollment strategies was unchanged, we cannot address the effect of uncertainty in parameters that govern characteristics of the contact network. This is a common challenge in network models [41].

Our study is the first to evaluate the cost-effectiveness of PrEP for PWID under alternate strategies for enrolling high-risk PWID. Consistent with previous studies on PrEP for MSM and heterosexuals [42–44], we find that PrEP is most valuable when delivered to individuals at highest risk of HIV acquisition. We find that strategies such as enrolling the sexual and needle-sharing partners of PWID enrolled in PrEP can improve the cost effectiveness of PrEP if the partners can be identified efficiently.

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R.F., M.L.B., and D.K.O. designed the study. R.F. collected data and built and ran the simulation model with advice from M.L.B. All authors contributed to analyzing the simulation results and writing the report. Financial support for this study was provided by Grant Number R01-DA15612 from the National Institute on Drug Abuse. D.K.O. was supported by the Department of Veterans Affairs.

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Conflicts of interest

There are no conflicts of interest.

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    cost–benefit analysis; HIV infections/epidemiology; HIV infections/prevention and control; preexposure prophylaxis; United States/epidemiology

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