We sought to create a model with a straightforward framework that would be easily understood and interpreted when used either as a personalized risk calculator in a patient-provider encounter or for rapid decision-making by policymakers without modeling expertise. We therefore constructed a decision analysis model that incorporates those parameters most likely to vary across patients and be estimable by providers or policymakers, including both non-modifiable factors (e.g. background HIV prevalence) and modifiable factors (e.g. PrEP adherence). Our primary outcomes were the number needed to treat (NNT) to prevent one HIV acquisition on the individual level and the cost per quality-adjusted life-year (QALY) gained on the population level. Whereas most global policy models have adopted a time horizon of 5–20 years of continuous PrEP use, clinical encounters and policy decisions in this high-risk population generally involve treatment decisions on a much shorter time frame. Thus, we modeled a 1-year duration of PrEP intervention costs and effectiveness to better reflect real-world patient-provider treatment plans. Similarly, we ignored secondary transmission (we included new HIV cases, but not future HIV cases attributable to the new cases), which is less relevant to clinical decisions for an individual patient. To assess the effects of these decisions, we compared our model against other more complex models that incorporated such effects. Our model can be downloaded from the risk calculator website (see below).

The decision tree demonstrating the model structure is shown in Figure 1. Key model parameters are listed in Table 1 [2], [5], [17]–[39]. We modeled HIV acquisition as an independent risk per unprotected receptive anal intercourse act with an HIV positive partner, as in prior studies [17], [40]. To this baseline acquisition risk we applied literature estimates of the relative risk and prevalence of modifying variables, including: insertive rather than receptive intercourse; antiretroviral therapy (ART) use in the infected partner; presence of herpes simplex virus-2 (HSV2), syphilis, gonorrhea, and chlamydia; condom use and PrEP use. Next we used estimates of HIV prevalence in the patients' community to calculate a per-act risk of HIV acquisition (i.e., regardless of a specific partner's HIV status). In this modeling framework, we made the simplifying assumption that all sex acts present an independent risk of HIV acquisition; we did not, for example, additionally model the number of partnerships or temporal heterogeneity in sexual behavior. This simplifying assumption allowed us to incorporate estimates of the monthly frequency of sexual activity [29] to estimate an individual patient's cumulative probability of HIV acquisition per month and per year. For the base-case scenario, epidemiologic parameters reflect generic US-wide estimates (e.g., from the Centers for Disease Control and Prevention, CDC); the corresponding risk calculators enable users to input model parameters most reflective of their specific circumstances.

We compared a strategy of PrEP, following CDC guidelines [3], against no PrEP. PrEP includes documenting negative HIV status and adequate renal function prior to initiation, quarterly clinic visits and HIV testing, bi-annual screening for sexually transmitted infections (STI) and bi-annual renal function testing. PrEP efficacy is highly dependent on adherence; thus we modeled PrEP at differing levels of adherence as per iPrEx subgroup analyses [2]. We compared PrEP to no PrEP in a number of specific scenarios:

While we chose these scenarios for illustrative purposes, the corresponding risk calculators enable users not only to replicate these results, but also to explore a wide range of potential patient behaviors (clinical effectiveness) or population characteristics (cost-effectiveness).

We used literature estimates to calculate costs and quality-adjusted life-years associated with each PrEP scenario vs. no PrEP, taking a societal perspective and lifetime analytic horizon. We estimated the cost of PrEP based on CDC recommendations for care (including drug costs, additional physician visits and laboratory testing beyond that which is recommended for persons not taking PrEP) and the existing literature [5]. We estimated the lifetime cost per additional case of HIV based on literature estimates of the annual cost of HIV care [31]. We also calculated the cost for the testing [5] and treatment [33] of additional sexually transmitted infections (gonorrhea, chlamydia and syphilis) for persons who engage in riskier sexual behavior (e.g. reduced condom use, more frequent sexual encounters) while on PrEP. For all costs, we adjusted to present value in 2012 U.S. dollars using the Medical Care component of the consumer price index [41], and applied a 3% discount rate for costs occurring beyond one year in the future [42]. We estimated QALYs associated with PrEP use based on literature estimates of life expectancy after HIV diagnosis [5], stage of infection [5], and disability weight associated with each stage [35]. We also calculated QALYs lost per additional case of STI in scenarios with behavioral disinhibition, using the disability weight [36] and the relative prevalence [37]–[39] of symptomatic urethral and epididymal gonorrhea/chlamydia; the disability weight [36] and the relative prevalence [33] of primary, secondary and tertiary syphilis; and the overall prevalence of gonorrhea, chlamydia and syphilis [28], [34]. We discounted QALYs for HIV and tertiary syphilis. We did not account for the possible reduction in quality of life stemming from emtricitabine- tenofovir disoproxil fumarate toxicity, or the development of drug resistant HIV, given the lack of evidence of either event in the iPrEx clinical trial.

We created two online, interactive risk calculators coupled to our model of HIV acquisition, which can be accessed at the following websites:

Individual risk calculator: https://ictrweb.johnshopkins.edu/ictr/utility/prep.cfm

Population cost-effectiveness calculator: https://ictrweb.johnshopkins.edu/ictr/utility/prep2.cfm

The personal risk calculator is designed to allow providers to input specific values for certain parameters likely to vary by patient: (1) frequency of condom use, (2) frequency of insertive vs. receptive anal intercourse, (3) number of sexual encounters per month, and (4) current involvement in a monogamous serodiscordant relationship (with or without partner ART use). For patients not in monogamous serodiscordant relationships, the calculator also incorporates (5) the HIV prevalence in the patient's community, providing CDC data for HIV prevalence among MSM stratified by geography, race and age, and allowing for modification by the patient/provider in order to best estimate the patient's sexual network. Given data for these five model parameters, the risk calculator displays point estimates for the annual risk of HIV acquisition for 5 scenarios: (1) No PrEP, (2) PrEP at expected adherence (44% efficacy, as seen in the overall iPrEx study results), (3) PrEP with behavioral disinhibition (15% decrease in condom use, 15% increase in sexual frequency and 15% increase in STI prevalence), (4) PrEP with high adherence (92% efficacy), and (5) PrEP with high adherence (92% efficacy) plus 100% condom use.

The cost-effectiveness calculator allows users to input population-specific values for certain parameters: (1) HIV prevalence, (2) prevalence of antiretroviral therapy use, and (3) prevalence of condom use. It also allows for the evaluation of monogamous serodiscordant relationships, a distinct and important group of potential users of PrEP. The risk calculator displays point estimates for the cost per QALY gained with PrEP at expected adherence (44% efficacy), and PrEP at high adherence (92% efficacy), with the latter not being an alternative intervention per se, but rather a demonstration of how effective PrEP could be if adherence is high.

We used the base-case model as a foundation for exploration of model variability and uncertainty in the results. For all model parameters, we performed both one-way sensitivity analysis and probabilistic uncertainty analysis, using point estimates and high/low estimates from the literature (Table 1). In the uncertainty analysis, we used Latin Hypercube Sampling to select values from beta distributions with shape parameter (alpha)  = 4 and minimum/maximum value as given in Table 1. We then calculated 95% uncertainty ranges as the boundaries of the 2.5^th and 97.5^th percentile from 10,000 simulations. We performed a three-way sensitivity analysis on three key model parameters (selected a priori as having particular influence on results): HIV prevalence, behavioral disinhibition, and PrEP adherence/efficacy. We describe the number needed to treat and cost-effectiveness at each point in a reasonable range of these three parameters.

This study did not involve human or animal subjects and was not subject to the Internal Review Board/Ethics Committee.

Table 2 describes the projected impact of PrEP in a series of individual cases, as calculated by the personalized risk calculator. In the base-case scenario (patient fitting generic population profiles for MSM in the US), the NNT to prevent one HIV infection was 64 (95% uncertainty range: 26 to 176). In Scenario 2, a patient engaging in behavioral disinhibition, PrEP efficacy decreased from 44% to 28%, thus increasing the NNT to 97 (95% UR: 46 to 222). In Scenario 3 (patient with high adherence but population-average baseline risk and sexual behavior), PrEP efficacy increased from 44% to 92% (per iPrEx study results), and the NNT dropped to 30 (95%: UR 14 to 69). In Scenario 4, a higher-risk setting with 35% baseline HIV prevalence, the relative risk reduction did not change, but the absolute risk reduction increased, leading to a lower NNT of 35 (95% UR: 21 to 57). In Scenario 5 (high baseline HIV prevalence and high adherence), both factors increased the absolute risk reduction and lowered the NNT to 17 (95% UR: 10 to 27). In contrast, with Scenario 6 (monogamous serodiscordant relationship with partner ART use), the lower baseline risk led to a lower absolute risk reduction and a higher NNT of 90 (95% UR: 39 to 157). In Scenario 7, the lowest-risk scenario (100% condom use, not in a serodiscordant relationship), the NNT was much higher (212, 95% UR: 88 to 523).

Table 2 also provides estimates of cost-effectiveness at the population level, as calculated by the population cost-effectiveness calculator. If PrEP were provided to a population representative of all MSM in the US, the cost per quality-adjusted life-year (QALY) gained was $160,000 (95% UR: cost saving to $740,000). Behavioral disinhibition (scenario 2) made PrEP less cost-effective, at $320,000 per QALY gained (95% UR: $45,000 to $1,000,000), whereas high adherence improved its cost-effectiveness, to $3,000 per QALY gained (95% UR: cost saving to $200,000). In settings with high baseline HIV prevalence (e.g. 35% in Baltimore, Maryland; Scenario 4), cost-effectiveness also improved from the baseline to $27,000 (95% UR: cost saving to $160,000), and in populations with both high HIV prevalence and high adherence (Scenario 5), PrEP was cost saving (95% UR: cost saving to $10,000 per QALY gained). The cost per QALY gained was highest in scenarios 6 (monogamous serodiscordant relationships with partner ART use) and 7 (100% condom use), at $280,000 (95% UR: $14,000 to $670,000) and $840,000 (95% UR: $230,000 to $2,500,000) respectively.

To complement the risk calculators, we performed a three-way sensitivity analysis to provide a more comprehensive visual description of the clinical effectiveness (Figure 2a–c) and cost-effectiveness (Figure 2d–f) of PrEP across a range of values for 3 key parameters: background HIV prevalence (5% increments), behavioral disinhibition (5% increments) and PrEP adherence (3 discrete levels, per iPrEx data). Scenarios 1–5 above are marked S1–S5 to demonstrate where they fit within this range. For any patient scenario with low PrEP adherence (Figure 2a), the NNT exceeded 50 unless the HIV prevalence was high (at least 35%) and behavioral disinhibition was low (less than 10% change in sexual risk). At low adherence and high behavioral disinhibition, PrEP was harmful, leading to an increased risk of HIV acquisition. For clinical scenarios with expected levels of PrEP adherence (Figure 2b), the NNT exceeded 50 for HIV prevalence levels below 25%. If patients took PrEP with high adherence (Figure 2c), the NNT was less than 50 in any setting where HIV prevalence was 15% or higher. With high adherence, the effect of behavioral disinhibition was greatly attenuated: at the national average of 19% HIV prevalence, the difference in the NNT between zero and 25% behavioral disinhibition was 1, compared to a difference of 96 with expected adherence and 322 with low adherence.

In populations where PrEP adherence was low (Figure 2d), the cost per QALY gained exceeded $100,000 for all scenarios except those with high HIV prevalence (at least 35%) and low behavioral disinhibition (less than 10% change in sexual risk). At low adherence and high behavioral disinhibition, no PrEP was less costly and more effective than (i.e., dominated) PrEP. At expected levels of PrEP adherence (Figure 2e), the cost per QALY gained exceeded $100,000 for HIV prevalence levels below 25%. At expected adherence, cost-effectiveness was highly dependent on the degree of behavioral disinhibition. For example, at 45% HIV prevalence, PrEP ranged from cost saving (no behavioral disinhibition) to $200,000 per QALY gained (25% increase in risky sexual behavior). For populations with high adherence (Figure 2f), PrEP was cost saving at HIV prevalence above 21%. As with clinical effectiveness, behavioral disinhibition had little impact on cost-effectiveness when PrEP was taken at high adherence.

One-way sensitivity analyses of key parameters (for which variation changed cost-effectiveness estimates by +/−50%) are shown in Figure 3. In addition to HIV prevalence, PrEP efficacy and the individual components of behavioral disinhibition (prevalence of condom use, STI prevalence, and frequency of sexual activity), other parameters with the highest impact on cost-effectiveness were the baseline risk of HIV acquisition per sex act, QALYs gained per case of HIV averted, and PrEP annual cost. If the annual cost of PrEP was reduced by roughly 50% to below $4772, PrEP was cost saving in the base-case scenario.