The Bernoulli-Process Model of HIV Transmission

Is increased screening and early antiretroviral treatment for HIV-1 worth the investment? An analysis of the public health and economic impact of improvement in the UK

OBJECTIVES

Early treatment of HIV-1 infection at all CD4 levels has demonstrated clinical and public health benefits. This analysis examined the costs, health outcomes, and cost-effectiveness of increased HIV-1 screening and early treatment initiation in the UK.

METHODS

A Markov model followed theoretical cohorts of men who have sex with men (MSM), heterosexuals, and people who inject drugs (PWID) with initially undiagnosed HIV-1 infection over their remaining lifetimes. The analysis examined increased HIV-1 screening (resulting in 10-50% improvements in diagnosis rates) versus current screening in sexual health services (SHS) and other settings, with all individuals initiating treatment within 3 months of diagnosis. Health status was modelled by viral load and CD4 cell count as individuals progressed to diagnosis and treatment. Individuals accrued quality-adjusted life-years (QALYs), incurred costs for screening and HIV-related clinical management, and were at risk of transmitting HIV-1 infection to their partners. Input parameter data were taken primarily from UK-specific published sources. All outcomes were discounted at 3.5% annually.

RESULTS

The model estimated that increased screening and early treatment resulted in fewer onward HIV transmissions, more QALYs, and higher total costs. For SHS, incremental cost-effectiveness ratios (ICERs) for heterosexuals (~£22 000/QALY gained) were within typical UK willingness-to-pay thresholds and were well below these thresholds for MSM (~£9500/QALY gained) and PWID (~£6500/QALY gained). Sensitivity analysis showed that model results were robust.

CONCLUSIONS

Increased HIV-1 screening and early treatment initiation may be a cost-effective strategy to reduce HIV transmission and improve health for MSM, heterosexuals, and PWID in the UK.

When are declines in condom use while using PrEP a concern? Modelling insights from a Hillbrow, South Africa case study

INTRODUCTION

Oral pre-exposure prophylaxis (PrEP) is a promising new prevention approach for those most at risk of HIV infection. However, there are concerns that behavioural disinhibition, specifically reductions in condom use, might limit PrEP's protective effect. This study uses the case of female sex workers (FSWs) in Johannesburg, South Africa, to assess whether decreased levels of condom use following the introduction of PrEP may limit HIV risk reduction.

METHOD

We developed a static model of HIV risk and compared HIV-risk estimates before and after the introduction of PrEP to determine the maximum tolerated reductions in condom use with regular partners and clients for HIV risk not to change. The model incorporated the effects of increased STI exposure owing to decreased condom use. Noting that condom use with regular partners is generally low, we also estimated the change in condom use tolerated with clients only, to still achieve 50 and 90% risk reduction on PrEP. The model was parameterized using data from Hillbrow, Johannesburg. Sensitivity analyses were performed to ascertain the robustness of our results.

RESULTS

Reductions in condom use could be tolerated by FSWs with lower baseline condom use (65%). For scenarios where 75% PrEP effectiveness is attained, 50% HIV-risk reduction on PrEP would be possible even with 100% reduction in condom use from consistent condom use as high as 70% with clients. Increased exposure to STIs through reductions in condom use had limited effect on the reductions in condom use tolerated for HIV risk not to increase on PrEP.

CONCLUSIONS

PrEP is likely to be of benefit in reducing HIV risk, even if reductions in condom use do occur. Efforts to promote consistent condom use will be critical for FSWs with high initial levels of condom use, but with challenges in adhering to PrEP.

Progression and Transmission of HIV/AIDS (PATH 2.0)

BACKGROUND

HIV transmission is the result of complex dynamics in the risk behaviors, partnership choices, disease stage and position along the HIV care continuum-individual characteristics that themselves can change over time. Capturing these dynamics and simulating transmissions to understand the chief sources of transmission remain important for prevention.

METHODS

The Progression and Transmission of HIV/AIDS (PATH 2.0) is an agent-based model of a sample of 10,000 people living with HIV (PLWH), who represent all men who have sex with men (MSM) and heterosexuals living with HIV in the U.S.A. Persons uninfected were modeled as populations, stratified by risk and gender. The model included detailed individual-level data from several large national surveillance databases. The outcomes focused on average annual transmission rates from 2008 through 2011 by disease stage, HIV care continuum, and sexual risk group.

RESULTS

The relative risk of transmission of those in the acute phase was nine-times [5^th and 95^th percentile simulation interval (SI): 7, 12] that of those in the non-acute phase, although, on average, those with acute infections comprised 1% of all PLWH. The relative risk of transmission was 24- to 50-times as high for those in the non-acute phase who had not achieved viral load suppression as compared with those who had. The relative risk of transmission among MSM was 3.2-times [SI: 2.7, 4.0] that of heterosexuals. Men who have sex with men and women generated 46% of sexually acquired transmissions among heterosexuals.

CONCLUSIONS

The model results support a continued focus on early diagnosis, treatment and adherence to ART, with an emphasis on prevention efforts for MSM, a subgroup of whom appear to play a role in transmission to heterosexuals.

A Bayesian Approach to Net Health Benefits: An Illustration and Application to Modeling HIV Prevention

Purpose. To conduct a cost-effectiveness analysis of HIV prevention when costs and effects cannot be measured directly. To quantify the total estimation of uncertainty due to sampling variability as well as inexact knowledge of HIV transmission parameters. Methods. The authors focus on estimating the incremental net health benefit (INHB) in a randomized trial of HIV prevention with intervention and control conditions. Using a Bernoulli model of HIV transmission, changes in the participants’ risk behaviors are converted into the number of HIV infections averted. A sampling model is used to account for variation in the behavior measurements. Bayes’s theorem and Monte Carlo methods are used to attain the stated objectives. Results. The authors obtained a positive mean INHB of 0.0008, indicating that advocacy training is just slightly favored over the control condition for men, assuming a $50,000 per quality-adjusted life year (QALY) threshold. To be confident of a positive INHB, the decision maker would need to spend more than $100,000 per QALY.

Drug Use and Sexual Risk Behaviours among Female Russian IDUs Who Exchange Sex for Money or Drugs

Countries of the former Soviet Union are experiencing the steepest increases in annual HIV incidence in the world. Over 80% of registered HIV cases in Russia have occurred among intravenous drug users (IDUs), but current conditions set the stage for a heterosexually-transmitted epidemic. IDUs who also trade sex for money or drugs may serve as a conduit, or ‘bridge’ group, through which HIV could make inroads into the general Russian population. The present study examined the prevalence of sex trading among female Russian IDUs, and further examined drug use, sexual behaviour, and perceived vulnerability in this group. Female IDUs ( n=100) in St Petersburg, Russia participated; 37% reported a history of sex trading. This group reported a mean of 49.5 male sexual partners in the previous month and an average of 15.4 unprotected vaginal intercourse acts in the previous 30 days. A significant minority (44%) also reported sharing injection equipment with others. Mathematical models to calculate risk estimates for HIV seroconversion indicated that participants were at significant risk of contracting HIV and infecting sexual partners. Despite significant rates of risk behaviours, most participants perceived themselves to be at little risk of contracting HIV. Effective HIV prevention programmes targeted at this group are urgently needed and are likely to be a cost-effective step in curtailing the spread of HIV In the region.

Cost-effectiveness of interventions to prevent HIV and STDs among women: a randomized controlled trial

Injection drug use is a leading transmission route of HIV and STDs, and disease prevention among drug users is an important public health concern. This study assesses cost-effectiveness of behavioral interventions for reducing HIV and STDs infections among injection drug-using women. Cost-effectiveness analysis was conducted from societal and provider perspectives for randomized trial data and Bernoullian model estimates of infections averted for three increasingly intensive interventions: (1) NIDA's standard intervention (SI); (2) SI plus a well woman exam (WWE); and (3) SI, WWE, plus four educational sessions (4ES). Trial results indicate that 4ES was cost-effective relative to WWE, which was dominated by SI, for most diseases. Model estimates, however, suggest that WWE was cost-effective relative to SI and dominated 4ES for all diseases. Trial and model results agree that WWE is cost-effective relative to SI per hepatitis C infection averted ($109 308 for in trial, $6 016 in model) and per gonorrhea infection averted ($9 461 in trial, $14 044 in model). In sensitivity analysis, trial results are sensitive to 5 % change in WWE effectiveness relative to SI for hepatitis C and HIV. In the model, WWE remained cost-effective or cost-saving relative to SI for HIV prevention across a range of assumptions. WWE is cost-effective relative to SI for preventing hepatitis C and gonorrhea. WWE may have similar effects as the costlier 4ES.

Contextual correlates of per partner unprotected anal intercourse rates among MSM in Soweto, South Africa

Men who have sex with men (MSM) throughout the world are at high-risk of HIV acquisition and transmission. Although individual behavior remains a central feature of HIV prevention efforts in sub-Saharan Africa and beyond, contextual factors likely influence behavioral risk. We identify contextual factors at the individual, dyadic (within the partnership), and extra-dyadic (relationships external to the focal dyad) levels that are associated with increased rates of unprotected anal intercourse with a given male partner among MSM in Soweto, South Africa. Drawing on data from The Soweto Men's Study, multilevel models were applied to 758 partnerships nested within 377 MSM respondents. Independent of overall sexual engagement, dyadic (e.g. description of partner as 'regular'), psychosocial (e.g. experiences of homonegativity), and sociocultural (e.g. income) contextual factors were significant predictors of differential 6-month rates of UAI with a given partner. By contrast, sexual partnerships outside of the focal sexual pair were not significantly related to UAI rates within the focal pair. Our findings support the need for continuing to understand and intervene on partner-level, psychosocial, and sociocultural dimensions of sexual behavior and sexual risk among MSM in Soweto.

Estimating the impact of state budget cuts and redirection of prevention resources on the HIV epidemic in 59 California local health departments

BACKGROUND

In the wake of a national economic downturn, the state of California, in 2009-2010, implemented budget cuts that eliminated state funding of HIV prevention and testing. To mitigate the effect of these cuts remaining federal funds were redirected. This analysis estimates the impact of these budget cuts and reallocation of resources on HIV transmission and associated HIV treatment costs.

METHODS AND FINDINGS

We estimated the effect of the budget cuts and reallocation for California county health departments (excluding Los Angeles and San Francisco) on the number of individuals living with or at-risk for HIV who received HIV prevention services. We used a Bernoulli model to estimate the number of new infections that would occur each year as a result of the changes, and assigned lifetime treatment costs to those new infections. We explored the effect of redirecting federal funds to more cost-effective programs, as well as the potential effect of allocating funds proportionately by transmission category. We estimated that cutting HIV prevention resulted in 55 new infections that were associated with $20 million in lifetime treatment costs. The redirection of federal funds to more cost-effective programs averted 15 HIV infections. If HIV prevention funding were allocated proportionately to transmission categories, we estimated that HIV infections could be reduced below the number that occurred annually before the state budget cuts.

CONCLUSIONS

Reducing funding for HIV prevention may result in short-term savings at the expense of additional HIV infections and increased HIV treatment costs. Existing HIV prevention funds would likely have a greater impact on the epidemic if they were allocated to the more cost-effective programs and the populations most likely to acquire and transmit the infection.

Risk for Heterosexual HIV Transmission Among Non-Injecting Female Partners of Injection Drug Users in Estonia

The HIV epidemic in Estonia, as with other eastern European countries, is currently concentrated among injection drug users (IDUs). Non-IDUs who have IDU sex partners could serve as a potential bridge in an expanding epidemic. We applied HIV transmission modelling to data collected from non-IDU/IDU heterosexual couples in Kohtla-Järve, Estonia to estimate HIV risk from IDUs to their sex partners based on self-reported sexual behaviors shared by the couple. IDUs and their current main non-injecting sex partners were recruited for an interviewer-administered survey and HIV testing. Bernoulli modelling techniques were applied to estimate the risk of HIV transmission (incidence) among HIV negative non-injecting female partners of male IDUs. The estimated HIV incidence in this population of non-injecting women with only main sexual partners in the last 6 months ranged from 3.24 to 4.94 HIV seroconversions per 100 person years depending on the value used in the models for the per act transmission rate during acute stage infection. Non-IDUs who have IDU sex partners are at high risk for HIV and could serve as a potential bridge to a more generalized epidemic. Whether this might lead to an expansion of the HIV epidemic beyond core groups in Estonia or other Eastern European countries warrants closer study.

HIV transmission rate modeling: a primer, review, and extension

Several mathematical modeling studies based on the concept of "HIV transmission rates" have recently appeared in the literature. The transmission rate for a particular group of HIV-infected persons is defined as the mean number of secondary infections per member of the group per unit time. This article reviews the fundamental principles and mathematics of transmission rate models; explicates the relationship between these models, Bernoullian models of HIV transmission, and mathematical models based on the concept of the "reproductive rate of infection"; describes an extension of existing transmission rate models to better incorporate the positive impact of HIV treatment; and discusses the limitations of the transmission rate modeling approach. Results from the extended transmission rate model indicate that approximately 51.6% of new sexually-transmitted infections in the US are due to the transmission risk behaviors of infected persons who are unaware of their infection, including 10.9% due to persons in the acute phase of HIV infection. Findings from this study suggest that significant reductions in HIV incidence likely will require a combination of increased antibody testing, enhanced early detection of acute HIV infection, appropriate medical care and antiretroviral medicine adherence counseling, and behavioral risk reduction interventions.

Predicting condom use using the Information-Motivation-Behavioral Skills (IMB) model: a multivariate latent growth curve analysis

BACKGROUND

The Information-Motivation-Behavioral Skills (IMB) model often guides sexual risk reduction programs even though no studies have examined covariation in the theory's constructs in a dynamic fashion with longitudinal data.

PURPOSE

Using new developments in latent growth modeling, we explore how changes in information, motivation, and behavioral skills over 9 months relate to changes in condom use among STD clinic patients.

METHODS

Participants (N = 1281, 50% female, 66% African American) completed measures of IMB constructs at three time points. We used parallel process latent growth modeling to examine associations among intercepts and slopes of IMB constructs.

RESULTS

Initial levels of motivation, behavioral skills, and condom use were all positively associated, with behavioral skills partially mediating associations between motivation and condom use. Changes over time in behavioral skills positively related to changes in condom use.

CONCLUSIONS

Results support the key role of behavioral skills in sexual risk reduction, suggesting these skills should be targeted in HIV prevention interventions.

The cost-effectiveness of HIV voluntary counseling and testing in China

China has experienced a dramatic increase in the number of HIV infections. To control the AIDS epidemic, free HIV voluntary counseling and testing has been made available in China. This study compared the cost-effectiveness of this program for 2 populations-the general population and men who have sex with men (MSM), to examine the value for money of this program. A Bernoulli-process model has been used to translate the changes in sexual behaviors to the number of HIV infections averted. Costs are estimated from a societal perspective. The outcomes are measured in terms of the incremental cost per HIV infection averted and the incremental cost per disability-adjusted life-year averted. The study found that the voluntary counseling and testing for the general population is not cost-effective based on the threshold adopted, whereas the same HIV prevention program for MSM is cost-saving. These results suggest that the efficiency of resources used could be substantially improved by appropriately targeting high-risk population groups. Therefore measures should be taken to increase the uptake of this intervention among high-risk groups.

Is Vancouver Canada's supervised injection facility cost-saving?

OBJECTIVE

To determine whether Vancouver's Insite supervised injection facility and syringe exchange programs are cost-saving--that is, are the savings due to averted HIV-related medical care costs sufficient to offset Insite's operating costs?

METHODS

The analyses examined the impact of Insite's programs for a single year. Mathematical models were used to calculate the number of additional HIV infections that would be expected if Insite were closed. The life-time HIV-related medical costs associated with these additional infections were compared to the annual operating costs of the Insite facility.

RESULTS

If Insite were closed, the annual number of incident HIV infections among Vancouver IDU would be expected to increase from 179.3 to 262.8. These 83.5 preventable infections are associated with $17.6 million (Canadian) in life-time HIV-related medical care costs, greatly exceeding Insite's operating costs, which are approximately $3 million per year.

CONCLUSIONS

Insite's safe injection facility and syringe exchange program substantially reduce the incidence of HIV infection within Vancouver's IDU community. The associated savings in averted HIV-related medical care costs are more than sufficient to offset Insite's operating costs.

Aggregate versus individual-level sexual behavior assessment: how much detail is needed to accurately estimate HIV/STI risk?

The sexual behaviors of HIV/sexually transmitted infection (STI) prevention intervention participants can be assessed on a partner-by-partner basis: in aggregate (i.e., total numbers of sex acts, collapsed across partners) or using a combination of these two methods (e.g., assessing five partners in detail and any remaining partners in aggregate). There is a natural trade-off between the level of sexual behavior detail and the precision of HIV/STI acquisition risk estimates. The results of this study indicate that relatively simple aggregate data collection techniques suffice to adequately estimate HIV risk. For highly infectious STIs, in contrast, accurate STI risk assessment requires more intensive partner-by-partner methods.

When do simpler sexual behavior data collection techniques suffice? An analysis of consequent uncertainty in HIV acquisition risk estimates

The "gold standard" for evaluating human immunodeficiency virus (HIV) prevention programs is a partner-by-partner sexual behavior assessment that elicits information about each sex partner and the activities engaged in with that partner. When collection of detailed partner-by-partner data is not feasible, aggregate data (e.g., total numbers of partners and acts of various types) must suffice. Lack of specificity in the primary data often translates into uncertainty in modeled outcomes, such as participants' risk of HIV acquisition. To our knowledge, no previous study has attempted to quantify this uncertainty. The results of the present analysis of the risk of HIV acquisition by men vacationing in Key West indicate that the use of aggregate rather than partner-by-partner data introduced relatively little uncertainty into the HIV risk estimates. Collection of aggregate data is a viable alternative to detailed partner-by-partner data, at least in some circumstances.

Modeling HIV transmission risk among Mozambicans prior to their initiating highly active antiretroviral therapy

Understanding sexual behavior and assessing transmission risk among people living with HIV-1 is crucial for effective HIV-1 prevention. We describe sexual behavior among HIV-positive persons initiating highly active antiretroviral therapy (HAART) in Beira, Mozambique. We present a Bernoulli process model (tool available online) to estimate the number of sexual partners who would acquire HIV-1 as a consequence of sexual contact with study participants within the prior three months. Baseline data were collected on 350 HAART-naive individuals 18-70 years of age from October 2004 to February 2005. In the three months prior to initiating HAART, 45% (n = 157) of participants had sexual relationships with 191 partners. Unprotected sex occurred in 70% of partnerships, with evidence suggesting unprotected sex was less likely with partners believed to be HIV-negative. Only 26% of the participants disclosed their serostatus to partners with a negative or unknown serostatus. Women were less likely to report concurrent relationships than were men (21 versus 66%; OR 0.13; 95%CI: 0.06, 0.26). Given baseline behaviors, the model estimated 23.2 infections/1,000 HIV-positive persons per year. The model demonstrated HAART along with syphilis and herpes simplex virus type 2 (HSV-2) treatment combined could reduce HIV-1 transmission by 87%; increasing condom use could reduce HIV-1 transmission by 67%.

Cost-Effectiveness of a Community-Level HIV Risk Reduction Intervention for Women Living in Low-Income Housing Developments

We conducted a cost-effectiveness analysis of a multi-site community-level HIV prevention trial that enrolled women living in 18 low-income housing developments in 5 U.S. cities. A mathematical model of HIV transmission was used to estimate the number of HIV infections averted and quality-adjusted life years (QALYs) saved by the community-level intervention, based on data obtained from community-wide sexual behavior surveys at baseline and 12-month follow-up. Results indicated that the intervention prevented approximately 1 infection per 3500 women reached by the intervention, at a total cost of 174,845 dollars. The cost per QALY saved by the intervention was 37,433 dollars and the cost per HIV infection averted was 732,072 dollars. The community-level intervention was moderately cost-effective in comparison with other HIV prevention programs for at-risk women. Synergistic approaches to HIV prevention that combine community-level sexual norm change interventions with more intensive risk reduction programs for high-risk women are needed. EDITORS' STRATEGIC IMPLICATIONS: The authors present a promising and efficient community-level HIV prevention approach, with effects beyond the limited scope of individual or small group interventions. This paper represents an example of how an analysis of cost-effectiveness can provide policymakers with information needed for difficult decisions about prevention resource allocations.

Probabilistic cost-effectiveness analysis of HIV prevention. Comparing a Bayesian approach with traditional deterministic sensitivity analysis

In cost-effectiveness analysis, the incremental cost-effectiveness ratio is used to measure economic efficiency of a new intervention, relative to an existing one. However, costs and effects are seldom known with certainty. Uncertainty arises from two main sources: uncertainty regarding correct values of intervention-related parameters and uncertainty associated with sampling variation. Recently, attention has focused on Bayesian techniques for quantifying uncertainty. We computed the Bayesian-based 95% credible interval estimates of the incremental cost-effectiveness ratio of several related HIV prevention interventions and compared these results with univariate sensitivity analyses. The conclusions were comparable, even though the probabilistic technique provided additional information.

A relative risk-based, disease-specific definition of sexual abstinence failure rates

Sexual abstinence programs have the potential to reduce the incidence of unplanned pregnancies and sexually transmitted diseases (STDs) among adolescents. Effectiveness measures are needed to help researchers assess the impact of sexual abstinence promotion programs on STD and pregnancy rates and to enable comparisons of abstinence effectiveness with other contraception and STD prevention methods. Abstinence "failure rates" have been proposed as one measure of program effectiveness. However, the concept of abstinence failure rates has not been adequately operationalized. The present study examines a novel mathematical framework for estimating abstinence failure rates, both theoretically and empirically. Examples are provided, and the advantages and disadvantages associated with the mathematical model-based approach are discussed.

When is an HIV infection prevented and when is it merely delayed?

HIV prevention programs are typically evaluated using behavioral outcomes. Mathematical models of HIV transmission can be used to translate these behavioral outcomes into estimates of the number of HIV infections averted. Usually, intervention effectiveness is evaluated over a brief assessment period and an infection is considered to be prevented if it does not occur during this period. This approach may overestimate intervention effectiveness if participants continue to engage in risk behaviors. Conversely, this strategy underestimates the true impact of interventions by assuming that behavioral changes persist only until the end of the intervention assessment period. In this article, the authors (a) suggest a simple framework for distinguishing between HIV infections that are truly prevented and those that are merely delayed, (b) illustrate how these outcomes can be estimated, (c) discuss strategies for extrapolating intervention effects beyond the assessment period, and (d) highlight the implications of these findings for HIV prevention decision making.