There are both HIV-serodiscordant couple data and population data to support HIV plasma viral load and stage of HIV infection in HIV transmission [15,28,29]. For male circumcision, HIV-serodiscordant couple data are not available; however, three RCTs confirmed unequivocally that it is protective for heterosexual HIV-negative men [24–26]. Pregnancy has been associated with HIV acquisition in a HIV-serodiscordant study  but not in a cohort study . Despite no data from HIV-serodiscordant studies, a large meta-analysis of 19 clinical studies showed a strong association of seropositive HSV-2 serology with HIV acquisition .
A role for GUD in HIV acquisition and transmission was found in two out of three HIV-serodiscordant studies [11,12,15] and a large meta-analysis of 25 heterosexual cohorts . Although HSV-2 seroconversion is associated with HIV acquisition in a cohort study , it was not included as a factor as there were no data from HIV-serodiscordant studies, longitudinal testing for HSV-2 is not routine practice and there is an overlap with GUD which is an independent risk factor in the risk score.
In regard to hormonal influences, the combined oral contraceptive (COCP) was not associated with HIV acquisition in a HIV serodiscordant or a cohort study [30,48] and the depot medroxyprogesterone acetate (DMPA) was not associated with HIV acquisition in two cohort studies [49,50]. Breast feeding was not associated with HIV acquisition in a HIV-serodiscordant couple study .
The estimates are, however, limited by the fact that the majority of anal intercourse estimates derive from MSM cohorts, with little data for anal intercourse amongst heterosexuals. In addition, estimates are not stratified according to HIV-infected partner viral load. However, as the majority of sex act HIV transmission studies were carried out prior to the widespread availability of ART, estimates obtained can be assumed to correspond to an ‘average’ or mean viral load set point of a chronically HIV-infected untreated individual [65–67].
To incorporate the effect of viral load on transmission risk per sex act, we had to adjust for the relative risks calculated for different viral loads assuming transmission estimates for type of sex act represented the risk for an ‘average’ viral load. A set point viral load calculated by Mei et al.  was used for the risk score. This estimate derived from individuals prospectively evaluated from primary HIV infection and the data were analysed using four methodologies and calculated a mean viral load set point of 4.20 Log10 copies/ml . For the risk score, the viral load category containing 4.20 Log10 copies/ml  was used as a reference point for the typical viral load of participants in studies that measured the transmission risk associated with different types of sex act.
By incorporating the biological and behavioural risk score, an overall evaluation of exposure is obtained.
Biological factors discussed are incorporated into the model as ‘risk multipliers’, represented by α, with subscripts denoting the particular factor. If a particular condition applies, then the multiplier takes the appropriate value determined from the literature; if the condition does not apply then the multiplier takes the value 1, so that the per-sex-act risk is not modified. Missing values were scored as 1.
For a single unprotected sex act, the risk of transmission is the product of the ‘baseline’ transmission probability for that type of sex act and the relevant risk-modifier coefficients (i.e. HIV viral load category, STI co-infection status), that is
When a risk multiplier does not affect a particular sex-act type it takes the value 1 so it does not affect the calculated risk – this is why multipliers for the effects of both pregnancy and circumcision on susceptibility appear in the generic formula, despite it being impossible for them to apply to the same individual.
When the number of unprotected sex acts exceeds 1, to calculate the risk of acquisition, it is necessary to consider the ‘escape probability’. The ‘escape probability’ is the probability of not becoming infected, which, for a single unprotected sex act, is 1 minus the per-act transmission probability. The escape probability for several sex acts of the same type with the same partner is the escape probability for a single act of that type with that partner raised to the power of the number of acts of that type. The risk of acquisition during those sex acts is 1 minus the total escape probability (as there are only two outcomes – acquiring infection or escaping it – the probability of those two outcomes must sum to 1). Therefore, the risk of HIV acquisition over all unprotected sex acts of a particular type with an HIV-infected partner is the following:
When a person has different types of unprotected sex acts with one partner, the escape probability for all sex acts of all types is the product of the escape probabilities for each type of sex act (considering the number of sex acts of each particular type). The transmission probability for all unprotected sex acts of all types with that partner is 1 minus the escape probability for all sex acts of all types, that is
These formulae apply to having one HIV-positive partner. When an individual has more than one HIV-infected sexual partner, the escape probabilities must be calculated for each partner and then multiplied together to calculate the escape probability for all sex acts of all types with all partners. The risk of acquisition is then 1 minus the escape probability for all sex acts of all types with all HIV-positive partners.
For example, for an uninfected man with an HIV-infected male partner and an HIV-infected female partner, the risk of HIV acquisition is,
where the number of unprotected acts of insertive anal intercourse with the female and males partners, respectively, are N IAI,F and N IAI,M.
Characteristics of the partner(s) that affect the risk score may not always be known. If the partner is known to be HIV-positive then there is a transmission risk, but if the status of the partner with respect to viral load, stage of HIV infection and GUD are not known then the multipliers can be varied between their values if present and 1 (the value if absent) to calculate the range of uncertainty in the estimate of risk that arises from the lack of information. Figure 1 shows a plot of possible scenarios using the HIV risk score and illustrates the range of variation in risk estimates obtained. If it is not known if the partner is HIV-infected or not then this additional uncertainty can be accounted for by estimating the probability that the partner is infected, given the prevalence in the relevant local population group.
As a transmission model, a Bernoulli model is easily described and manipulated, requires few parameters, has clinical relevance and has been empirically verified in an HIV seroconversion study in Africa . However, as with any model, there are limitations due to its assumptions and supporting data. Firstly, the model assumes that all viral loads have a transmission risk, rather than a threshold below which no transmission is possible. This concurs with models of HIV transmission  and reports of sexual and vertical transmission occurring from individuals with an undetectable viral load [70,71] but contrasts with two studies of HIV-serodiscordant couples, in which no transmission events occurred with viral load below 1500 copies/ml both on ART and ART naive [72,73]. However, the absence of transmission in a study does not rule out the possibility of a low transmission risk. Mathematical models suggest that although the risk of transmission on effective suppressive ART is not zero it is very low . The exact risk of transmission between HIV-serodiscordant couples is currently under investigation in the International Partners study .
Secondly, the model assumes that only a limited number of factors affect susceptibility to HIV infection. This is untrue given the multiple mechanisms contributing to HIV susceptibility (genetic [7,8] and biological  and infectiousness (viral phenotype, load and stage of infection [11,15,16]); if such risks are quantified then they can be incorporated into the model providing the status of the individual which is known. Specifically in the context of HIV-serodiscordant research in which evaluation of CCR5 haplotype of the exposed uninfected and viral co-receptor phenotype of the HIV-infected individual may be available, manipulation of the model could more accurately reflect HIV transmission risk. Finally, due to a lack of data available, the model assumes that all risk factors are independent co-factors of HIV transmission and that the presence of a co-factor affects equally all relevant types of sex act. It was not able to specifically evaluate sex or infection-site-specific (i.e. pharynx, rectum or urethra) risks for incident STI, except for HSV-2 seropositivity  and was also unable to account for interactions of STI, circumcision status and genital tract HIV viral load on HIV infectivity. As such the viral load transmission data used in the risk score were derived from vaginal sex within HIV-serodiscordant couples in Africa  and therefore may not be directly applicable to non-African settings or MSM. To enhance the accuracy of the model more data are required on the role of HIV co-factors specifically within MSM populations, the impact of site-specific STI and the possible amplifying effects of biological co-factors.
In order to ensure that robust data were used to develop the HIV risk model an in-depth literature review was carried out and in contrast to previous publications this review focused on both MSM and heterosexual transmission of HIV. [31,75,76] Effort was made to identify confounding factors, such as HIV viral load, heterogeneity in study design, differences in population characteristics, including STI rates, circumcision rates and sexual behaviour and/or insufficient power due to small sample size. Many studies (especially cross-sectional studies) are limited by the use of historical data as a proxy HIV acquisition, a lack of sexual behaviour data and an inability to detect the co-transmission of HIV and STI. Hence such studies conferred lower priority in developing the risk score.
Studies of HIV-serodiscordant couples were prioritized as they are able to assess the effect of STI on both the infectiousness and susceptibility to HIV, whilst controlling for infectivity mediated via plasma viral load, sex act type and sex frequency. It is accepted, however, that all estimates are affected by unadjusted inclusion of condom-protected acts in the count of sex acts.
The HIV risk score may underestimate risk for a number of reasons: Firstly, the exclusion of bacterial STI; secondly, the lack of information concerning actual risk per site; thirdly the potential for two factors to exponentially increase transmission risk; fourthly, the use of plasma viral load as a surrogate for genital tract HIV viral load. The fact that different ART agents have differential penetration into genital tract mucosae  means that the two sites may reflect one another and has contributed towards the controversy surrounding the Swiss statement . Finally, the viral load set point used in the model (4.2 RNA copies/ml) fits into the second highest viral load category in the Quinn et al.  transmission data (4.17–4.88 RNA copies/ml). This means that viral load up to 0.68 Log10 higher are categorized as set point (i.e. transmission risk, which may lead to further underestimation in HIV transmission risk).
Validation and assessment of the practical utility of the HIV exposure risk score is required from prospective cohorts of heterosexual  (e.g. HPTN052 study) and MSM HIV-serodiscordant couples. In testing the model, sensitivity analysis will need to be carried out to quantify uncertainty in calculated individual risk arising from uncertainty in parameter estimates from literature (represented by 95% CIs) and uncertainty in the reported behaviour of individuals . Subsequently, the score has potential to be used both in HIV research and HIV (both primary and secondary) prevention. It could also be modified to incorporate partners of known HIV status but unknown HIV viral load using population data (on ART usage, HSV-2 seroprevalence, circumcision status, and STI rates) to numerate the algorithm.
J.F.: model design, manuscript; P.J.W.: model design, manuscript; J.W.: manuscript; G.G.: model design, manuscript; H.W.: model design, manuscript; S.F.: model design, manuscript.
P.J.W. and G.G. thank the Medical Research Council for Centre funding.
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