Rebecca Frances Baggaley
email: r.baggaley@imperial.ac.uk

Richard G White

Marie-Claude Boily

Review article: HIV transmission risk through anal intercourse: systematic review, meta-analysis and implications for HIV prevention

Keywords: HIV, anal intercourse, infectivity, transmission probability, review, meta-analysis HIV, anal intercourse, infectivity, transmission probability, review, meta-analysis, HAART

published or not. The documents may come

• Unprotected anal intercourse (AI) is a high risk practice for HIV transmission (higher risk than vaginal (VI) or orogenital intercourse), probably with substantial variation in infectiousness and susceptibility to infection between individuals, and in infectiousness over the duration of infection. The significant heterogeneity between infectiousness estimates means that pooled AI HIV transmission probabilities should be used with caution.

• Most studies did not collect the necessary sexual activity information required to gain a better understanding of the relationship between per-act and per-partner risk. Variation across study estimates may also partly be explained by differences in distributions of risk factors in sampled populations, study designs and various (time-varying) characteristics of the type of sexual behaviour, characteristics of the infected partner and those of the uninfected partner.

• We found no evidence of a difference in per-act AI infectivity between heterosexual and MSM couples.

• Model estimates of the impact of HAART in reducing HIV transmission and the mitigating effect of AI can vary substantially, depending on the assumptions made. Empirical evidence is therefore urgently needed in order to inform model estimates, which remain highly uncertain.

Nevertheless, our analysis illustrates the large excess in HIV risk that individuals may experience over time if they occasionally engage in unprotected AI with an infected partner.

Prevention messages must emphasise the high risk associated with AI and that control measures such as condoms must be used for both VI and AI.

Introduction

Studies systematically reviewing much-needed estimates of HIV infectiousness for various modes of transmission have recently been published, [START_REF] Gisselquist | Running on empty: sexual co-factors are insufficient to fuel Africa's turbocharged HIV epidemic[END_REF][START_REF] Gisselquist | HIV infections in sub-Saharan Africa not explained by sexual or vertical transmission[END_REF][START_REF] Brody | Assessing the role of anal intercourse in the epidemiology of AIDS in Africa[END_REF][START_REF] Kloos | Some neglected and emerging factors in HIV transmission in Ethiopia[END_REF] partly in response to discussions regarding the relative importance of each mode for HIV epidemics worldwide.(1, 2) However, none have specifically focused on anal intercourse (AI), despite its role driving HIV epidemics among men who have sex with men (MSM). AI may also contribute substantially to heterosexual epidemics in sub-Saharan Africa and elsewhere. [START_REF] Brody | Assessing the role of anal intercourse in the epidemiology of AIDS in Africa[END_REF] AI within heterosexual relationships is not an uncommon practice but is often underreported. [START_REF] Kloos | Some neglected and emerging factors in HIV transmission in Ethiopia[END_REF][START_REF] Smith | Underreporting sensitive behaviors: the case of young women's willingness to report abortion[END_REF] It is estimated that the absolute number of women in the United States (US) practising unprotected receptive AI (URAI) is approximately seven-fold higher than the number of MSM practising URAI, [START_REF] Halperin | Heterosexual anal intercourse: prevalence, cultural factors, and HIV infection and other health risks, Part I[END_REF] while 75% of study participants in the South African site of a multi-centre microbicides trial reported URAI during follow-up. [START_REF] Van Damme | Effectiveness of COL-1492, a nonoxynol-9 vaginal gel, on HIV-1 transmission in female sex workers: a randomised controlled trial[END_REF] Highly active antiretroviral therapy (HAART) is likely to substantially reduce risk from AI, as demonstrated by randomised controlled trials for mother-to-child transmission [START_REF] Cooper | Combination antiretroviral strategies for the treatment of pregnant HIV-1-infected women and prevention of perinatal HIV-1 transmission[END_REF] and observational studies for heterosexual partnerships. [START_REF] Reynolds | ART reduced the rate of sexual transmission of HIV among HIV-discordant couples in rural Rakai, Uganda. 16th Conference on Retroviruses and Opportunistic Infections[END_REF][START_REF] Sullivan | Reduction of HIV transmission risk and high risk sex while prescribed ART: Results from discordant couples in Rwanda and Zambia[END_REF] Although some ecological evidence suggests a reduction in AI infectiousness due to HAART may have occurred, [START_REF] Bezemer | A resurgent HIV-1 epidemic among men who have sex with men in the era of potent antiretroviral therapy[END_REF] no direct empirical evidence is yet available. However, the high infectiousness associated with AI, as reviewed here, indicates that even with a substantial reduction due to HAART, the residual infectiousness could still present a high risk to partners, especially if coupled with risk compensation. [START_REF] Bezemer | A resurgent HIV-1 epidemic among men who have sex with men in the era of potent antiretroviral therapy[END_REF] Our aims were systematically to review the literature on estimates of unprotected AI (UAI) per-act and per-partner transmission probabilities for heterosexuals and MSM; to investigate the relationship between per-act and per-partner summary estimates and to explore the implications of practising URAI for prevention of HIV transmission in the presence of HAART.

Methods

The systematic review was undertaken following MOOSE guidelines for reviews of observational studies. ( [START_REF] Boily | Heterosexual risk of HIV-1 infection per sexual act: systematic review and meta-analysis of observational studies[END_REF] (details provided in Supplementary Information).

Selection criteria and data extraction:

Empirical per-act and per-partner (irrespective of partnership duration and frequency of sex acts) estimates were extracted. Abstracts pre-1990, studies using sample sizes <10 and estimates derived from dynamical modelling studies fitted to empirical HIV prevalence curves were excluded. Estimates where infection of partners was ascertained clinically [START_REF] Gazzard | Clinical findings and serological evidence of HTLV-III infection in homosexual contacts of patients with AIDS and persistent generalised lymphadenopathy in London[END_REF] or only through questioning the index, [START_REF] Flateby | Steady sexual relationship with an HIV-positive partner and the progression rate to AIDS[END_REF] rather than by laboratory HIV diagnosis were excluded. Per-partner estimates from studies of heterosexuals were restricted to including only those sexual partners where AI was practiced for ≥50% of all sex acts within the partnership. There was no other restriction by study design or language of publication. Each relevant publication was examined by two investigators for data extraction.

Quantitative data synthesis and statistical methods:

Meta-analysis Stata 10.0 produced random effects model summary estimates. For studies not providing a point estimate, the arithmetic midpoint of the confidence bounds or estimate range was used. For studies reporting estimates with an uncertainty range (reflecting uncertainty to model assumptions) rather than a 95% confidence interval (95%CI), a standard error or sufficient information to derive these directly, we approximated the standard error from symmetric and asymmetric intervals as 1/1.96 the largest absolute value (to account for asymmetric intervals) of the widths between the point estimate and the sensitivity bounds.

Relationship between per-act and per-partner transmission probability

We investigated the relationship between per-act and per-partner AI transmission probabilities over n sex acts using the following Bernouilli process which assumes independence of risk for each sex act within a partnership [START_REF] Rottingen | The epidemiological and control implications of HIV transmission probabilities within partnerships[END_REF][START_REF] Wilson | Relation between HIV viral load and infectiousness: a model-based analysis[END_REF]:

( ) , , 1
1 n p a c a β β = -- (1)
where , p a β and , c a β are the per-partner ( p ) and per-act ( c ) transmission probability for AI ( a ), respectively. For heterosexual populations practising both vaginal intercourse (VI) and AI, equation [START_REF] Gisselquist | Running on empty: sexual co-factors are insufficient to fuel Africa's turbocharged HIV epidemic[END_REF] becomes:

( ) ( ) ( ) 1 , , , 1 1 1
d n dn p all c v c a β β β - = -- - (2)

Intervention impact: HAART

We assessed the potential reduction in HIV infectivity caused by HAART reducing viral load, using two published functions of infectivity by viral load. [START_REF] Wilson | Relation between HIV viral load and infectiousness: a model-based analysis[END_REF][START_REF] Abu-Raddad | Analytic insights into the population level impact of imperfect prophylactic HIV vaccines[END_REF][START_REF] Modjarrad | Impact of small reductions in plasma HIV RNA levels on the risk of heterosexual transmission and disease progression[END_REF][START_REF] Salomon | Evaluating the impact of antiretroviral therapy on HIV transmission[END_REF][START_REF] Fraser | Variation in HIV-1 set-point viral load: epidemiological analysis and an evolutionary hypothesis[END_REF] In brief the difference between the two functions is that Function 1 was based on results from the Rakai study of HIV transmission in heterosexual couples (presumed through vaginal intercourse (VI) transmission) [START_REF] Quinn | Viral load and heterosexual transmission of human immunodeficiency virus type 1. Rakai Project Study Group[END_REF] and assumes a linear relationship between infectiousness and log serum viral load; function 2 was based on data from a Zambian cohort of discordant couples [START_REF] Fideli | Virologic and immunologic determinants of heterosexual transmission of human immunodeficiency virus type 1 in Africa[END_REF] and assumed a logistic function between infectivity and plasma viral load, which provides better fits to the low number of transmissions observed for low viral loads of index individuals. [START_REF] Fraser | Variation in HIV-1 set-point viral load: epidemiological analysis and an evolutionary hypothesis[END_REF]We assume that successful HAART reduces blood viral load from an average, baseline 0 V to 1 V copies/ml. Further details are provided in Supplementary Information.

Results

Search results

62,643 titles were searched and 27 potentially appropriate publications identified, three of which were identified through bibliographies of searched articles. Four publications reporting per-act(24-27) and 12 reporting per-partner(28-39) estimates were included. These were from MSM (n=12 [START_REF] Degruttola | Infectiousness of HIV between male homosexual partners[END_REF][START_REF] Vittinghoff | Per-contact risk of human immunodeficiency virus transmission between male sexual partners[END_REF][START_REF] Cheingsong-Popov | Prevalence of antibody to human T-lymphotropic virus type III in AIDS and AIDS-risk patients in Britain[END_REF][START_REF] Weller | Human immunodeficiency virus (HIV) infection in the regular sexual partners of homosexual men with AIDS and persistent generalised lymphadenopathy[END_REF][START_REF] Coates | Risk factors for HIV infection in male sexual contacts of men with AIDS or an AIDS-related condition[END_REF][START_REF] Goldsmith | Antibody to human lymphotropic virus type III: immunologic status of homosexual contacts of patients with the acquired immunodeficiency syndrome and the acquired immunodeficiency-related complex[END_REF][START_REF] Osmond | Time of exposure and risk of HIV infection in homosexual partners of men with AIDS[END_REF][START_REF] Giesecke | Partner notification as a tool for research in HIV epidemiology: behaviour change, transmission risk and incidence trends[END_REF][START_REF] Kaplan | Modeling HIV infectivity: must sex acts be counted?[END_REF][START_REF] Palenicek | Longitudinal study of homosexual couples discordant for HIV-1 antibodies in the Baltimore MACS Study[END_REF][START_REF] Seage | Risk of human immunodeficiency virus infection from unprotected receptive anal intercourse increases with decline in immunologic status of infected partners[END_REF][START_REF] Samuel | Infectivity of HIV by anal and oral intercourse among homosexual men. Estimates from a prospective study in San Francisco[END_REF]), heterosexual (n=3 [START_REF] Halperin | High level of HIV-1 infection from anal intercourse: a neglected risk factor in heterosexual AIDS prevention[END_REF][START_REF] Leynaert | Heterosexual transmission of human immunodeficiency virus: variability of infectivity throughout the course of infection. European Study Group on Heterosexual Transmission of HIV[END_REF][START_REF] Nicolosi | The efficiency of male-to-female and female-to-male sexual transmission of the human immunodeficiency virus: a study of 730 stable couples. Italian Study Group on HIV Heterosexual Transmission[END_REF]) or mixed (n=1(34)) study populations. Per-partner estimates from

Nicolosi et al's study of heterosexuals, where AI was practiced "often or always" (≥50% of all intercourse) within the partnership were included; those with less frequent practice were excluded. [START_REF] Nicolosi | The efficiency of male-to-female and female-to-male sexual transmission of the human immunodeficiency virus: a study of 730 stable couples. Italian Study Group on HIV Heterosexual Transmission[END_REF] Figure S1, Supplementary Information, summarises the search strategy. All identified studies were from industrialised countries. Figure 1 summarises study estimates for per-act and per-partner AI transmission probabilities as forest plots, including summary estimates from the meta-analyses. Details of included and excluded studies are in Tables S1 andS2 of Supplementary Information, respectively. insertive AI (0.04%, 95%CI 0.01-0.11), based on partners of index cases who were "HIV infected or of unknown serostatus" were excluded because no attempt was made to estimate the unknown HIV status of index cases by using HIV prevalence as a proxy for exposure to an HIV infected partner.( 25)

Study design and estimate type

The included studies employed three study designs: retrospective-partner (n=11 [START_REF] Degruttola | Infectiousness of HIV between male homosexual partners[END_REF][START_REF] Halperin | High level of HIV-1 infection from anal intercourse: a neglected risk factor in heterosexual AIDS prevention[END_REF][START_REF] Leynaert | Heterosexual transmission of human immunodeficiency virus: variability of infectivity throughout the course of infection. European Study Group on Heterosexual Transmission of HIV[END_REF][START_REF] Cheingsong-Popov | Prevalence of antibody to human T-lymphotropic virus type III in AIDS and AIDS-risk patients in Britain[END_REF][START_REF] Nicolosi | The efficiency of male-to-female and female-to-male sexual transmission of the human immunodeficiency virus: a study of 730 stable couples. Italian Study Group on HIV Heterosexual Transmission[END_REF][START_REF] Weller | Human immunodeficiency virus (HIV) infection in the regular sexual partners of homosexual men with AIDS and persistent generalised lymphadenopathy[END_REF][START_REF] Coates | Risk factors for HIV infection in male sexual contacts of men with AIDS or an AIDS-related condition[END_REF][START_REF] Goldsmith | Antibody to human lymphotropic virus type III: immunologic status of homosexual contacts of patients with the acquired immunodeficiency syndrome and the acquired immunodeficiency-related complex[END_REF][START_REF] Osmond | Time of exposure and risk of HIV infection in homosexual partners of men with AIDS[END_REF][START_REF] Giesecke | Partner notification as a tool for research in HIV epidemiology: behaviour change, transmission risk and incidence trends[END_REF][START_REF] Seage | Risk of human immunodeficiency virus infection from unprotected receptive anal intercourse increases with decline in immunologic status of infected partners[END_REF]), prospective discordant-couple (n=1( 36)) and simple-prospective (longitudinal cohort, n=4 [START_REF] Vittinghoff | Per-contact risk of human immunodeficiency virus transmission between male sexual partners[END_REF][START_REF] Kaplan | Modeling HIV infectivity: must sex acts be counted?[END_REF][START_REF] Porco | Decline in HIV infectivity following the introduction of highly active antiretroviral therapy[END_REF][START_REF] Samuel | Infectivity of HIV by anal and oral intercourse among homosexual men. Estimates from a prospective study in San Francisco[END_REF]) studies. In retrospective-partner studies, the infection status of each partner becomes known only at the time of the study. The index case and time of infection are determined based on exposure to a salient risk factor. In prospective discordant-couple studies, stable (preferably monogamous) HIVserodiscordant couples are followed up after diagnosis of the index partner. These studies also provide per-partner HIV transmission rates but, with only one included study (and only 10 couples(36)), we report and use cross-sectional results at the end of follow-up for the meta-analysis. With simpleprospective studies, individuals (not necessarily monogamous) are recruited following sexual contact with potentially infected, high-risk partners and serostatus monitored. As index cases are not recruited, HIV exposure is estimated using HIV prevalence in the pool of potential partners and the reported coital frequency. Therefore prospective studies suffer from problems of selection bias (prospective discordant-couple) and uncertainty estimating numbers of HIV exposures (simple-prospective) and are not necessarily superior to the retrospective-partner study design.

Per-act estimates were derived from retrospective-partner (n=3 [START_REF] Degruttola | Infectiousness of HIV between male homosexual partners[END_REF][START_REF] Halperin | High level of HIV-1 infection from anal intercourse: a neglected risk factor in heterosexual AIDS prevention[END_REF][START_REF] Leynaert | Heterosexual transmission of human immunodeficiency virus: variability of infectivity throughout the course of infection. European Study Group on Heterosexual Transmission of HIV[END_REF]) and simple-prospective (n=1(25)) studies. Per-partner estimates were derived from retrospective-partner (n=8(28-34, 37)), prospective-discordant couple (n=1 [START_REF] Palenicek | Longitudinal study of homosexual couples discordant for HIV-1 antibodies in the Baltimore MACS Study[END_REF]) and simple-prospective (n=3 [START_REF] Kaplan | Modeling HIV infectivity: must sex acts be counted?[END_REF][START_REF] Porco | Decline in HIV infectivity following the introduction of highly active antiretroviral therapy[END_REF][START_REF] Samuel | Infectivity of HIV by anal and oral intercourse among homosexual men. Estimates from a prospective study in San Francisco[END_REF]) studies. For both URAI-only and UIAI-only per-partner estimates, three were derived from retrospective-partner [START_REF] Nicolosi | The efficiency of male-to-female and female-to-male sexual transmission of the human immunodeficiency virus: a study of 730 stable couples. Italian Study Group on HIV Heterosexual Transmission[END_REF][START_REF] Coates | Risk factors for HIV infection in male sexual contacts of men with AIDS or an AIDS-related condition[END_REF][START_REF] Giesecke | Partner notification as a tool for research in HIV epidemiology: behaviour change, transmission risk and incidence trends[END_REF] and one from simple-prospective [START_REF] Samuel | Infectivity of HIV by anal and oral intercourse among homosexual men. Estimates from a prospective study in San Francisco[END_REF] 1. For per-partner transmission probabilities, retrospective-partner studies reported crude estimates, while prospective studies tended to report adjusted estimates. This made it difficult to disentangle the effect of study design from adjustment for multiple exposures. In addition, all estimates where the standard error had to be approximated using an uncertainty range quoted by authors, were adjusted estimates.

Infectiousness of anal intercourse for heterosexuals and MSM

Reliability of estimates

All per-partner summary estimates displayed considerable heterogeneity. Summary estimates calculated using adjusted estimates were considerably lower than those using crude estimates (Figure 1, Table 1). However, the reliability of summary adjusted estimates is questionable because only the crude combined URAI-UIAI summary estimate was based on more than five estimates. Interestingly, while crude per-partner estimates from MSM populations may overestimate per-partner infectivity because of competing exposures due to frequent lack of monogamy, (28, 30-34, 36, 37, 39) they were in good agreement with crude per-partner estimates from heterosexual couples reporting high frequency of AI and 100% monogamy(29) (Figure 1). [START_REF] Kaplan | Modeling HIV infectivity: must sex acts be counted?[END_REF][START_REF] Palenicek | Longitudinal study of homosexual couples discordant for HIV-1 antibodies in the Baltimore MACS Study[END_REF][START_REF] Porco | Decline in HIV infectivity following the introduction of highly active antiretroviral therapy[END_REF] versus retrospective [START_REF] Cheingsong-Popov | Prevalence of antibody to human T-lymphotropic virus type III in AIDS and AIDS-risk patients in Britain[END_REF][START_REF] Nicolosi | The efficiency of male-to-female and female-to-male sexual transmission of the human immunodeficiency virus: a study of 730 stable couples. Italian Study Group on HIV Heterosexual Transmission[END_REF][START_REF] Weller | Human immunodeficiency virus (HIV) infection in the regular sexual partners of homosexual men with AIDS and persistent generalised lymphadenopathy[END_REF][START_REF] Coates | Risk factors for HIV infection in male sexual contacts of men with AIDS or an AIDS-related condition[END_REF][START_REF] Goldsmith | Antibody to human lymphotropic virus type III: immunologic status of homosexual contacts of patients with the acquired immunodeficiency syndrome and the acquired immunodeficiency-related complex[END_REF][START_REF] Osmond | Time of exposure and risk of HIV infection in homosexual partners of men with AIDS[END_REF][START_REF] Giesecke | Partner notification as a tool for research in HIV epidemiology: behaviour change, transmission risk and incidence trends[END_REF][START_REF] Seage | Risk of human immunodeficiency virus infection from unprotected receptive anal intercourse increases with decline in immunologic status of infected partners[END_REF]) gave similar findings because both adjusted estimates were derived from simple-prospective studies, while the remaining prospective study, of serodiscordant couples, was small (n=10(36)).

Heterogeneity of infectiousness

Despite providing a single per-act URAI estimate, DeGruttola et al discussed variability of infectiousness between individuals and suggested that 10-20% of infected MSM may have far greater infectiousness (~≥10% per-act).( 24 reporting partners known to be HIV-infected. Therefore, the index cases were unlikely to be in the highly infectious acute HIV stage because of the time lag between infection and HIV diagnosis and disclosure of their status to their partners included in the study. Therefore the true average per-act infectivity across all infection stages may be higher than our 1.4% summary estimate because retrospectivepartner studies may miss the acute infection stage, or may be lower because Vittinghoff's prospective study may have misattributed some transmission events from unidentified HIV exposures.

Relationship between per-act and per-partner infectivity for anal intercourse

Figure 2 illustrates the relationship between per-act and cumulative HIV risk over a partnership through URAI (by number of sexual acts), compared to per-partner combined URAI-UIAI summary estimates from our meta-analysis (drawn as horizontal lines). The figure indicates, for example, that only 36 URAI acts would be required to produce the per-partner Combined URAI-UIAI summary estimate of 39.9% if we assume per-act URAI HIV transmission probability is 1.4%. If 50% of acts are receptive and 50% insertive, 60 unprotected AI acts are required if we assume UIAI per-act risk is 0.3% (same as for VI;

see Figure 2 legend for details) and 51 acts if the UIAI per-act risk is 0.6%. Competing risk from UIAI increases the total number of unprotected acts necessary for transmission per partnership only by relatively modest amounts, especially when the increase in transmission probability of UIAI compared to VI is large, because UIAI infectiousness becomes closer to that of URAI. As suggested previously, [START_REF] Degruttola | Infectiousness of HIV between male homosexual partners[END_REF] under the model assumptions, it is difficult to explain per-partner risk estimates as a function of per-act estimates. The results imply relatively few UAI acts per relationship among the partnerships included in the per-partner studies. As too few MSM per-partner studies reported length of partnership or number of sex acts per partnership (Table S1), it is difficult to test this hypothesis. While some of the partnerships in the per-partner studies may have been relatively short with few sexual acts, this is unlikely to be the case for all partnerships and all studies. For example, Nicolosi et al reported a median partnership duration of 2.9 years,(29) implying a relatively large number of acts. Figure S2 shows how empirical per-partner study estimates do not show the expected increase in infectivity with increasing number of sexual exposures to the index partner predicted by the Bernoulli process (equation ( 1)) in absence of . Therefore high infectiousness associated with primary infection may account for the high per-partner estimates observed for some partnerships consisting of few acts.

F o r R e v i
However, relatively few short duration partnerships are likely to occur while infected individuals experience primary infection, because this period is very short (approximately three months(40)), although this will depend on the sexual network structure. Late-stage infection is also associated with high infectiousness,(27) so the same argument could apply, although sexual activity of AIDS patients is likely to be much lower.

Implications for the effectiveness of interventions: HAART

Figure 3a illustrates the relationship between per-partner HIV risk and total sex acts involving exposure to HIV-infected partners not on HAART, considering both VI/UIAI and URAI exposure (see legend for details). Using function 1 (Figure 3b), the predicted HIV transmission probabilities per-act for VI/UIAI and URAI with successful HAART are 0.013% and 0.061% respectively i.e. 96% lower than without therapy. Under these assumptions, 1000 sex acts leads to a male-to-female per-partner HIV risk of which supports the hypothesis that UIAI is substantially less infectious than URAI. However, the significant heterogeneity between per-partner estimates led to wide confidence intervals, primarily due to differences in analytic methods and study design. Thus these "average" AI transmission probabilities should be used with caution.

The large discrepancy between crude and adjusted per-partner estimates (Table 1) makes interpretation of the results particularly difficult, especially because similar adjustments used to quantify per-act VI estimates were found to have little impact. [START_REF] Boily | Heterosexual risk of HIV-1 infection per sexual act: systematic review and meta-analysis of observational studies[END_REF][START_REF] Powers | Rethinking the heterosexual infectivity of HIV-1: a systematic review and meta-analysis[END_REF] The combined URAI-UIAI summary estimate using adjusted per-partner estimates was approximately six times lower than for the summary of crude estimates. As many MSM study subjects may have multiple partners, adjusted estimates may be more reliable. However, the 42.9% (95%CI per-act estimates identified, are difficult to reconcile with the low summary estimate for adjusted perpartner infectiousness. Most studies did not collect the necessary sexual activity information required to gain a better understanding of the relationship between per-act and per-partner risk. Variation across study estimates may also partly be explained by differences in distributions of risk factors in sampled populations, study designs and various (time-varying) characteristics of the type of sexual behaviour, characteristics of the infected partner and those of the uninfected partner. For example, duration of exposure to an infected partner, frequency of unprotected acts per-partner and presence of various cofactors for transmission, such as condom use, will differ (Table S1). While HIV transmission for heterosexual men engaging in AI will predominantly occur by insertive intercourse, MSM experience risk through both insertive and/or receptive AI.

As suggested previously, [START_REF] Degruttola | Infectiousness of HIV between male homosexual partners[END_REF] the difficulty in reconciling per-act and per-partner estimates highlights the difficulty in specifying a unique estimate of AI and supports that there is considerable heterogeneity in infectivity between individuals, over the course of infection and/or that our assumption of independence of risk per-act within a partnership is invalid.( 42) DeGruttola et al in 1989 suggested that such heterogeneity leads to underestimation of the number of partners who would be infected after few acts and overestimation of numbers who would be infected after many acts. Heterogeneity in per-act or perpartner HIV infectiousness has also been reported in other studies for VI [START_REF] Boily | Heterosexual risk of HIV-1 infection per sexual act: systematic review and meta-analysis of observational studies[END_REF][START_REF] Powers | Rethinking the heterosexual infectivity of HIV-1: a systematic review and meta-analysis[END_REF] and intercourse for MSM. [START_REF] Leynaert | Heterosexual transmission of human immunodeficiency virus: variability of infectivity throughout the course of infection. European Study Group on Heterosexual Transmission of HIV[END_REF][START_REF] Osmond | Time of exposure and risk of HIV infection in homosexual partners of men with AIDS[END_REF][START_REF] Giesecke | Partner notification as a tool for research in HIV epidemiology: behaviour change, transmission risk and incidence trends[END_REF] Additional evidence of heterogeneity in per-partner estimates by potential risk factors such as STI history are summarised in Table S4, but the number of studies is limited. Estimates stratified by risk categories (Tables S3 andS4) may suffer from publication bias, as they are more likely to be reported if differences are significant.

URAI per-act estimates are substantially higher than for male-to-female VI (0.08%, 95%CI 0.06-0.11% developed countries; 0.30%, 95%CI 0.14-0.63% developing countries).( 13) Most studies of heterosexual couples have found an increased male-to-female transmission risk among couples practising AI, even if only occasionally. [START_REF] Boily | Heterosexual risk of HIV-1 infection per sexual act: systematic review and meta-analysis of observational studies[END_REF][START_REF] Powers | Rethinking the heterosexual infectivity of HIV-1: a systematic review and meta-analysis[END_REF][START_REF] Lazzarin | Man-to-woman sexual transmission of the human immunodeficiency virus. Risk factors related to sexual behavior, man's infectiousness, and woman's susceptibility. Italian Study Group on HIV Heterosexual Transmission[END_REF][START_REF] Mayer | Heterosexual HIV transmission[END_REF][START_REF] Silverman | Use and effectiveness of condoms during anal intercourse. A review[END_REF][START_REF] Scott | Genital herpes: audit of cases referred by general practitioners to a department of genito-urinary medicine[END_REF][START_REF] Nicolosi | The efficiency of male-to-female and female-to-male sexual transmission of the human immunodeficiency virus: a study of 730 stable couples. Italian Study Group on HIV Heterosexual Transmission[END_REF][START_REF] Seidlin | Heterosexual transmission of HIV in a cohort of couples in New York City[END_REF][START_REF] Chamberland | Heterosexually acquired infection with HIV: a view from the III International Conference on AIDS[END_REF][START_REF] Padian | Male-tofemale transmission of human immunodeficiency virus[END_REF] Rectal mucosa lacks the protective humoral immune barrier present in cervicovaginal secretions [START_REF] Belec | Cervicovaginal overproduction of specific IgG to human immunodeficiency virus (HIV) contrasts with normal or impaired IgA local response in HIV infection[END_REF] Our AI transmission probability estimates are considerably higher than oro-genital risks, which were found to be very low, but non-zero.( 53) For example, our per-act URAI summary estimate is 35-fold larger than the highest per-act oro-genital estimate (0.04% for unprotected receptive oro-genital intercourse, 95%CI 0.01-0.17%( 25)). Thus, practicing oral sex with an HIV-infected individual considerably reduces the risk of HIV acquisition compared to that for URAI and UIAI, but does not reduce it to zero. Individuals often make sophisticated choices regarding the balance of risk and pleasure; [START_REF] Frost | Understanding why gay men seek HIV-seroconcordant partners: intimacy and risk reduction motivations[END_REF][START_REF] Davies | On male homosexual prostitution and HIV[END_REF] this difference in risk should be appropriately communicated to relevant populations.

Studies have demonstrated that a substantial percentage of heterosexuals engage in AI with an opposite-gender partner [START_REF] Aral | Temporal trends in sexual behaviors and sexually transmitted disease history among 18-to 39-year-old Seattle, Washington, residents: results of random digit-dial surveys[END_REF][START_REF] Baldwin | Heterosexual anal intercourse: an understudied, high-risk sexual behavior[END_REF][START_REF] Friedman | Prevalence and correlates of anal sex with men among young adult women in an inner city minority neighborhood[END_REF][START_REF] Lewis | The prevalence of high-risk sexual behavior in male intravenous drug users with steady female partners[END_REF][START_REF] Gross | Anal sex among HIVseronegative women at high risk of HIV exposure. The HIVNET Vaccine Preparedness Study 2 Protocol Team[END_REF] and that rates of condom use for heterosexual AI are lower than for VI. [START_REF] Halperin | Heterosexual anal intercourse: prevalence, cultural factors, and HIV infection and other health risks, Part I[END_REF][START_REF] Leichliter | Prevalence and correlates of heterosexual anal and oral sex in adolescents and adults in the United States[END_REF] More recently, research in the US and the United Kingdom has demonstrated an increase in the proportion of heterosexuals reporting practicing AI, [START_REF] Aral | Temporal trends in sexual behaviors and sexually transmitted disease history among 18-to 39-year-old Seattle, Washington, residents: results of random digit-dial surveys[END_REF][START_REF] Satterwhite | Changes in sexual behavior and STD prevalence among heterosexual STD clinic attendees: 1993-1995 versus 1999-2000[END_REF][START_REF] Mosher | Sexual behavior and selected health measures: men and women 15-44 years of age, United States[END_REF][START_REF] Johnson | Sexual behaviour in Britain: partnerships, practices, and HIV risk behaviours[END_REF] although this rise may be attributable to social changes affecting reporting bias. The proportion of heterosexually-acquired HIV infection attributable to AI depends largely on the frequency of UAI, which varies greatly by population and setting, and the HIV risk profile of the partners of heterosexuals. Table 2 presents a summary of studies identified through a non-exhaustive review of PubMed, documenting the proportion of participants reporting any AI over a defined period for various populations and settings published in the last ten years. Although these findings may not all be representative of the general population due to small samples and selection biases, the high rates of AI are in line with those investigated with our model.

The majority of surveys were conducted in industrialised countries; more and carefully collected data on Our analysis of how the impact of HAART on HIV transmission may be mitigated by AI suffers from several limitations due to its simplicity and the difficulty in quantifying AI infectiousness highlighted in this review (for example, per-act VI risk was taken from a meta-analysis for male-to-female transmission in developing countries,(13) but our per-act URAI summary estimate represents industrialised countries only because no relevant studies from developing countries were identified; we assume that infectiousness varies with viral load similarly for AI and VI and that coital frequency remains constant over time; and again we stress the need for caution in utilising our quantitative pooled estimates).

Nevertheless, it serves to vividly illustrate the large excess in HIV risk that individuals may experience over time if they occasionally engage in UAI with an infected partner. Thus prevention messages must emphasise the high risk associated with AI and that control measures such as condoms must be used for both VI and AI.

Drawing conclusions on the use of HAART for HIV prevention is beyond the scope of this paper.

However, the contrasting quantitative results obtained regarding the impact of HAART on per-partner transmission risk using the two functions (Figures 3b-e) highlight that caution is required when relying on viral load data to predict the potential impact of HAART on transmission and the importance of clearly describing the model assumptions. Different viral load functions produce different predictions (Figure 3). Figures 3d-e

Conflicts of interest

We declare that we have no commercial or other association that might pose a conflict of interest. Scenario a) represents the impact of URAI on per-partner HIV risk assuming a constant per-act probability for URAI (1.4%, Table 1) and for penile-vaginal intercourse (summary estimate of peract penile-vaginal intercourse, male-to-female transmission for developing countries: 0.3%; [START_REF] Boily | Heterosexual risk of HIV-1 infection per sexual act: systematic review and meta-analysis of observational studies[END_REF] we assume, in the absence of per-act HIV estimates for UIAI identified by our review, that HIV transmission probability is the same as for female-to-male penile-vaginal intercourse). Scenario N -number of study estimates; p -p-value; P-DC -prospective discordant-couple study design; Q -heterogeneity statistic; R-P -retrospective-partner study design; S-P -simple prospective study design; UIAI -unprotected insertive anal intercourse; URAI -unprotected receptive anal intercourse. Crude estimates:

estimates calculated through simple derivation as number of seroconversions out of number of sexual acts involving exposure.

Adjusted estimates: estimates derived using more sophisticated calculation of transmission probability.

Fixed effects summary estimates can be found in Table S5, Supplementary Information.

Supplementary methods

Search strategy

The literature search to September 6 th 2008 was conducted in three stages. First, PubMed, Science Direct and NLM Gateway online databases were searched to September 2006 using search terms:

"HIV transmission probability" OR "HIV transmission probabilities" OR "HIV infectivity" OR "HIV infectiousness" NOT "perinatal" NOT "mother to child" NOT "mother-to-child" and by replacing "HIV" by the terms, "LAV", "HTLV-III" and "HTLV III". homosexual OR risk OR female OR male OR anal))). Titles were evaluated and obviously irrelevant publications discarded. Potentially relevant publications' abstracts were evaluated, where they were available on the online database. Obviously irrelevant publications were again discarded and all other manuscripts were retrieved as pdfs or paper copies for evaluation. Bibliographies of relevant articles were checked and experts in the field were contacted in order to identify additional relevant publications. One contacted author provided additional information.

Intervention impact: HAART

We assessed the potential reduction in HIV infectivity caused by HAART reducing viral load, using two published functions of infectivity by viral load. [START_REF] Wilson | Relation between HIV viral load and infectiousness: a model-based analysis[END_REF][START_REF] Abu-Raddad | Analytic insights into the population level impact of imperfect prophylactic HIV vaccines[END_REF][START_REF] Modjarrad | Impact of small reductions in plasma HIV RNA levels on the risk of heterosexual transmission and disease progression[END_REF][START_REF] Salomon | Evaluating the impact of antiretroviral therapy on HIV transmission[END_REF][START_REF] Fraser | Variation in HIV-1 set-point viral load: epidemiological analysis and an evolutionary hypothesis[END_REF] We assume that successful HAART reduces blood viral load from an average, baseline 0 4), main text. Function 1 uses the function given in equation ( 3) main text but using rate rather than per-act of HIV transmission, where the HIV transmission rate at 10 4.5 log 10 copies/ml is set to be the same as that predicted using function 2. The observed transmission rates for viral load strata reported in Quinn et al [START_REF] Quinn | Viral load and heterosexual transmission of human immunodeficiency virus type 1. Rakai Project Study Group[END_REF] are also plotted. a) shows the deviation in predicted transmission rates at high viral loads; b) is the same graph on a smaller scale, showing the deviation in predicted transmission rates at low viral loads.

V to 1 V copies/ml.

F o r R e v i e w

O n l y 36 ARC -AIDS-related complex; ART -antiretroviral therapy; CT -Chlamydia trachomatis; HAART -highly active antiretroviral therapy; MSM -men who have sex with men; M-to-F -male-to-female; NG -Neisseria gonorrhoea; NR -not recorded; PIAI -protected insertive anal intercourse; STI -sexually transmitted infection; UIAI -unprotected insertive anal intercourse; URAI -unprotected receptive anal intercourse; ZDV -zidovudine (AZT). 1 Authors reported in the Discussion section that results of their model allowing the per act risk to vary between individuals implied an even broader range of risk of transmission than the 0.5-3.0% main result reported in the abstract: they state that, "50% of the partners of infected men have a sero-conversion risk per exposure of less than 0.02 [2%]; 10-20% of infected partners have a great than 0.10 [10%] risk of seroconversion per sexual exposure."

2 95%CI were derived from available information because it was not reported in the publication.

F o r R e v i e w

O n l y 39 3 Publication additionally provides estimates for protected receptive anal intercourse (0.18%, 95%CI 0.10-0.28) and unprotected (0.06%, 95%CI 0.02-0.19) and protected (0.04%, 95%CI 0.01-0.11) insertive anal intercourse, but these outcomes are per exposure "with an HIV infected or unknown serostatus partner" because there were too few such contacts with known infected partners to provide stable per act estimates and have therefore been excluded from the analysis. 4 There were 7 seroconverters who had practised URA with a known HIV infected partner, with 564 URAI contacts. However the per act estimate was calculated using the entire dataset (which included 49 seroconverters) which took into account exposures of all types.

5 Unadjusted per at URAI estimate reported as 0.6% (95%CI 0.1-2.0). 6 The 20 partners were from only six index cases recruited for the study. 7 Probabilities were independent of the duration of relationship.

8 Derived from 3.4% standard error reported in the publication. 9 Defined as sexual contacts that involve URAI. Frequency of sex acts involving receptive anal intercourse

  transmission risk through anal intercourse: systematic review, meta-analysis and implications for HIV prevention

β

  are per-act transmission probabilities for VI ( v ) and receptive AI ( a ), respectively; and d is the proportion of n sex acts which are AI rather than VI.

  and unprotected AI are required from populations in developing countries to explore the influence of AI on generalised epidemics.[START_REF] Boily | The role of heterosexual anal intercourse for HIV transmission in developing countries: are we ready to draw conclusions?[END_REF]

24 Figure legends and TablesFigure 1

 241 Figure legends and Tables

Figure 2

 2 Figure 2Relation between per-partner HIV transmission risk (cumulative probability of HIV transmission) and the number of sexual acts with an HIV infected partner, using our summary per-act unprotected receptive anal intercourse (URAI) estimate of 1.4% (95%CI 0.2,2.5). The intersection between the modelled per-partner HIV transmission risk (y-axis) and our metaanalytic per-partner combined URAI and unprotected insertive AI (UIAI) summary estimates (plotted as horizontal lines), predicts the required average number of acts per partnership (xaxis), under our model assumptions (see Methods). Adjusted estimates control for exposures due to multiple partners and crude estimates do not. a) All acts assumed to be URAI; b) 50% acts URAI, 50% acts UIAI, assuming per-act UIAI has the same HIV transmission probability as penile-vaginal intercourse (summary estimate of per-act penile-vaginal intercourse (VI), male-tofemale transmission for developing countries: 0.3%;(13) c) as for b) but UIAI HIV transmission probability is 0.6%. Competing risk from UIAI increases the total number of unprotected acts necessary for transmission per partnership only by relatively modest amounts, especially when the increase in transmission probability of UIAI compared to VI is large, because UIAI infectiousness becomes closer to that of URAI.

Figure 3 25 to

 325 Figure 3 Relation between per-partner HIV risk (cumulative probability of HIV transmission) andthe number of all sexual acts (whether penile-vaginal or penile-anal) that uninfected MSM or heterosexual women are exposed to with HIV infected men, exploring the impact of different frequencies of unprotected receptive anal intercourse (URAI) within the partnership (if in a monogamous HIV discordant relationship) or amongst all sexual HIV exposures that an uninfected individual encounters. Frequency of sexual acts involving URAI: 0-20% represent ranges for women in heterosexual partnerships, with the remainder of sexual exposures assumed

b) uses function 1

 1 to investigate impact of HAART, predicting per-partner HIV risk within a discordant couple where the index male has successful viral suppression due to highly active antiretroviral therapy (HAART); scenario c) investigates the same, by using function 2 (note change of y-axis scale). Scenarios d) and e) use function 2 (separating graphs for women and MSM for clarity), additionally including viral rebound as a result of treatment failure for a proportion of the duration of exposure. The derived relationship between URAI infectiousness and plasma viral load calculated in function 2 is illustrated in FigureS3. * Q statistic calculated using Cochran's Q test for heterogeneity, summing the squared deviations of each study's estimate from the overall pooled estimate, weighting the contribution of each study by its inverse variance.[START_REF] Cochran | The combination of estimates from different experiments[END_REF] Under the hypothesis of homogeneity among the transmission probability estimates, the Q statistic follows a chi-square distribution with k-1 degrees of freedom, with k being the number of studies. From this, the p value for heterogeneity can be derived. † I 2 calculated as described in Higgins et al.(73) I 2 lies between 0% and 100%; 0% indicates no observed heterogeneity and larger values show increasing heterogeneity.

Function 1

 1 was based on results from the Rakai study of HIV transmission in heterosexual couples (presumed through vaginal intercourse (VI) transmission)[START_REF] Quinn | Viral load and heterosexual transmission of human immunodeficiency virus type 1. Rakai Project Study Group[END_REF] and assumes a linear relationship act and per-partner estimates: per-act estimates underestimate HIV transmission risk for partnerships involving only a few sex acts, compared with per-partner estimates. They are likely to overestimate the risk for partnerships involving many (>100) sex acts.

Figure S3

 S3 Figure S3Penile-anal and penile-vaginal transmission probabilities by plasma viral load: a) HIV transmission rates per year and b) HIV transmission per-act. Penile-vaginal transmission rate estimates derived from Fraser et al[START_REF] Fraser | Variation in HIV-1 set-point viral load: epidemiological analysis and an evolutionary hypothesis[END_REF] and penile-vaginal per-act and penile-anal estimates inferred using the functions described in the Methods section, main text.

Figure S4

 S4 Figure S4 Comparison of functions 1 and 2 to derive infectiousness by viral load. Graphs show derived relationships for penile-vaginal HIV transmission rate per year. Function 2 uses the function given in equation (4), main text. Function 1 uses the function given in equation (3) main text but using rate rather

Figure 2 Cumulative

 2 Figure 2

  Figure 3 a) b)

Figure S3 F

 S3 Figure S3

Figure S4

  Figure S4

  TableS3summarises heterosexual per-partner estimates which have been stratified by frequency of AI practice. TableS4summaries AI study estimates stratified by different risk factors.

	The only per-act estimates included were for URAI. Vittinghoff et al's estimates for protected receptive
	AI (0.18%, 95%CI 0.10-0.28), unprotected insertive AI (UIAI) (0.06%, 95%CI 0.02-0.19) and protected

  study data.

	8
	We categorised study estimates into "crude" and "adjusted". "Crude" estimates are based on the HIV
	status of partners of index cases and assume that the index case was the only source of exposure. In
	high-risk populations, multiple exposures to HIV through sexual contact with other partners and through
	other types of sexual practice may lead to overestimation of infectivity. Thus "Adjusted" estimates are
	based on statistical models to control for multiple exposures. One study also adjusted for multiple
	modes of sexual transmission: from URAI, UIAI, protected AI and oro-genital intercourse.(25) No study
	provided both crude and adjusted estimates. Brief details on adjusted estimates are provided in Table
	S1, Supplementary Information. Numbers of per-act and per-partner estimate by adjustment type and
	r o F study design are given in Table
	R
	e v
	i e
	w
	O n l
	y

Table 1

 1

	shows the per-act and per-partner summary estimates by exposure (combined URAI-UIAI,
	URAI-only and UIAI-only). Two per-act URAI estimates were based on studies among MSM(24, 25) and
	two among heterosexual couples.(26, 27) The per-act summary estimate was 1.4% (95%CI 0.2-2.5) (or
	1.8% [95%CI 0.3-3.2] if Halperin et al's abstract estimate is excluded due to lack of further detail on
	methods(26)). No significant differences in per-act URAI estimates between heterosexual couples and
	MSM was found (p=0.674). However, while MSM estimates(24, 25) were similar to each other (Q=0.2,
	p=0.635, I 2 =0%), heterosexual estimates(26, 27) were heterogeneous (Q=10.5, p=0.001, I 2 =90%,
	Figure 1, Table 1). Most per-partner estimates were derived from studies on MSM. Exceptions were
	Nicolosi et al, studying heterosexual couples,(29) and Giesecke et al, who enrolled a small proportion of
	heterosexual participants.(34) Cheingsong-Popov et al did not describe study participants but it appears
	likely, given the 1984 publication date, that the AIDS and AIDS-related complex patients reporting AI
	were MSM.(28) There was no evidence that the heterosexual combined URAI-UIAI crude per-partner
	estimate(29) was significantly different from the eight crude estimates from MSM (p=0.821).

  Leynaert et al was a retrospective-partner study where the exposure period was only crudely estimated.(27) Although some transmissions in Vittinghoff et al's prospective study may have occurred as a result of acute infection exposure, the study estimate only included study participants

	10
	infection.(24-27)
	F o r
	R
	e v
	i e
	w
	O n l
	y

) Table

S4

, Supplementary Information, summarises the few per-act and per-partner estimates stratified by risk factors. The only per-act estimate stratified by infection stage (primary infection and AIDS stages each separately estimated as 18.35% [95%CI 2.08,34.6]; asymptomatic incubation stage 1.38% [95%CI 0.0-3.38])

[START_REF] Leynaert | Heterosexual transmission of human immunodeficiency virus: variability of infectivity throughout the course of infection. European Study Group on Heterosexual Transmission of HIV[END_REF]

reflects variability in infectiousness within an individual over time. However it is likely that none of the four average per-act AI infectivity estimates adequately captures the contribution of high infectiousness during acute, pre-seroconversion

  The discrepancies between per-act and per-partner estimates (Figures2, S2) may partly be explained by condom use, competing risks from exposure to HIV outside the main partnership, or some degree of heterogeneity in transmission probability per-act between individuals and within individuals over time, implying that our assumption of independence of risk per-act within a partnership is invalid. If there is heterogeneity in infectiousness or susceptibility between individuals, this may explain the saturation of per-partner risk at lower levels than predicted using our per-act summary estimate. The four per-act estimates represent exposure without condoms: DeGruttola and Leynaert et al reported <1% condom use[START_REF] Degruttola | Infectiousness of HIV between male homosexual partners[END_REF][START_REF] Leynaert | Heterosexual transmission of human immunodeficiency virus: variability of infectivity throughout the course of infection. European Study Group on Heterosexual Transmission of HIV[END_REF] and Vittinghoff and Halperin et al adjusted for it.[START_REF] Vittinghoff | Per-contact risk of human immunodeficiency virus transmission between male sexual partners[END_REF][START_REF] Halperin | High level of HIV-1 infection from anal intercourse: a neglected risk factor in heterosexual AIDS prevention[END_REF] In contrast, many per-partner studies reported "some condom use" but generally did not quantify

	11
	heterogeneity.
	e
	w
	O n l
	y

frequency (although it appears that condom use was generally very inconsistent within partnerships).

If we assume the 18.35% per-act URAI estimate of Leynaert et al associated with primary infection,

[START_REF] Leynaert | Heterosexual transmission of human immunodeficiency virus: variability of infectivity throughout the course of infection. European Study Group on Heterosexual Transmission of HIV[END_REF]

only 3 URAI acts are necessary for per-partner HIV risk to exceed 40.4% (per-partner URAI-only summary estimate, results not shown)

  As expected, our per-partner HIV risk estimates with HAART, even assuming continuous viral suppression, are larger than Wilson et al's[START_REF] Wilson | Relation between HIV viral load and infectiousness: a model-based analysis[END_REF] estimates using the same function, because we used recent and higher baseline per-act VI infectivity estimates from developing country

	12
	always receptive. studies only (due to the lack of AI infectivity studies from developing countries, per-act URAI was
	informed by developed country studies only) .(13) Using function 2 (Figures 3c-e), the predicted per-act
	VI/UIAI and URAI estimates with successful HAART are 0.0002% and 0.0011% respectively i.e. 99.9%
	lower than without therapy. Under these assumptions, 1000 sex acts leads to a male-to-female per-
	partner HIV risk of <0.5% even where AI constitutes 20% of all sex acts, <1% for MSM practising URAI
	and UIAI with equal frequency and 1.1% for MSM solely practising URAI (Figure 3c). However, if viral
	rebound occurs due to treatment failure, per-partner transmission risks become much larger (Figures F r o 3d-e).
	R
	e v
	i e
	w
	O n l
	y
	12.2% if no AI is practised (i.e. only VI is practiced) and 12.6%, 14.3%, 16.3% and 20.2% if AI is

practised for 1%, 5%, 10% and 20% of all sex acts, respectively. For MSM, 1000 acts leads to perpartner risk of 30.9% if partners alternate URAI and UIAI, and 45.6% if the initially uninfected partner is

Discussion

Four per-act URAI estimates produced a summary estimate of 1.4% (95%CI 0.2-2.5) and per-partner summary estimates were 39.9% (95%CI 22.5-57.4), 40.4% (95%CI 6.0-74.9) and 21.7% (95%CI 0.2-43.3) for combined URAI-UIAI, URAI and UIAI transmission respectively. Competing risk from UIAI only marginally increases HIV transmission per partnership (39.9% for combined, 40.4% for URAI only)

  14per-partner infectivities may differ due to dissimilar frequencies of practising AI within heterosexual and MSM relationships. However, the only heterosexual per-partner study consisted of couples with high frequency of AI (≥50% of sexual acts)[START_REF] Nicolosi | The efficiency of male-to-female and female-to-male sexual transmission of the human immunodeficiency virus: a study of 730 stable couples. Italian Study Group on HIV Heterosexual Transmission[END_REF] and therefore, given the much higher risk of transmission during AI than VI, estimates should be comparable to those from MSM studies. Our review extends previous HIV infectivity research because we investigated per-act and per-partner AI infectivity among MSM and heterosexuals. However, we found no AI estimates from developing countries and, given the different distributions in risk factors such as STI prevalences and HIV subtypes between settings, we may underestimate overall AI infectiousness for developing countries, as has been suggested for peract VI infectiousness.[START_REF] Boily | Heterosexual risk of HIV-1 infection per sexual act: systematic review and meta-analysis of observational studies[END_REF][START_REF] Powers | Rethinking the heterosexual infectivity of HIV-1: a systematic review and meta-analysis[END_REF]

	F o r
	R
	e v
	i e
	w
	O n l
	y

and is more susceptible to traumatic abrasions which may facilitate transmission.

[START_REF] Levy | The transmission of HIV and factors influencing progression to AIDS[END_REF]

We found no evidence of a difference in per-act AI infectivity between heterosexual and MSM couples, possibly because they are biologically similar practices, yet

  16heterosexual as well as MSM sex lives, particularly in regions with high HIV incidence, so that we can design and implement measures to minimise the role that it plays in HIV transmission.

	F o r
	R
	e v
	i e
	w
	O n l
	y
	increasing interest in HAART use as a prevention tool.(66, 67) Modelling cannot be used as a substitute
	for empirical evidence, and data are starting to become available.(68)
	In terms of product development, oral pre-exposure prophylaxis may be more appropriate for use
	among populations where there is a high frequency of AI if adherence to condom use or rectal
	microbicide use is poor, or if microbicide efficacy is lower for AI than VI. All microbicide trials potentially
	suffer from bias from AI.(69-71) There must be greater understanding of the role that AI plays in

demonstrate the sensitivity of results to frequency of viral rebound and to the infectiousness associated with these rebounds. Further work in this area is necessary given the

Table 2 Summary of selected epidemiological studies investigating practice of anal intercourse amongst heterosexual populations published in the last 10 years.

 2

	Study	Population	Age (years)	Sample	% reporting AI	Exposure period
				size
	Industrialised countries
	Pollack, unpublished data 1999,	US population survey, women	18-49	1071	6.1%	Past 6 months
	from 1992 National AIDS
	Behavioral Methodology Study 4,5
	Laumann et al 1994 (74) 4	US population survey	18-59	3432	23%	Ever
					10% men	Past year
					9% women	Past year
					2.3% men	Last sex
					1.2% women	Last sex
			50-54		3% men	Past year
					2% women	Past year
			25-29		2.4% women	Last sex
	Gross et al 2000 (60)	US HIV negative women "at high risk of HIV	11% 18-25	1268	32%	Past 6 months
		infection"	38% 26-35
			51% ≥36
	Baldwin et al 2000 (57)	US random sample of sexually experienced	Mean 21, all <30	647	23%	Ever
		university students (oversampling ethnic groups)

  PubMed was searched by titles. Science Direct and NLM Gateway were searched by abstracts, titles, keywords and authors. The PubMed search was updated twice (to June 29 th 2007, and again to September 6

th 2008) using more efficient search terms and Boolean operators, for matches under any field: (HIV OR LAV OR HTLV III OR HTLV-III OR AIDS OR human immunodeficiency virus OR human T-lymphotropic virus III OR acquired immunodeficiency) AND (infectiousness OR infectivity OR probability OR contact OR contacts OR partner OR partners OR wives OR spouses OR husbands OR couples OR discordant OR (transmission AND (heterosexual OR

Table S1 Details of studies estimating transmission probabilities for anal intercourse Study Setting/Study design/Population/Date Stage of HIV infection/other risk factors, uncontrolled cofactors

 S1

					37 38
	Study Study	Setting/Study design/Population/Date Setting/Study design/Population/Date	Stage of HIV infection/other risk factors, uncontrolled Stage of HIV infection/other risk factors, uncontrolled	Transmission probability, Transmission probability,
			cofactors cofactors	% (x/n, 95% CI) % (x/n, 95% CI)
	Weller et al 1987 (30) URAI PER ACT ESTIMATES URAI DeGruttola et al 1989 (24) Leynaert et al 1998 (27) Vittinghoff et al 1999 (25) 3 Halperin et al 2002 (abstract) (26) and S.C. Shiboski, personal communication 2003 Combined URAI AND UIAI UK retrospective-partner, MSM, regular (≥6 months) US retrospective-partner (132 MSM -some infected, some uninfected -and 155 sexual partners from the previous 30 months). Binomial model fitted to data, assuming a constant risk of transmission throughout infection, but authors explored models allowing different infectivity levels across index cases. Uninfected as well as infected individuals were included as index cases in order to account within the model for HIV transmission events occurring outside the primary relationship. European retrospective-partner (part of a prospective multi-centre study). 499 heterosexual couples; 359 with male index, of whom 20% engaged in AI. All data used to inform a probabilistic model to estimate per act infectivity for multiple types of intercourse at different stages of infection of index (but only URAI, no UIAI). 1987-1992, M-to-F transmission. US simple-prospective multi-centre study (1583 high risk MSM, followed for up to 18 months (total 2633 person-years) with at least one sexual contact with an HIV positive or unknown serostatus partner),1992-1994. Modified Bernoulli regression model using data from men with complex patterns of exposure [multiple types of exposure (URAI, protected insertive AI, etc.)]. Regression of participants with multiple exposures with multiple partners. US California Partner Study, recruited 1985-1986, M-to-F transmission, retrospective-partner study. Described in Padian et al 1987 (89): 59 male index cases and their female partners. Abstract does not report absolute prospective, MSM 1994-1999 Porco et al 2004 (93) US San Francisco Men's Health Study: simple-PER PARTNERSHIP ESTIMATES communication. 1987-1991, combined male and female index cases (2.1, 51.3); further information provided through personal transfusion recipients, MSM, recruited from health clinics penile-vaginal intercourse transmission probabilities: 10.3 Nicolosi et al 1994 (29) Italy retrospective-partner, sexual partners of IDU, transmission probabilities but the ratio of URAI to M-to-F F o r R e v i e w 51% AIDS, 49% ARC <100% monogamy, 15% AIDS and 20% ARC amongst index cases, <1% condom use Contact partner had no other "risk factors for HIV other than sexual contacts with the index case"; 0% systematic condom use, history of STI in index or partner since 1980 among some couples. No IDU exposure. STI (NG, CT, urethritis) considered as covariates within the model. Information on index cases limited: partner reported sexual contacts as HIV positive, negative or unknown serostatus. Frequency of condom use reported and estimates adjusted accordingly. MSM population in San Francisco between 1994 and 1999. Study Used probabilistic risk model. Assumed constant HIV prevalence in intercourse) AI as frequency of sexual practice: often or always (≥50% 100% monogamous. Some condom use, STI history. No IDU, transfusion or needle exposure, CSW contact, MSM, Adjusted for condom use, history of STI, IDU in males 5 O n l y sexual partners of AIDS patients, no date Partners of index cases were not monogamous Coates et al 1988 (31) 9 Canada retrospective-partner, healthy sexual contacts of Not stated Partnership duration: median 26 months and 30 months for MSM with AIDS or ARC (≥1 contact within 1 year of seroconcordant and serodiscordant couples, respectively Cumulative incidence over 6 months: 0.0 Goldsmith et al 1987 (32) US retrospective-partner, MSM with sexual contact with HIV infected MSM 6 , 1981-1983 AIDS or ARC index's diagnosis), 1984-1985 Giesecke et al 1992 (34) 7 Sweden retrospective-partner, partner notification of all All (heterosexuals and MSM) patients diagnosed in Sweden (heterosexuals and MSM), Partners of index cases were not monogamous (mean 396 and 278 lifetime male sexual partners for seroconverters and non-seroconverters, respectively) Partnership duration: 15 of 20 were long-term partnerships (2 months -12 years); 5 were only 1 or 2 exposures, 9-13 months prior to study recruitment STI history (mean 4.5 and 2.5 episodes for seroconverters and non-seroconverters, respectively) Osmond et al 1988 (90) US retrospective-partner (recruitment for a case-control study), sexual partners of MSM AIDS patients (at least 10 sexual contacts within 2 years of index case's AIDS diagnosis), 1983-1984 100% AIDS Partners of index cases were not monogamous Partnership duration: median 29 months (range: 2-221 months); 11% any condom use with index (0% had consistent condom use) Coates et al 1988 (31) Canada retrospective-partner, healthy sexual contacts of MSM with AIDS or ARC (≥1 contact within 1 year of index's diagnosis), 1984-1985 51% AIDS and 49% ARC Partners were not monogamous Cumulative incidence over 3 months: 0.0 Kaplan 1990 (35) Using data from Grant et al 1987, simple-prospective (91) (see Table S2, excluded studies, for details) Bernoulli model (alternative non-parametric model gave an estimate of 5.3, no 95% CI provided) Giesecke et al 1992 (34) 7 Sweden retrospective-partner, partner notification of all patients diagnosed in Sweden (heterosexuals and MSM) 1989-1990 MSM only Palenicek et al 1992 (36) US prospective discordant-couple, sexual partners of MSM practicing URAI and/or UIAI during follow-up 1988-1990 0% AIDS at enrolment Not all partners were monogamous; duration of partnership ≥3 months (75% ≥3 years) UC: STI history, ART (20% ZDV) 20% URAI (without ejaculation), 70% UIAI Duration of follow-up: 1 year Seage et al 1993 (92) US retrospective-partner, sexual partners of MSM 1985-1990 Partners of index cases were not monogamous intercourse) 1989-1990 Samuel et al 1994 (39) Using data from Grant et al 1987, simple-prospective (91) (see Table S2, excluded studies, for details) Estimates based on a series of models with varying assumptions, including: timescale used, inclusion or exclusion of condom use and ejaculation, and whether the model type includes additional transmission risk from other routes i.e. UIAI and oro-genital sex. Model assumptions include: choice of partner is not affected by their infection status and infectivity is constant over time. Nicolosi et al 1994 (29) Italy retrospective-partner, sexual partners of IDU, transfusion recipients, MSM, recruited from health clinics 1987-1991, male index cases No IDU, transfusion or needle exposure, CSW contact, MSM, 100% monogamous. Some condom use, STI history. AI as frequency of sexual practice: often or always (≥50% intercourse) UIAI Coates et al 1988 (31) 10 Canada retrospective-partner, healthy sexual contacts of MSM with AIDS or ARC (≥1 contact within 1 year of index's diagnosis), 1984-1985 Not stated Giesecke et al 1992 (34) 7 Sweden retrospective-partner, partner notification of all All (heterosexuals and MSM) F o r R e v i e w patients diagnosed in Sweden (heterosexuals and MSM), 1989-1990 Samuel et al 1994 (39) Using data from Grant et al 1987, simple-prospective (91) (see Table S2, excluded studies, for details) Estimates based on a series of models with varying assumptions, including: timescale used, inclusion or exclusion of condom use and ejaculation, and whether the model type includes additional transmission risk from other routes i.e. UIAI and oro-genital sex. Model assumptions include: choice of partner is not affected by their infection status and infectivity is constant over time. transfusion recipients, MSM, recruited from health clinics 1987-1991, female index cases 100% monogamous. Some condom use, STI history. AI as frequency of sexual practice: often or always (≥50% O n l y Nicolosi et al 1994 (29) Italy retrospective-partner, sexual partners of IDU, No IDU, transfusion or needle exposure, CSW contact, MSM,	60.0 Transmission probability, (21/35, 43.6-74.4) % (x/n, 95% CI) 0.5-3.0 1 3.38 (NR/359, 1.85,4.91) 2 0.82 (0.24, 2.76) 4 12.0 (5.3-18.7) 42.9 (18/42, 29.1-57.8) 0.4 (0.08,2.0) 69.5 (114/164, 62.1-76.0) 70.0 36.2 (17/47, 24.0-50.5) (14/20, 48.1-85.5) 72.6 (85/117, 63.9-79.9) 58.5 (144/246, 52.3-64.5) 5.1 (2.2-8.0) 43.6 (17/39, 29.3-59.0) 0.0 (0/10, 0.0-27.8) 30.5 (57/187, 24.3-37.4) ~10 (range: 4.2-12.0) 46.4 (13/28, 29.5-64.2) 36.6 (30/82, 27.0-47.4) 18.4 (7/38, 9.2-33.4) 0.15-1.5 35.7 (5/14, 16.3-61.2)
	Cheingsong-Popov et al	UK retrospective-partner ,regular or casual sexual	AIDS and ARC participants had multiple partners and serostatus of partners was	41.7	(15/36, 27.1-57.8)
	1984 (28)	partners of AIDS or ARC patients (likely MSM but not	No further information inferred using prevalence data. Aim of study is to prove a
		explicitly stated) 1983-1984	significant difference between infectivity in pre-and post-HAART
			eras, rather than obtain infectivity estimates per se. Estimate is
			infectiousness in absence of ART.

Table S4 Details of transmission probabilities for anal intercourse: stratified by different risk categories

 S4 Osmond et al 1988 (90) Sexual contact ended before index's AIDS diagnosis Sexual contact continued after index's AIDS diagnosis Sexual contact ended before index's AIDS diagnosis: RAI usual with index: no yes Sexual contact continued after index's AIDS diagnosis: RAI usual with index: no yes

	per-partner HIV transmission risk per-partner HIV transmission risk	F o r R e v Risk categories Leynaert et al 1998 (27) Primary Infection (first 3 months) Study PER ACT ESTIMATES Incubation (CD4 ≥200/mm 3 ) AIDS (CD4 <200/mm 3 ) PER PARTNER ESTIMATES HIV disease stage Giesecke et al 1992 (34) Combined: asymptomatic symptomatic URAI: asymptomatic symptomatic UIAI: asymptomatic symptomatic Contact frequency Weller et al 1987 (30) Transmission by frequency of RAI: < once/month > once/month Osmond et al 1988 (90) RAI usual with index: no yes 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 200 400 600 800 Number of unprotected sexual acts 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 200 400 600 800 F o r R e v i e w O n l y Transmission probability, % (x/n, 95% CI) 18.35 1.38 18.35 (2.08,34.6) (0.00,3.38) (2.08,34.6) 66.7 81.3 59.4 73.0 62.5 100.0 (46/69, 54.9-76.6) (39/48, 68.1-89.8) (19/32, 42.3-74.5) (27/37, 57.0-84.6) (15/24, 42.7-78.8) (24/24, 86.2-100.0) 35.7 63.6 34.9 50.0 13.3 37.5 (10/28, 20.7-54.2) (7/11, 35.4-84.8) (15/43, 22.4-49.8) (2/4, 15.0-85.0) (4/30, 5.3-29.7) (3/8, 13.7-69.4) 26.7 80.0 (4/15, 10.9-52.0) (16/20, 58.4-91.9) 1000 1000 Number of unprotected sexual acts	43
	per-partner HIV transmission risk	0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%	200	400	i e w O n l 600 800 1000 y
				Number of unprotected sexual acts

10

Defined as sexual contacts that do not involve URAI.

62,643 abstracts identified from PubMED and title examined 788 abstracts examined 218 studies retrieved for more detailed evaluation 27 potentially appropriate studies identified 16 studies included in principal meta- analyses 570 abstracts excluded due to non-relevance 61,855 titles excluded due to non-relevance 12 per-partner estimate studies 3 studies identified through bibliographies (2 abstracts, 1 book chapter) 194 abstracts excluded for relating to other modes of transmission 4 per-act estimate studies Figure S1 11 studies excluded for failing to meet inclusion criteria and/or superseded by later publications

	0% 1% 5% 10% 20% 50% 100% Time with viral rebound: 20%, rebound to 5000 copies/ml Time with viral rebound: 80%, rebound to 500 copies/ml Time with viral rebound: 20%, rebound to 500 copies/ml y l 1000 n 0 from resource-poor settings 600 800 Number of unprotected sexual acts 400 O 16 from industrialised countries Time with viral rebound: 80%, rebound to 5000 copies/ml F o r R w e i X Seage et al (37) v Coates et al (31) e number of sexual contacts: Per-act URAI 95%CI (0.2-2.5%), two 0 200 Figure S2 0% 20% 40% 60% 80% 100% per-partner HIV risk d) lines on figure F o r R e v i e w O n l y 0% 20% 40% 60% 80% 100% 0 2 0 4 0 6 0 8 0 1 0 0 Cumulative probability of transmission Number of sexual acts Per-partner estimates stratified by Per-act URAI summary estimate (1.4%) a) b) penile-anal sex penile-vaginal sex 40% 60% 80% 100% F o r R e v i e w O n l y 0% 20% 10 100 1,000 10,000 100,000 1,000,000 Probability	0 c) e)	200	400 Number of unprotected sexual acts 600 800	1000 0% 20% 40% 60% 80% 100%	risk per-partner HIV
		MSM Heterosexual	MSM	Heterosexual	Mixed
	Combined URAI UIAI	0	0	10	1	0
	URAI	2	2	2	1	1
	UIAI	0	0	2	1	1
	Stratifying by risk factors	0	1	5	0	0

of HIV transmission per year HIV plasma viral load (copies/ml)

		2.5%
		2.0%
		1.5%
		1.0%
	Probaability	0.0% 0.5%	100	1,000	10,000	100,000	1,000,000

of HIV transmission per-act HIV plasma viral load (copies/ml)

Authors report that results must be interpreted with caution as some younger pupils may have had difficulty in understanding some of the more sensitive questions (questionnaire

Acknowledgements

We thank Dr Steven Shiboski for providing further data.

Funding

This work was supported by the Wellcome Trust ([GR082623MA to RFB, GR078499MA to RGW]); UK Medical Research Council (MRC) to RGW and the Bill and Melinda Gates Foundation to MCB and RGW. We thank the MRC for Centre funding. The views expressed herein are those of the authors and do not necessarily reflect the official policy or position of the Bill and Melinda Gates Foundation, Wellcome Trust or MRC.

was self-administered), "in particular questions on orogenital and anal sex". 2 Not specified in the publication. 3 Total completing NATSAL 2000 questionnaire, including non-heterosexuals (% reporting AI is for heterosexual practices only). 4 Results taken from review by Halperin 1999 (6). 5 Lance M. Pollack personal communication, September 1999 to D. Halperin [START_REF] Halperin | Heterosexual anal intercourse: prevalence, cultural factors, and HIV infection and other health risks, Part I[END_REF]. 6 Unprotected AI only. 7 A further 0.6% of men reported ever having had AI with another man.

8 Seventeen (0.8%) of men and 68 (2.3%) of women reported not knowing if they had ever experienced AI. None of these men were HIV positive, but among women, 'not knowing' was significantly associated with HIV infection, compared to the group of women reporting no AI experience.

between infectiousness and log serum viral load [START_REF] Wilson | Relation between HIV viral load and infectiousness: a model-based analysis[END_REF][START_REF] Abu-Raddad | Analytic insights into the population level impact of imperfect prophylactic HIV vaccines[END_REF][START_REF] Modjarrad | Impact of small reductions in plasma HIV RNA levels on the risk of heterosexual transmission and disease progression[END_REF][START_REF] Salomon | Evaluating the impact of antiretroviral therapy on HIV transmission[END_REF]: each ten-fold increment in viral load is associated with a 2.45-fold increase in the risk of HIV transmission per-act.

( )

where

where , ,max rate v β , the maximum infection rate per annum, is 0.317 per year; 50 V , the viral load at which infectiousness is half its maximum, is 13,938 copies/mL and k , the steepness of increase in infectiousness as a function of viral load, is 1.02. [START_REF] Fraser | Variation in HIV-1 set-point viral load: epidemiological analysis and an evolutionary hypothesis[END_REF] We translated transmission rates ( ) [START_REF] Gisselquist | Running on empty: sexual co-factors are insufficient to fuel Africa's turbocharged HIV epidemic[END_REF] from main text rewritten as:

where n represents unprotected sex acts/year for the Zambian population.

In the absence of data for anal intercourse (AI) transmission by viral load, we assumed that the relationships between infectiousness and viral load defined in equations ( 3) and ( 4) hold for AI as well as VI. [START_REF] Wilson | Relation between HIV viral load and infectiousness: a model-based analysis[END_REF] The increased infectiousness of AI relative to VI, g , can be defined as where we assumed , c v β is 0.3% (male-to-female estimate for developing countries from Boily et al (13)) and , c a β from our meta-analysis (see Findings).

To estimate reduction in infectiousness with HAART we first estimate a "typical" infectiousness for untreated individuals by assuming a baseline viral load for index cases 0 V of 10 4.5 HIV RNA copies/ml which falls to 1 V , 10 copies/ml, with effective HAART, with treatment initiated before formation of the partnership (following Wilson et al [START_REF] Wilson | Relation between HIV viral load and infectiousness: a model-based analysis[END_REF]). For function 1, we assume that our meta-analysis , c a β estimate represents infectiousness at 10 4.5 HIV RNA copies/ml and use this to derive , c a β at 10 copies/ml using equation (3). For function 2, we derive n as 83 unprotected acts/year (7 acts/month) by using equation ( 5) and assuming ( )

To explore the impact of treatment failure (failure to suppress viral load) on cumulative HIV risk, we modify equation ( 2) as follows:

(

where h is the proportion of time (or the proportion of sex acts if frequency of sex is constant over time) that an individual experiences treatment failure and r V is the level of viral rebound. No follow-up of partner -data on serostatus ascertained from questionnaire of "index" only. MSM -Men who have sex with men; M-to-F -male-to-female HIV transmission. [START_REF] Nicolosi | The efficiency of male-to-female and female-to-male sexual transmission of the human immunodeficiency virus: a study of 730 stable couples. Italian Study Group on HIV Heterosexual Transmission[END_REF] Cross-sectional, combined Mto-F and F-to-M Often or always (≥50% intercourse) (M-to-F) Often or always (≥50% intercourse) (F-to-M) Often or always (≥50% intercourse) (combined) Sometimes (<50% intercourse) (M-to-F) Sometimes (<50% intercourse) (F-to-M) Sometimes (<50% intercourse) (combined) Never (M-to-F) Never (F-to-M) Never (combined) ) F-to-M -female-to-male HIV transmission; M-to-F -male-to-female HIV transmission. 1 Median number of episodes of anal intercourse = 17 (range: 1-1650). 2 Frequency of this practice within the partnership not specified.

Figure legends

N -number of study estimates; p -p-value; Q -heterogeneity statistic; UIAI -unprotected insertive anal intercourse; URAI -unprotected receptive anal intercourse.

Crude estimates: estimates calculated through simple derivation as number of seroconversions out of number of sexual acts involving exposure.

Adjusted estimates: estimates derived using more sophisticated calculation of transmission probability.

F o r R e v i e w O n l y

URAI only