Epidemiology ) e l a c s g o l ( d a o l l a r i V (iii) (ii) (i) (months) Regimen switched (months) (years) Time since HIV infection Figure 1 Schematic representation of the three assumed trajectories of (log) viral load after treatment initiation: (i) suppression achieved and adherence good (dotted line); (ii) suppression achieved but adherence poor (solid line); and (iii) suppression not achieved (dashed line). The circles indicate when the regimen was changed. Parameter values are presented in table 1 and details are provided in the online supplementary appendix. infect his uninfected sexual partner over the course of ﬁrst-line treatment. We examined only the special case where a partner- ship is maintained over the entire duration of ﬁrst-line treatment and did not include the effect of STIs on the chance of HIV transmission. In most analyses, the functional relationship between plasma viral load and the chance of transmission in each unprotected sex act was based on a Hill function ﬁtted to observational data on HIV transmission in Zambia by Fraser et al.20 This function is supported by recent review of trans- mission rates15 16 and is denoted the ‘Fraser et al’ assumption. The function was rescaled to match the observed approximate transmission risk for each sex act for MSM (w0.01 for men with log-viral loads of w4.5 log-copies)13 (supplementary ﬁgure S2). An alternative assumption for the relationship (linear trend in log-risk and log-viral load21: see ﬁgure S2) was used as well in sensitivity analyses: this is denoted the ‘Wilson et al’ assump- tion. We assumed that there were 100 sex acts a year in the partnership and that the efﬁcacy of condoms in reducing transmission is 95%. In uncertainty analyses, the model assumption for which there was least directly relevant data was varied independently in a Monte Carlo analysis: speciﬁcally, the frequency of sex acts per years (uniform between 50 and 150), the efﬁcacy of condoms when used (uniform between 85% and 100%) and chance of transmission per sex act without treatment (uniform from 0.0075 to 0.0125). A combined 95% uncertainty interval (the range between the 2.5th and 97.5th centiles of the resultant distribution) was calculated. In the model, reﬂecting clinical guidelines,22 patients with undetectable viral loads are monitored every 4 months. When viral load is detectable, the patient returns for another appointment after 8 weeks and the treatment regimen is then changed if retesting conﬁrms the ﬁnding. Various scenarios for condom use in partnerships were considered: (i) never using condoms; (ii) using condoms in 30% of sex acts24; (iii) not using condoms if viral load was un- detectable at the last measurement in the past 6 months; and, (iv) always using condoms. Scenario (iii) corresponds to the way that the EKAF statement has been interpreted and we consid- ered two variants whereby the decision not to use condoms is based on the last measurement in the past 3 months (instead of 6 months) or the last viral load measurement ever taken (ie, irrespective of time). RESULTS We found that men receiving treatment pose a substantial risk of HIV transmission (22% (9e37% in uncertainty analysis)) to their partners if they do not use condoms (ﬁgure 2), and the relationship between viral load and transmission is as described by Fraser et al.20 This risk is generated in three ways: (i) treat- ment is not sufﬁcient to suppress viral load, so transmission can occur even if the regimen is quickly changed; (ii) the level of virus can rebound quickly and reach high levels before detection and change of regimen; (iii) even with suppressed viral loads, the risk of transmission is not zero, so that over the many sex acts during treatment, the cumulative chance of transmission becomes non-negligible. Using condoms 30% of the time reduces the chance of transmission but only marginally (to 17% (7e29% in Natural history parameters for HIV infection receiving ﬁrst-line treatment (Source: ATHENA cohort data17) Refer to the technical appendix for Table 1 details Parameter 18 Log10 viral load at treatment initiation (normal distribution) Fraction achieving suppression* Fraction with good adherencey Waiting time until viral suppression, if suppression and good adherence (exponential distribution) Waiting time until viral suppression, if suppression and not good adherence (exponential distribution) Waiting time (months) until viral rebound, if good adherence (double Weibull distribution), assuming shortened (s) survival times (used unless otherwise stated) or extended (e) survival. Waiting time until viral rebound, if not good adherence (Weibull distribution) Rate of increase in log10 viral load on rebound, if good adherencez Rate of increase in log10 viral load on rebound, if not good adherencez Maximum survival time with non-suppressed viral load Log10 viral load if no suppression (normal distribution) Value Mean 5.1 Variance 0.40 0.70 0.94 Median 5.38 Median 5.92 Shape1 1.14 (e) 10.23 (s) Scale1 456.65 (e) 153.25 (s) Shape2 1.92 (e) 1.25 (s) Scale2 20.70 (e) 41.58 (s) Weighting 0.91 (e) 0.77 (s) Shape1 1.14 Scale1 132.86 Rate 0.07 (se¼0.002) Rate 0.16 (se¼0.01) Max 1 Mean 3.80 Variance 0.84 Log copies per microlitre Unit Fraction Fraction Months Months Months Months Log10 copies per microlitre per month Log10 copies per microlitre per month Years Log copies per microlitre Sex Transm Infect 2011;87:17e21. doi:10.1136/sti.2010.042622 *Suppression is deﬁned as at least two consecutive viral load measurements <500 HIV RNA copies per millilitre. yAdherence is classiﬁed as good or poor based on the measurement of plasma drug levels. zAt all times in the simulation, viral load is limited to less than or equal to the 95th centile of viral loads at treatment initiation in the ATHENA data (equal to six log-copies).