Determinants of Per-Coital-Act HIV-1 Infectivity Among African HIV-1-Serodiscordant Couples
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- "the findings only apply to heterosexual couples, and not men who have sex with men, a group that is likely to have a much higher transmission rate"
J Infect Dis. (Jan 2012)
"unadjusted per-act risks of unprotected MTF and FTM transmission of 0.0019 and 0.001 (1 in 900 apprx).....observed differences in MTF and FTM infectivity appear to be largely driven by measurable differences in plasma viral load of the HIV-1-infected partner......Our results underscore the importance of >antiretroviral therapy and, possibly, treatment of coinfections [19, 20], to reduce plasma HIV-1 viral load in HIV-1-infected partners, and condom promotion, male circumcision, and treatment of symptomatic STIs for HIV-1-uninfected partners as potential interventions to reduce HIV-1 transmission......Each log10 increase in plasma HIV-1 RNA increases the per-act risk of transmission by a factor of 2.89 so that the estimated per act risk of transmission without a condom at 3 (1,000 c/ml), 4 (10,000 c/ml), 5 (100,000c/ml), and 6 logs is 0.00028, 0.00082, 0.0024, and 0.0068, respectively."
"analyzed data from a prospective study of African HIV-1-serodiscordant couple.....In this prospective study of 3297 African HIV-1 discordant couples, we found unadjusted per-act risks of unprotected MTF and FTM transmission of 0.0019 and 0.001 (1 in 900 apprx)......after adjustment for plasma HIV-1 RNA levels and the HIV-1-uninfected partner's HSV-2 serostatus and age, the relative risk of MTF versus FTM transmission was almost 1.0, suggesting that much of the gender difference in infectivity could be explained by higher plasma HIV-1 RNA in HIV-1-infected men than women and other gender-related differences.....the findings only apply to heterosexual couples, and not men who have sex with men, a group that is likely to have a much higher transmission rate..... we found a 2.14-fold increased risk of infection associated with HSV-2 positivity in the HIV-1-uninfected partnerSeveral gender-specific factors also significantly influenced the per-act risk of HIV-1 transmission, including circumcision status of the HIV-1-uninfected male partner (associated with reduced susceptibility), T. vaginalis infection in the HIV-1-uninfected female partner at enrollment (associated with increased susceptibility), and cervicitis or vaginitis in the female HIV-1-uninfected partner at the HIV-seroconversion visit (also associated with increased susceptibility). However, because symptoms of cervicitis or vaginitis and diagnosis of HIV-1 infection occurred in the same interval, the relative timing of cervicitis or vaginitis with HIV-1 seroconversion could not be ascertained.....condom use decreased HIV-1 infectivity by 78%. couples in this study reported that 93% of acts were protected and 100% condom use was reported in 82% of the intervals. Nonetheless, 56 transmissions occurred in intervals with 100% reported condom use, suggesting that condom use was overreported and that the estimated effect of condom use may be attenuated compared with the true effect.
James P. Hughes,1,5 Jared M. Baeten,2,3,9 Jairam R. Lingappa,2,3,4 Amalia S. Magaret,4,10 Anna Wald,2,9 Guy de Bruyn,6
James Kiarie,7 Mubiana Inambao,8 William Kilembe,8 Carey Farquhar,2,9 Connie Celum,2,3,9 and the Partners in
Prevention HSV/HIV Transmission Study Team
1Department of Biostatistics, 2Department of Medicine, 3Department of Global Health, and 4Department of Pediatrics, University of Washington,
Seattle; 5Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, Seattle, Washington; 6Perinatal HIV Research Unit,
University of Witwatersrand, Johannesburg, Republic of South Africa; 7Department of Obstetrics and Gynecology, University of Nairobi and Kenyatta
National Hospital, Kenya; 8Rwanda-Zambia HIV Research Group (RZHRG), Ndola, Zambia; 9Department of Epidemiology and 10Department of
Laboratory Medicine, University of Washington, Seattle
(See the editorial commentary by Gray and Wawer on pages 351-2.)
Background. Knowledge of factors that affect per-act infectivity of human immunodeficiency virus type 1 (HIV-1) is important for designing HIV-1 prevention interventions and for the mathematical modeling of the spread of HIV-1.
Methods. We analyzed data from a prospective study of African HIV-1-serodiscordant couples. We assessed transmissions for linkage within the study partnership, based on HIV-1 sequencing. The primary exposure measure was the HIV-1-seropositive partners' reports of number of sex acts and condom use with their study partner.
Results. Of 3297 couples experiencing 86 linked HIV-1 transmissions, the unadjusted per-act risks of unprotected male-to-female (MTF) and female-to-male (FTM) transmission were 0.0019 (95% confidence interval [CI], .0010-.0037) and 0.0010 (95% CI, .00060-.0017), respectively. After adjusting for plasma HIV-1 RNA of the HIV-1-infected partner and herpes simplex virus type 2 serostatus and age of the HIV-1-uninfected partner, we calculated the relative risk (RR) for MTF versus FTM transmission to be 1.03 (P = .93). Each log10 increase in plasma HIV-1 RNA increased the per-act risk of transmission by 2.9-fold (95% CI, 2.2-3.8). Self-reported condom use reduced the per-act risk by 78% (RR = 0.22 [95% CI, .11-.42]).
Conclusions. Modifiable risk factors for HIV-1 transmission were plasma HIV-1 RNA level and condom use, and, in HIV-1-uninfected partners, herpes simplex virus 2 infection, genital ulcers, Trichomonas vaginalis, vaginitis or cervicitis, and male circumcision.
Human immunodeficiency virus type 1 (HIV-1) infectivity is defined as the probability of transmission per coital act with an infected partner. Knowledge of HIV-1 infectivity and factors that affect it are important for patient counseling, design of prevention interventions, and the mathematical modeling of the spread of disease. Infectivity can be estimated from prospective HIV-1 serodiscordant partner studies, although such studies are technically challenging to conduct . In particular, obtaining accurate counts of sex acts during the interval between HIV-1 tests is difficult, especially if the interval is long. In addition, failure to identify and eliminate transmissions from outside the study partnership may lead to inflated estimates of infectivity and misclassification of risk factors. Measuring cofactors of transmission risk, particularly those that change over time (eg, sexual behavior or plasma HIV-1 RNA concentration), is also difficult, and assessing the effect of multiple cofactors on transmission requires large sample sizes.
A recent meta-analysis  reviewed 26 studies that estimated HIV-1 infectivity. The pooled estimates of male-to-female (MTF) and female-to-male (FTM) transmission in low-income settings were 0.0030 and 0.0038 per act, respectively. However, in 14 studies that followed serodiscordant couples, the median number of couples was only 73, and only 4 of these studies [3-6] included >200 couples. The ability of most studies to examine cofactors of transmission was, therefore, limited. Last, only a few studies [4, 6, 7] have evaluated the role of plasma HIV-1 RNA on infectivity, and only 2 studies [4, 6] have used molecular confirmation to determine linkage of transmissions .
In this study, we analyze data from a longitudinal cohort of >3400 African HIV-1-serodiscordant heterosexual couples. We estimate the infectivity of HIV-1 and evaluate factors that affect infectivity. Importantly, and unique to this study, these data include repeated measurements of plasma HIV-1 RNA in the HIV-1-infected partner and molecular confirmation to determine linkage of all transmissions.
In this prospective study of 3297 African HIV-1 discordant couples, we found unadjusted per-act risks of unprotected MTF and FTM transmission of 0.0019 and 0.001, respectively. However, after adjustment for plasma HIV-1 RNA levels and the HIV-1-uninfected partner's HSV-2 serostatus and age, the relative risk of MTF versus FTM transmission was almost 1.0, suggesting that much of the gender difference in infectivity could be explained by higher plasma HIV-1 RNA in HIV-1-infected men than women and other gender-related differences. Our unadjusted per-act risks are somewhat lower than the meta-analytic results of Boily et al for low-income settings , similar to those reported by Wawer et al  (when MTF and FTM transmissions are combined), and higher than the metaestimate for Africa reported by Powers et al . Similarly to the approach of Wawer et al , we restricted our analysis to molecularly confirmed transmissions. Several gender-specific factors also significantly influenced the per-act risk of HIV-1 transmission, including circumcision status of the HIV-1-uninfected male partner (associated with reduced susceptibility), T. vaginalis infection in the HIV-1-uninfected female partner at enrollment (associated with increased susceptibility), and cervicitis or vaginitis in the female HIV-1-uninfected partner at the HIV-seroconversion visit (also associated with increased susceptibility). However, because symptoms of cervicitis or vaginitis and diagnosis of HIV-1 infection occurred in the same interval, the relative timing of cervicitis or vaginitis with HIV-1 seroconversion could not be ascertained. After adjustment for plasma HIV-1 RNA levels, antiretroviral agent use in the HIV-1-infected partner did not significantly predict transmission.
This study is the first to estimate HIV-1 infectivity after adjusting for time-varying plasma HIV-1 RNA. Over a relatively broad range of plasma HIV-1 RNA levels (2-6 log10 copies/mL), we found that the relationship between log infectivity and log10 plasma HIV-1 RNA level was approximately linear and that each 10-fold increase in plasma HIV-1 RNA level was associated with a 2.9-fold increase in per-act transmission risk, underscoring the importance of a high plasma HIV-1 RNA level to HIV-1 transmission risk. We found no significant evidence of a "saturation effect" (a plasma HIV-1 RNA level above which infectivity does not increase), although only 1% of follow-up intervals and 3 transmissions occurred during periods with plasma HIV-1 RNA level of ≥6.0 log10 copies/mL.
We found that reported condom use decreased HIV-1 infectivity by 78%. This is consistent with a previous meta-analysis that reported an 80% protective effect of condoms . Although the protective effect of condoms is expected, our results are unique because condom use was measured and analyzed on a per-act basis. In contrast to previous studies that reported low rates of condom use (eg, in Rakai ), <20% of couples reported occasional condom use and none reported consistent condom use), couples in this study reported that 93% of acts were protected and 100% condom use was reported in 82% of the intervals. Nonetheless, 56 transmissions occurred in intervals with 100% reported condom use, suggesting that condom use was overreported and that the estimated effect of condom use may be attenuated compared with the true effect.
Previous studies have highlighted the increased risk of transmission associated with HSV-2 and GUD. In a meta-analysis, the presence or history of GUD in either partner was associated with a 5.3-fold increased risk of HIV-1 transmission . We did not find an elevated risk of transmission associated with GUD by exam or self-report in the HIV-1/HSV-2 dually infected partner. However, we found a 2.14-fold increased risk of infection associated with HSV-2 positivity in the HIV-1-uninfected partner, which is similar to the 2- to 3-fold increased risk of HIV-1 acquisition associated with prevalent HSV-2 infection from meta-analyses [15, 16]. Also, similar to Powers et al , we found an independent 2.65-fold increased risk of infection associated with GUD by self-report or exam in HIV-1-uninfected partners.
The strengths of this study include the large number of couples, molecular confirmation of HIV-1 transmission between the study partners, repeated plasma HIV-1 RNA measurements over follow-up, and relatively short intervals of 3 months between HIV-1 tests. The study also had limitations. Because only couples that had not previously transmitted HIV-1 were enrolled in the study, if transmission risk varies significantly between couples, the highest-risk individuals would be expected to transmit early and never enter the cohort; such a "survivorship bias" could lead to an underestimate of infectivity. Supporting this possibility is the significant decline in infectivity with age and the evidence of additional unexplained heterogeneity in infectivity seen in the analysis of model fit. Nonetheless, no significant decline in infectivity was observed over follow-up in these data (after adjustment for covariates), and partnership duration was not a significant predictor of infectivity in our multivariate model. Enrolling stable discordant couples also meant that the likelihood of enrolling acute or recently infected partners was low, limiting our ability to assess the impact of HIV-1 stage on infectivity.
An important limitation of any infectivity study is the difficulty in measuring the number of sex acts in the interval between HIV-1 tests. Imprecision in act counts may arise from a number of sources.A 2- to 3-week lag between HIV-1 infection and detection may lead to imprecision in act counts over the relevant risk period. Also, we analyzed the number of acts reported by the HIV-1-infected partner, whose visit intervals did not always correspond precisely to the intervals between the HIV-1 tests of the HIV-1-uninfected partner. Finally, the observation that HIV transmissions occurred during intervals when the HIV-1-infected partner reported only protected sex indicates that condom use was overreported. Nonetheless, a simulation study (see Appendix; supplementary data) suggests that unbiased (with respect to condom use) misreporting of acts does not lead to significant bias in estimates of infectivity or the RR of other covariates and overreporting of condom use and underreporting of nonuse does bias estimates of infectivity (ie, the RR of condom use would be attenuated toward 1.0) but would have little effect on the RR of other covariates.
In summary, observed differences in MTF and FTM infectivity appear to be largely driven by measurable differences in plasma viral load of the HIV-1-infected partner, condom use, and HSV-2 status and age of the HIV-1-uninfected partner. Notably, after adjustment for plasma HIV-1 RNA, HSV-2 status, age, and condom use, we found no significant difference between MTF and FTM infectivity. This strong dependence of HIV-1 infectivity on cofactors suggests that the relationship of (unadjusted) MTF and FTM infectivity may vary substantially across different settings with different distributions of these key cofactors. HIV-1 infectivity increased log-linearly with log10 plasma HIV-1 RNA across the range of plasma HIV-1 RNA levels in this cohort (2-6 log10). Our results underscore the importance of >antiretroviral therapy [17, 18], and, possibly, treatment of coinfections [19, 20], to reduce plasma HIV-1 viral load in HIV-1-infected partners, and condom promotion, male circumcision, and treatment of symptomatic STIs for HIV-1-uninfected partners as potential interventions to reduce HIV-1 transmission.
At enrollment, HIV-1-infected partners were primarily female (67%) and their median age was 32 years (interquartile range [IQR], 26-38 years); 34% of HIV-1-infected males were circumcised (Table 1). The median plasma HIV-1 RNA concentration at enrollment was 3.91 log10 copies/mL (IQR, 3.16-4.53 log10 copies/mL). HIV-1-uninfected partners were slightly older (median, 33 [IQR, 28-40]), 68% were HSV-2 seropositive, and 55% of men were circumcised. HIV-1-infected partners had genital herpes recurrences (genital ulcer disease [GUD]) on exam or self-reported symptoms in the prior interval) at 9.2% of quarterly follow-up visits and HIV-1-uninfected partners had GUD on exam or by self-report at 5.2% of quarterly follow-up visits.
The median number of unprotected and protected acts over the preceding 30 days, as reported by the HIV-1-infected partners at enrollment, was 0 (IQR, 0-1) and 3 (IQR, 1-5), respectively. Over follow-up, the median rate of unprotected and protected acts per 30 days, as reported by the HIV-1-infected partners, was 0 (IQR, 0-0) and 3.3 (IQR, 1.8-5.9), respectively, and 93% of sex acts were reported as protected. The median total number of sex acts per 30 days declined steadily from 4.0 at enrollment to 2.5 by month 24.
Overall, 86 linked transmission events were observed during follow-up. Table 2 shows the relationship between total number of reported acts within a testing interval and the HIV-1 test result at the end of that interval. There were 3 transmissions (3.5%) in which the HIV-1-infected partner reported 0 acts in the interval immediately prior to a linked infection (although in 1 of these cases, the report only covered a portion of the interval). In none of these cases did the HIV-1-uninfected partner report sex acts with anyone other than their study partner. These 3 transmissions cannot be included in estimates of infectivity as they lead to an infinite likelihood in the statistical analysis.
In a model that included only condom use and gender, the estimated risks of unprotected MTF and FTM transmission were 0.0019 (95% CI, .0010-.0037) and 0.0010 (95% CI, .00060-.0017), respectively (relative risk [RR] = 1.95; P = .003). However, after adjustment for plasma HIV-1 RNA and HSV-2 status and age of the uninfected partner (all of which differed significantly depending on the gender of the HIV-1-infected partner), the RR for MTF transmission was attenuated to 1.03 (P = .93), suggesting that the higher risk of MTF transmission was largely due to higher viral loads in men (over follow-up, mean viral load measurement in men = 4.1 log10 copies/mL; in women = 3.8 log10 copies/mL) and other sources of confounding.
Log10 plasma HIV-1 RNA was entered linearly into model (2). A more complex functional form using cubic splines did not significantly improve the fit (P = .2, comparing the linear model to the spline model). Figure 1 shows the relationship between infectivity and log10 plasma HIV-1 RNA in a model that includes plasma HIV-1 RNA and reported condom use only. Each log10 increase in plasma HIV-1 RNA increases the per-act risk of transmission by a factor of 2.89 so that the estimated per act risk of transmission without a condom at 3, 4, 5, and 6 logs is 0.00028, 0.00082, 0.0024, and 0.0068, respectively.
Table 3 shows the RR, overall and by gender, for characteristics of the HIV-1-infected and HIV-1-uninfected partner in univariate analyses. In a multivariate model (Table 4), plasma HIV-1 RNA and condom use reported by the HIV-1-infected partner and age, HSV-2 serostatus, GUD by exam or self-report, T. vaginalis (at enrollment), cervicitis or vaginitis (during follow-up), and male circumcision status of the HIV-1-uninfected partner remained significant. Circumcision in male HIV-1-uninfected partners was associated with significantly lower infectivity (RR, 0.53 [95% CI, .29-.96]), and infectivity also declined as the age of the HIV-1-uninfected partner increased (RR, 0.82 per 5-year increase [95% CI, .71-.94]). We found similar results when the age of the HIV-1-infected partner was substituted for that of the uninfected partner in the model. Condom use reduced infectivity by 78% (RR, 0.22 [95% CI, .11-.42]). However, 56 linked transmissions occurred in intervals in which all acts were reported to be protected. The protective effects of reported condom use was similar regardless of whether the HIV-1-infected partner was male (RR, 0.14) or female (RR, 0.29) (P value for gender by condom interaction = 0.29). HSV-2 seropositivity (RR, 2.14; [95% CI, 1.18-3.88]), GUD by exam or self-report (RR, 2.65 [95% CI, 1.35-5.19]), T. vaginalis infection at enrollment (RR, 2.57 [95% CI, 1.42-4.65]) and a clinical diagnosis of vaginitis or cervicitis during follow-up (RR, 3.63 [95% CI, 1.47-8.92]) in the HIV-1-uninfected partner were independently associated with an elevated per-act risk of transmission. Characteristics of the HIV-1-infected partner (including recurrent genital herpes by exam or self-report, T. vaginalis positivity, antiretroviral agent use, and circumcision status), presence of other curable STI (C. trachomatis, T. pallidum) in either partner, urethritis in male partners, partnership duration, and time on study were not significant in the multivariate analysis (P > .20).
We also found evidence of additional unexplained heterogeneity in infectivity-the addition of a random effect for infectivity significantly improved the fit (P = .005; data not shown). This suggests that there are unmeasured viral, host, or behavioral factors that induce additional variation in infectivity among couples; inaccurate reporting of the number of acts and condom use may also contribute to unexplained heterogeneity.
We used data from the Partners in Prevention Herpes Simplex Virus (HSV)/Human Immunodeficiency Virus (HIV) Transmission Study, a randomized clinical trial of HSV-2 suppressive therapy for prevention of HIV-1 transmission (ClinicalTrials.gov NCT00194519). Stable, HIV-1-serodiscordant couples in which the HIV-positive partner was also infected with HSV-2 were enrolled at 14 sites in eastern and southern Africa and followed for ≤24 months. The primary objective of the trial was to evaluate the efficacy of daily acyclovir HSV-2-suppressive therapy for preventing HIV-1 transmission. No significant difference in transmission risk was seen between the intervention and control groups. The design, methods, and primary outcomes have been described previously [9, 10].
Among the 3408 enrolled couples, confirmatory testing at the end of the trial found that 27 partners initially categorized as "HIV-1 infected" did not meet the HIV-1 (n = 3) or HSV-2 (n = 24) serologic eligibility criteria. An additional 24 couples were excluded from this analysis after the HIV-1-uninfected partner was determined to have been HIV-1 positive at enrollment by retrospective polymerase chain reaction (PCR) testing. Finally, 60 couples provided no postenrollment HIV-1 test data. Thus, 3297 couples were included in this analysis.
At enrollment, demographic data were collected on each partner, participants were tested for sexually transmitted infections (STIs), men were examined to determine circumcision status, and the HIV-1-uninfected partner was tested to determine HSV-2 serostatus. At quarterly visits, each participant underwent a genital examination and the uninfected partner was tested for HIV-1 seroconversion. Participants received comprehensive HIV-1 prevention measures, including HIV-1 risk-reduction counseling (both individually and as a couple), quarterly syndromic STI treatment, and free condoms.
Plasma HIV-1 RNA in the infected partner was measured at enrollment, 3, 6, and 12 months, and study exit (typically, 24 months). We used the most recent viral load prior to or concurrent with each HIV-1 test as a time-varying covariate in our analyses, except that prior viral loads were not carried forward if antiretroviral therapy was started.
Information on the number of sex acts during follow-up comes from 2 sources: HIV-1-infected partners were interviewed monthly, and they provided information on the numbers of acts with the study partner, with and without a condom, since their last visit (by protocol, 1 month prior). The total reported number of sex acts with the study partner between HIV-1 tests (by protocol, 3 months)-our primary exposure measure-was obtained by summing data over all the monthly visits of the HIV-1-infected partner in the testing interval. Because the 2 partners' visits did not always coincide exactly, the reported number of acts in the testing interval was scaled by a factor equal to the length of the testing interval divided by the number of days covered by the HIV-1-infected partner's reports. For example, if the interval between HIV-1 tests was 90 days, but the HIV-1-infected partner's behavioral data covered only 60 days in that interval, then the reported number of acts was increased by a factor of 90 divided by 60. A secondary source of information was provided by the HIV-1-uninfected partners who were asked about their number of acts (with study partner, with or without condom) over the month preceding each HIV-1 test. These data were not used directly in the analyses but were used to help evaluate the impact of mismeasurement of the number of acts (see Appendix; supplementary data). Because HIV-1 serostatus was not available from nonstudy partners, acts with these partners were not included in any analyses.
The protocol was approved by the University of Washington Human Subjects Review Committee and ethical review committees at local and collaborating organizations. Participants provided written informed consent.
During follow-up, the HIV-1-uninfected partners were tested quarterly by HIV-1 rapid tests; positive results were confirmed by Western blotting. After the study was complete, preseroconversion plasma samples were tested for HIV-1 RNA by PCR to more precisely determine the timing of infection; the time of HIV-1 infection was defined as the earlier of positive serology or PCR. Plasma HIV-1 RNA was quantified using the COBAS TaqMan real-time HIV-1 RNA assay, version 1.0 (Roche Diagnostics).
Each confirmed HIV-1 transmission was classified as "linked" (transmission between study partners) or "unlinked" (HIV-1 acquisition from a nonstudy partner) on the basis of sequencing of plasma samples from the source and infected partner for the C2-V3-C3 regions of env and the p17/p24 regions of gag, phylogenetic analysis, and posterior probability of linkage using pairwise nucleotide distances between sequences . Only linked transmissions are included in this analysis; couples with unlinked transmissions were censored from the analysis at the time of HIV-1 infection.
Serologic testing for HSV-2 and nucleic acid amplification testing for STIs (Chlamydia trachomatis, Neisseria gonorrhoeae, and Trichomonas vaginalis) were done at study enrollment, as previously described . Syphilis serology was performed at enrollment using rapid plasma reagin with confirmation by the microhemagglutination test for Treponema pallidum at sites with that capacity. During follow-up, genital ulcers and other STI symptoms (eg, urethritis or vaginal discharge) were evaluated by history in the prior 30 days and on quarterly exams.
Jewell and Shiboski  relate per-act infectivity (λ), number of acts over the interval between HIV-1 tests (n), and covariates (X) to the probability of HIV-1 transmission from the infected partner to the uninfected partner, p(X;n), using the model:
(1)For small values of λ, ß may be interpreted as the log relative risk of infectivity for each unit change in X. We modified model (1) to
(2)where n0 acts are unprotected and n1 acts are protected, λ0 and λ1 are the infectivities without and with a condom, respectively, and ß represents the log relative risks. We used maximum likelihood methods (Stata procedure ml) to estimate the parameters of model (2), test hypotheses, and form confidence intervals.
For comparability to previous studies, we fit a model that included only gender and condom use (yes/no, for each act) to estimate the per-act risk of unprotected MTF and FTM transmission. To assess the impact of other covariates on infectivity, we first fit a base model that included plasma HIV-1 RNA concentration and condom use. Randomization group, demographic factors (gender, age, partnership duration at enrollment), time on study, STIs (by lab test at baseline and syndromic diagnoses over follow-up), HSV-2 in the HIV-1-uninfected partner, and circumcision status of the male partner were added to the base model individually, with separate terms for the HIV-1-infected and the HIV-1-uninfected partner, where appropriate. We included in a multivariate model all covariates that were significant at P < .1 when added to the base model, and we used backward elimination (eliminating terms that were not significant at the P = .05 level) to develop a final model. All reported P values are 2-sided. Analyses were performed using Stata 11 software .
We investigated heterogeneity in λ (beyond that which can be explained by the covariates X) by including a random intercept in the linear predictor (Xß ) in model (1) .