Incidence rates and risk behavior

At the beginning of the first study period we analyzed, 534 study participants were uninfected (). Over the four study visits, we observed little change in the number of overall receptive anal intercourse partnerships reported for the previous 12 months, but a significant increase in the number of unprotected partnerships reported for the 12 months preceding each study visit (

*P* < 0.001, GEE marginal Poisson model [

17]). Despite the increasing trend in self-reported unsafe sex, no increase in seroconversion was seen (

*P* = 0.33); indeed, lower incidence rates were seen in the two post-HAART study periods. The increase in reported risk behavior coincided with a stable or declining incidence during the study period, suggesting a decline in infectivity.

| **Table 1**Summary statistics for the four study periods. |

To assess this possibility, we first used the risk model given in the

Appendix [

10–

14] to test the hypothesis that the transmission probability per partnership was the same in the post-HAART study periods as it was in the pre-HAART study periods. We estimated the transmission probability per-partnership to be 0.0276 pre-HAART, and 0.011 post-HAART, and rejected the hypothesis that the transmission probability was constant (

*P* = 0.028). Having found this evidence of a decline in the per-partnership transmission probability, we next determined which of its two components (infectivity or prevalence) was responsible for the decline. Although precise prevalence estimates are not available, we showed that unrealistic declines in prevalence would be required to explain the observed decline in the transmission probability. We assumed plausible prevalence scenarios, and for each scenario, we estimated the infectivity and tested the hypothesis that the infectivity was the same before and after HAART was introduced. First, assuming a constant prevalence of 23% among the partners of the men (the cohort prevalence of HIV among men reporting receptive anal intercourse at the 1992 baseline of the study [

9]), we found that the per-partnership infectivities (with asymptotic standard errors in parentheses) at each study visit were 0.118 (0.042) and 0.124 (0.049) for the pre-HAART study periods, and 0.055 (0.032) and 0.044 (0.020) for the two post-HAART study periods. Combining the two pre- and the two post-HAART time periods into two estimates to increase statistical power, we obtained an estimate of 0.120 (0.034) per partnership in the first two periods, and 0.048 (0.017) per partnership in the last two periods, for an overall 60.4% decline in HIV infectivity (

*P* = 0.028). Finally, a goodness-of-fit test yielded no evidence of insufficient fit (

*P* = 0.63; see

Appendix).

Although the above analyses assumed a constant prevalence, in fact HIV prevalence is believed to have been declining among homosexual men prior to HAART (because HIV deaths were continuing to outweigh recent infections [

18]), but to have been increasing after the introduction of HAART due to substantial declines in AIDS mortality [

19]. Assuming increased prevalence after the introduction of HAART yields stronger evidence in favor of an infectivity decline; if, for example, we assume that after the introduction of HAART, the prevalence increased 17.2% (relative to the pre-HAART value), then the infectivity decline would be significant at the 0.01 level. If, however, we assume a decrease in prevalence, then the reduced incidence shown earlier () would be partially explained by the assumption of reduced prevalence among partners; assuming that the prevalence decreased more than 9.3% relative to baseline yields

*P*-values greater than 0.05 for the test of constant infectivity.

To systematically examine infectivity estimates over a wide range of possible prevalence patterns, we chose a Latin Hypercube Sample [

20–

22] of 10 000 random prevalence patterns, with the prevalence at each study visit uniformly distributed over the plausible (though arbitrary) range 0.1 to 0.3 (other plausible choices yield similar results). For each random prevalence scenario, we performed the hypothesis test of constant infectivity. The

*P*-value was less than 0.1 in all of the 4986 scenarios in which the average prevalence was greater post-HAART than pre-HAART; the

*P*-value exceeded 0.05 only in 17 unrealistic scenarios for which the prevalence was very high at visits one and three and very low for visits two and four. Finally, infectivity estimates for representative prevalence patterns are shown in . Thus, for plausible assumed patterns of the prevalence over the 6 years of follow-up, infectivity decline is a robust finding.

| **Table 2**Estimated infectivity of HIV under different assumptions regarding age-class specific prevalence and prevalence over time. |

In addition to probable variations in time, HIV prevalence varies with age among homosexual men in San Francisco [

23–

25]. As in the first three study periods, our study subjects were asked how many of their total partners were under 30 years of age, we adjusted for the fraction of partners under 30 years of age as described in the

Appendix. The Urban Men’s Health Study, a random-digit-dialing survey of homosexual men in San Francisco conducted between 1996 and 1998 [

25], yielded 6.0% of men under 30 years of age reported being HIV-infected, and 22.4% of men 30 and older reported being HIV-infected (L. Pollack, pers. comm.; random-digit-dialing samples should include sexually inactive men at lower risk for HIV infection than the partners of the men in our study.) As before, we chose a Latin Hypercube Sample of 10 000 prevalence scenarios, and for each, performed the hypothesis test of constant infectivity; for each study period, the prevalences among men under 30 and among men 30 years old and over were chosen from a uniform distribution between 0.1 and 0.3. Only 14 unrealistic scenarios (with high prevalence at periods 1 and 3 and low prevalence at periods 2 and 4 among men 30 years old and over) yielded a

*P*-value greater than 0.05 with an increasing prevalence. Finally, selected estimates for various age- and period-specific scenarios are also included in . Thus, after adjusting for self-reported age of the partners, we continue to conclude that the infectivity declined after the introduction of HAART.

We compared the characteristics of those individuals who remained in the study with those who were never known to seroconvert, but who were lost to follow-up. We found no significant differences between dropouts and those remaining for age, education, number of male sexual partners, number of partners with whom anal or oral sex was reported, recreational drug use, and self-reported sexually transmitted diseases. Drop-outs were more likely to report being bisexual, a difference captured by including the number of receptive anal intercourse partners in our models.

To quantify the potential importance of bias due to frailty selection (the differential removal of individuals with a higher per-partnership infectivity), we conducted a Monte Carlo sensitivity analysis [

26]. We assumed that the infectivity was constant for each individual, but differed between individuals, with some individuals having a per-partnership risk of zero and others having a higher per-partnership risk. We kept the overall average per-partnership infectivity (the fraction of individuals in the high per-partnership risk group times their per-partnership risk) equal to 0.1. We repeatedly simulated HIV infection given reported risk behaviors and different sizes of the high per-partnership risk group, and determined the probability of rejecting the null hypothesis of constant decline. From a logistic model fit to these simulation results, we estimated that to have a 20% chance of finding an apparent infectivity decline, we would have needed approximately 15% of the population to be in the high per-partnership risk group (and their per-partnership infectivity would be approximately 0.69 ≈ 0.1/0.15); to have a 10% chance of finding an apparent infectivity decline, we would have needed approximately 36% of the population in the high per-partnership risk group (and their per-partnership infectivity would be approximately 0.28 ≈ 0.1/0.36). Less extreme distributions of heterogeneity of risk yield small probabilities of finding an apparent infectivity decline; for instance, assuming a risk of 0.05 per partnership in half of the individuals and a risk of 0.25 per partnership in the other half yielded 6.3% out of 1000 simulations in which a false infectivity decline was observed – scarcely different from the 5% we would expect given the assumed 5% type I error rate of the test.

As partners of high-risk men may themselves be at high risk, we repeated the estimation of the infectivity decline assuming that individuals with five or more unprotected partnerships have 50% higher prevalence of infection among their partners than individuals with fewer than five partners. Under this assumption, the infectivity decline remains statistically significant (*P* = 0.019); the estimated per-partnership infectivity was 0.107 for the first two study periods and 0.040 for the last two periods.

Finally, we also obtained an estimate of the degree of protection afforded by (reported) consistent condom usage (see

Appendix). Under the assumption of 23% prevalence, HIV infectivity in partnerships for which condoms were always reportedly used was 5.4% of the infectivity for those partnerships not protected by condoms (95% bootstrap confidence interval [

27], 0.0 to 0.16). For the first twelve scenarios shown in , this estimate is 5.4%, and this estimate is 5.5% for the remaining seven.