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Modelling the effect of combination antiretroviral treatments on HIV incidence

Law, Matthew G.a; Prestage, Garretta; Grulich, Andrewa; Van de Ven, Paulb; Kippax, Susanb

EPIDEMIOLOGY & SOCIAL
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SDC

Objective To assess the competing effects on HIV incidence in homosexual men of the decreased infectiousness of men with HIV receiving effective combination antiretroviral treatments and homosexual men engaging in unprotected anal intercourse with increased numbers of partners (levels of unsafe sex).

Methods A mathematical model of HIV transmission in homosexual men was developed, based on the HIV epidemic in Australia in 1996, when effective antiretroviral treatments first became widely available. Uncertainties in parameters were modelled using 1000 simulations. The effect of treatments on decreasing infectiousness was randomly sampled with a median 10-fold decrease in infectiousness (range 100-fold to no decrease). Levels of unsafe sex were randomly sampled with a median 50% increase in unsafe sex (range 100% to no increase). The percentage change in HIV incidence after one year was obtained by comparison with a null model in which there was no decrease in infectiousness as a result of treatment and no change in unsafe sex.

Results Results of the models suggested that whereas increased levels of unsafe sex were linearly associated with increases in HIV incidence, decreases in infectiousness because of treatments were non-linearly associated with decreases in HIV incidence. An assessment of the competing effects suggested that decreases in infectiousness of two-, five-, and 10-fold would be counterbalanced by increases in unsafe sex of approximately 40, 60 and 70%, respectively.

Conclusion These models suggest that apparently large decreases in infectiousness as a result of treatment could be counterbalanced in terms of new HIV infections by much more modest increases in unsafe sex.

From the aNational Centre in HIV Epidemiology and Clinical Research, and bNational Centre in HIV Social Research, University of New South Wales, Darlinghurst, NSW 2010, Australia.

Received: 18 August 2000;

revised: 24 November 2000; accepted: 8 February 2001.

Sponsorship: The National Centre in HIV Epidemiology and Clinical Research and the National Centre in HIV Social Research are funded by the Commonwealth Department of Health and Aged Care.

Correspondence to Dr M.G. Law, National Centre in HIV Epidemiology and Clinical Research, University of New South Wales, 376 Victoria Street, Darlinghurst, NSW 2010, Australia. Tel: +61 2 9332 4648; fax: +61 2 9332 1837; e-mail: mlaw@nchecr.unsw.edu.au

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Introduction

Antiretroviral treatments have been shown to be effective in reducing the rate of HIV transmission from mother to child [1–3]. A recent cohort study has also shown that the risk of HIV transmission between discordant heterosexual partners in Uganda was lower if the HIV-infected partner had a low HIV viral load [4]. These findings raise the possibility that the widespread use of combination antiretroviral treatments could, through decreases in HIV viral loads, lead to reduced rates of new HIV infections at a population level.

The effect that widespread combination antiretroviral treatments might have in reducing new HIV infections through reduced HIV viral loads in individuals receiving treatment has been the subject of much debate in Australia, particularly as there is evidence that optimism surrounding reduced HIV infectiousness is associated with increased rates of unsafe sex (unprotected anal intercourse) among homosexually active men [5–7], among whom approximately 85% of all HIV infections in Australia have occurred [8]. Clearly, any reduction in new HIV infections through the reduced infectiousness of individuals receiving combination antiviral treatments could be counterbalanced by increased numbers of new HIV infections that may result from increased rates of unsafe sex.

The possible effects of the widespread use of combination antiretroviral treatments and levels of unsafe sex on HIV incidence among homosexual men in San Francisco has already been assessed by Blower et al.[9] using a mathematical model. To assess the effects on HIV incidence among homosexual men in Australia, we developed a mathematical model similar to that used by Blower et al.[9]. In this paper we use this mathematical model to investigate the effects of these and other factors on short-term trends in HIV incidence.

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Methods

A mathematical model of HIV infection among homosexual men in Australia was developed. The model aimed to capture two essential features of HIV transmission, which were thought to be particularly important regarding the impact of combination antiretroviral treatments and levels of unsafe sex on HIV incidence: (i) An uninfected homosexual man would be less likely to have unsafe sex (unprotected anal intercourse) with a man diagnosed with HIV than with a man undiagnosed (regardless of his true HIV status); (ii) For an HIV-infected homosexual man to become less infectious as a result of combination antiretroviral treatment he must be diagnosed with HIV infection, and also be treated.

In attempting to model these features, it is important to take account of the fact that both the proportion of HIV-infected homosexual men diagnosed, and the proportion treated, increase with the greater severity of HIV disease. The model developed therefore split HIV disease into five separate groups of homosexual men: uninfected men; HIV-infected men with a CD4 cell count greater than 500 cells/μl; HIV-infected men with a CD4 cell count between 200 and 500 cells/μl; HIV-infected men with a CD4 cell count of less than 200 cells/μl; the development of an AIDS-defining opportunistic infection or cancer (AIDS). These groups were taken to be uni-directional in the sense that, for example, an HIV-infected man with a CD4 cell count of less than 200 cells/μl was not modelled to be able to return to groups with higher CD4 cell counts on starting treatment. Assumptions regarding the numbers of men in each group, the proportions diagnosed and receiving treatment, the average duration of untreated men remaining in each group, and the effect of treatment on these durations are summarized in Table 1[10–15]. These assumptions correspond broadly to the HIV epidemic in homosexual men in Australia in 1996, when effective triple combination antiretroviral treatments first became widely available [10]. The HIV transmission equations underlying the mathematical model are given in the Appendix 1.

Table 1

Table 1

New HIV infections in uninfected homosexual men were modelled to depend on the product of the average number of HIV-infected partners with whom they have unprotected anal intercourse (the level of unsafe sex) and the average probability of HIV transmission occurring with that partner (infectiousness) (see Appendix 1). This product was chosen to have the value 0.8, giving approximately 400 new HIV infections in homosexual men in Australia if combination antiretroviral treatment had no effect on infectiousness, and if there was no increase in the levels of unsafe sex, corresponding to what is thought to have been the number of new infections in Australia in 1996 [8].

To reflect the current uncertainty in many of the factors included in the model, a simulation approach was adopted. Uncertainty was allowed in the following factors, and 1000 sets of these factors were generated using simple random sampling for each factor. Each of these 1000 combinations of factor values was run through the model to give an estimate of the number of HIV infections in the following year.

  •  The average effect of combination antiretroviral treatment on infectiousness, allowing for non-compliance with treatment in some men, was sampled from a uniform distribution (on a logarithm scale) with a median 10-fold decrease in infectiousness, and limits of no decrease and a 100-fold decrease;
  •  Changes in unsafe sex were sampled from a uniform distribution with a median value of a 50% increase, with limits of no increase and a 100% increase;
  •  Uncertainty in the proportions of HIV-infected men diagnosed with HIV infection in each group before AIDS (see Table 1) was included by sampling from a uniform distribution with median value 0 (i.e. the exact values in Table 1), with limits of ±10%. In all simulations, all men with AIDS were taken to be diagnosed with HIV;
  •  Uncertainty in the proportions of diagnosed HIV-infected men receiving treatment in each group (see Table 1) was included by sampling from a uniform distribution with median value 0 (i.e. the exact values in Table 1), with limits of ±10%;
  •  Uncertainty in the effect of treatment on improving average durations lived in each group was included by sampling from a uniform distribution with median value 1.0 (i.e. a multiplicative factor of no effect), with limits of 0.75 and 1.25 times the factors given in Table 1;
  •  The effect of HIV diagnosis in reducing levels of unsafe sex between uninfected men and HIV-diagnosed men was sampled from a uniform distribution with a median value of 0.5 (twofold reduction in the level of unsafe sex) with limits of 0.25 and 0.75. This assumption is based on the following data from HIV-negative participants in the Sydney Men And Sexual Health (SMASH) study in 1997. Of 24 HIV-negative participants reporting any anal intercourse with regular HIV-positive partners, nine (38%) reported unprotected anal intercourse. This compares with 199 HIV-negative participants reporting any anal intercourse with regular HIV-negative partners, of whom 149 (75%) reported unprotected anal intercourse.

The percentage change in annual HIV incidence after one year given by each set of factor values was calculated by comparison with the annual number of HIV infections given by the null model with values as in Table 1, no effect of treatment on infectiousness, and no increase in unsafe sex.

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Results

The modelled percentage changes in annual HIV incidence for each of the 1000 simulations are plotted against the uncertainties in the proportions of men diagnosed with HIV, the proportions of diagnosed men treated, the effect of treatment on improving survival and the effect of HIV diagnosis on reducing rates of unsafe sex in Fig. 1Fig. 2Fig. 3Fig. 4, respectively (see Table 1). These figures show that decreases in HIV incidence are associated with greater proportions of men diagnosed with HIV, greater proportions of men receiving treatment, and HIV diagnosis leading to larger reductions in unsafe sex. Improved survival did not appear to be associated with a change in HIV incidence, at least with the low prevalence of HIV infection (approximately 10%) and over the ranges of survival improvement considered in these models.

Fig. 1.

Fig. 1.

Fig. 2.

Fig. 2.

Fig. 3.

Fig. 3.

Fig. 4.

Fig. 4.

Decreases in HIV incidence were also associated with greater decreases in infectiousness as a result of treatments (Fig. 5), although it appears that this association is non-linear, with little extra decrease in HIV incidence if treatment were to decrease infectiousness by a factor greater than 10-fold. The model suggests that, with a median increase in the levels of unsafe sex of 50%, approximately a 25% decrease in HIV incidence could be expected with a 10-fold or greater decrease in infectiousness as a result of treatment. Conversely, if treatment has only modest effects in decreasing infectiousness, and particularly less than a twofold decrease, increases in HIV incidence would be expected. In contrast to the non-linear pattern seen with the decrease in infectiousness as a result of treatments, increased levels of unsafe sex appeared to be linearly associated with increased HIV incidence (Fig. 6).

Fig. 5.

Fig. 5.

Fig. 6.

Fig. 6.

The relationship between decreased infectiousness as a result of treatment and increases in unsafe sex on changes in HIV incidence are explored further in Fig. 7. This figure shows for each of the 1000 simulations the level of change in HIV incidence (split into six roughly equal strata) plotted by a decrease in infectiousness and increases in unsafe sex. Increases in HIV incidence are shown as black squares (> 20% increase) and black dots (0–20% increase), whereas decreases in HIV incidence are plotted in shades of grey. This figure illustrates how any reduction in HIV incidence through decreased infectiousness as a result of treatment could be counterbalanced by increasing levels of unsafe sex. Decreases in infectiousness of two-, five- and 10-fold would be counterbalanced by increases in unsafe sex of approximately 40, 60 and 70%, respectively. It also appears that if the effect of treatment on decreasing infectiousness is modest and less than a twofold reduction, then an increase in HIV incidence would be expected with any increases in levels of unsafe sex.

Fig. 7.

Fig. 7.

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Discussion

The mathematical model of HIV transmissions among homosexual men developed here suggests that decreases in HIV incidence through large decreases in infectiousness as a result of combination antiretroviral treatment could be counterbalanced by much more modest increases in the levels of unsafe sex, although it should be noted that these increases do constitute quite important changes in sexual behaviour. The reason why such large decreases in infectiousness as a result of treatment could be counterbalanced by more modest increases in unsafe sex lies in the fact that treatment can only decrease infectiousness in men who are diagnosed with HIV and receiving treatment. In the models developed here, which broadly reflect the HIV epidemic among homosexual men in Australia in 1996, the time when effective combination antiretroviral treatments first became widely available, the assumptions correspond to 83% of all HIV-infected homosexual men being diagnosed, of whom 68% were receiving antiretroviral treatment. This corresponds to only 56% of all HIV-infected homosexual men receiving antiretroviral treatment with the associated decrease in infectiousness. Infectiousness is therefore unaffected by treatments in 44% of HIV-infected homosexual men.

The results presented here are broadly consistent with those of a previously published model [9], which suggested that a 10-fold decrease in infectiousness as a result of treatment could be counterbalanced by only a 10% increase in the levels of unsafe sex. This increase in the levels of unsafe sex required to counterbalance an average 10-fold decrease in infectiousness is, however, rather lower than the increase of approximately 70% suggested by our model. This discrepancy may result from differences in the models used, with Blower et al. [9] modelling the transmission of drug-resistant strains, which was not allowed for in our model, but not splitting HIV disease natural history into separate states based on CD4 cell counts and AIDS, as was the case in our model. However, the most likely explanation for this discrepancy appears to result from the differing way in which the uptake of effective combination antiretroviral treatment was modelled. Our models essentially assume that treatment uptake, and increases in the levels in unsafe sex, were instantaneous and coincident, giving a clear picture of the trade-off between the two in terms of changes in HIV incidence. In the models of Blower et al. [9], increases in the levels of unsafe sex were assumed to be instantaneous, whereas the uptake of antiretroviral treatments was modelled to increase gradually over time to a maximum of between 50 and 90% of all HIV-infected men. The 10% increase in the levels in unsafe sex needed in the models of Blower et al. [9] to overcome a 10-fold decrease in infectiousness corresponds to the first year after the availability of treatments, in which only a relatively small proportion all HIV-infected men were modelled to be receiving treatment.

The likely effect of antiretroviral treatments in reducing infectiousness is uncertain. Probably the best data regarding the relationship between HIV viral load and risk of HIV transmission comes from the cohort study of Quinn et al. [4], and suggests that a 1 log lower viral load corresponded to a 2.45 reduction in the rate of HIV transmission. Effective combination antiretroviral treatment produces an average 2–3 log reduction in HIV viral load [16], at least over a 12 month period. This suggests that the effect of treatment is likely to be in the range of a two- to 10-fold decrease in infectiousness. In Australia there are some data to suggest that there have been some increases in the levels of unsafe sex since the advent of effective combination antiretroviral treatments. The prevalence of unprotected anal intercourse with casual partners reported by homosexual men in Sydney and Melbourne has increased by between 20 and 50% since 1996 [5–7,17], although data on other cities in Australia suggest very little or no increase over this time period [18–20]. These increases in the levels of unsafe sex are of the order of magnitude that our models indicate would counterbalance any decrease in HIV incidence if treatments had a fivefold reduction in infectiousness. There has also been an increase in the reported diagnoses of gonorrhoea in New South Wales since 1998, including an increase in rectal gonococcal isolates in men, from 72 in 1997 to 158 in 1998 [8]. These gonorrhoea rates corroborate the increases in unsafe sex reported in behavioural surveys, but are also a further cause for concern. Concurrent infection with a sexually transmissible infection (STI) is known to increase the risk of HIV transmission [21]. The role of increased rates of STI on new HIV transmissions is not included in our model, suggesting that the increases in unsafe sex required to counterbalance the effect of treatments may be lower than our models indicate. Taken together, these data suggest that new HIV infections in homosexual men may be on the verge of increasing in Australia, and in particular in Sydney, in the near future.

The available epidemiological data show that new HIV diagnoses among men who reported homosexual contact or no known exposure to HIV have declined slowly in Australia from 764 in 1995 to 466 in 1998 and 500 in 1999, whereas newly acquired HIV diagnoses (defined as new HIV diagnoses with a previous negative HIV test within 12 months or a concurrent seroconversion illness) have also decreased slightly from 200 in 1995 to 135 in 1998 and 134 in 1999. Although these epidemiological surveillance data should be interpreted cautiously, and in particular should not be cited as good evidence of declining HIV incidence in Australia since 1995, they are at least some evidence that any increases in unsafe sex in homosexual men in Australia have not yet resulted in substantial increases in HIV incidence.

The mathematical model developed in this paper is, by necessity, a simplified model of HIV transmissions among homosexual men, and in particular assumes that trends in new HIV infections can be modelled on the basis of average rates of HIV diagnosis, antiretroviral treatment, and unsafe sex in homosexual men. The model aimed to capture two essential features of HIV transmission that were thought to be particularly important regarding the impact of combination antiretroviral treatments and the levels of unsafe sex on HIV incidence. First, that an uninfected homosexual man would be less likely to have unsafe sex with a man diagnosed with HIV than with a man undiagnosed (regardless of true HIV status). Second, that for an HIV-infected homosexual man to become less infectious as a result of combination antiretroviral treatment he must be diagnosed with HIV infection, and also receive treatment. There are, however, two important limitations in the model. First, that increased rates of unsafe sex could lead to increased rates of STI, which carry an independent increased risk of HIV transmission. The models could therefore underestimate the negative impact of increased unsafe sex on HIV incidence. Second, the model assumes that men take up antiretroviral treatment independent of their HIV viral load. If men with higher viral loads are more likely to adopt treatment, the models may underestimate the effect of treatments on reducing HIV transmissions, particularly if there is some threshold level of HIV viral load below which HIV transmission is virtually impossible [4].

The models presented in this paper suggest that reduced HIV transmissions through apparently large decreases in infectiousness as a result of combination antiretroviral treatment could be counterbalanced by much more modest increases in the levels of unsafe sex. Although the available epidemiological data provide little evidence of increasing HIV incidence in Australia, increased rates of unprotected anal intercourse with casual partners among homosexual men, linked with increased rates of rectal gonorrhoea, suggest that an increase in HIV incidence among homosexual men in Australia, and particularly in Sydney, is a real possibility. The fact that there are data suggesting recent increases in HIV incidence among homosexual men in San Francisco, USA [22] and Ontario, Canada [23] lend support to this possibility. The need for the continued adoption of safe sexual practices among homosexual men in the era of effective combination antiretroviral treatments needs to be reinforced.

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References

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Appendix 1. HIV transmission equations

Notation

X = number of uninfected homosexual men

Y1 = number of infected men with CD4 cell count > 500 cells/μl

Y2 = number of infected men with CD4 cell count between 200 and 500 cells/μl

Y3 = number of infected men with CD4 cell count < 200 cells/μl

Y4 = number of infected men living with AIDS

NX = number of new uninfected homosexual men each year

1/g = mean duration of sexual activity in homosexual men

pdi = proportion diagnosed with HIV in group Yi (i = 1,2,3,4)

pti = proportion of those diagnosed treated in group Yi

1/li = mean survival in group Yi (to group Yi + 1).

ftsi = effect of treatment on increasing average survival in group Yi

fdu = effect of diagnosis on reducing rate of unsafe sex between uninfected men and HIV-diagnosed men

ftu = increased levels of unsafe sex

ftinf = average decrease in infectiousness as a result of treatments, allowing for non-compliance with treatment in some men

c = average annual number of HIV-infected partners with whom uninfected men have unprotected anal intercourse (the level of unsafe sex). This includes inadvertent unsafe sex through incorrect condom use or condom failure.

b = average probability of HIV transmission occurring with that partner (infectiousness)

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Transmission equations

EQUATION where EQUATION where EQUATION where EQUATION where EQUATION where EQUATION

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Notes

Values, and simulated uncertainties, of parameters are given in Table 1, or are described in the text. The value of the product b×c (= 0.8) was chosen to give approximately 400 infections per year in the absence of treatment or any increase in unsafe sex.

Keywords:

Antiretroviral therapy; HIV incidence; homosexual men; mathematical models; sexual behaviour

© 2001 Lippincott Williams & Wilkins, Inc.