The authors of a pair of new studies have created mathematical models to show how a small per-act risk of HIV transmission can translate to more substantial long-term risk after many sexual acts. While these studies’ findings can’t be applied to individual circumstances and aren’t necessarily an exact roadmap to navigating risk, they do teach important lessons about how to think about risk. One of them notably demonstrates how adopting multiple risk-reduction strategies is likely more effective than using just a single means of protection against HIV transmission.

French researchers recently published a paper in Clinical Infectious Diseases (CID) that estimated the maximum risk of HIV transmission within a mixed-HIV status (serodiscordant) heterosexual couple in which the HIV-positive partner was on antiretrovirals (ARVs) and there was regular viral load monitoring, along with testing for sexually transmitted infections (STIs) and treatment if necessarily. They found that if 1 million such couples each had sex without a condom once after the HIV-positive partner had been on ARVs for longer than six months, the maximum number of HIV transmissions that would likely occur would be either 87 or 130 (0.0087 percent or 0.013 percent), and there could in fact be zero transmissions.

The reason for the two different “upper bounds” of the estimate range is that when researchers reviewed various studies of serodiscordant couples, they couldn’t determine the timing of one of the HIV transmissions that occurred. After of 113,480 sex acts, 17 percent of which did not involve condoms, between 1,672 mixed-HIV status couples, a total of four of the HIV-negative partners acquired the virus. Three of these transmissions definitely occurred before the HIV-positive partner had been taking ARVs for longer than six months. A fourth transmission occurred during the first year that the partner living with the virus was on HIV therapy, but there is not enough information to conclude whether that transmission took place before or after six months of treatment.

To account for this uncertainty, the researchers performed two calculations: one assuming that fourth transmission took place before six months of treatment, which would presume that the maximum per-contact risk of transmitting the virus after someone is on ARVs for longer than six months is smaller (87 out of 1 million); and another calculation assuming that the fourth transmission took place after six months, meaning that the maximum risk of passing on HIV after six months of therapy is larger (130 out of 1 million).

If it is indeed true that no one in the study was infected after his or her partner was on therapy for more than six months, it may seem strange that the estimated risk of transmission when anyone is on ARVs for more than half a year wouldn’t be zero. Granted, the researchers say the reality could be that the risk of transmission is zero, but they express their estimate in a range with zero as the minimum and the two upper bounds as the maximums. These ranges are what’s known in statistics as a “confidence interval.” Such an interval is the best range of an estimate as to where the actual real-world figure may fall, based on the amount of data at hand and its ability to predict the real world. Even if no one transmits HIV, the estimate must account for the possibility that with a larger data set there still could be transmissions. The larger the amount of data showing no transmissions, the smaller the confidence interval could be, because more data with less statistical “noise” means better accuracy in predicting real life.

The French researchers calculated that they would need more than 12 times extra data to shrink the smaller upper bound estimate of 87 transmissions out of 1 million sex acts to less than 10 transmissions per 1 million. An even greater amount of data would be needed to taper the 130 per 1 million estimate to that point. The investigators already had to include studies in their review that only account for the HIV-positive person being in regular care and on treatment, as opposed to restricting the data set only to those with a fully suppressed viral load. Such a restriction would have left them with much less data and, consequently, much less statistical heft to their findings. Actually coming up with 12 times more data would be a significant challenge, they concluded. Which helps to illustrate one of the reasons why it will be impossible to completely prove that there is zero chance of transmitting after six months of therapy. The bottom line is that there is always that room for chaos where statistics are concerned.

The researchers then calculated how the maximum per-contact risk would evolve over time into what is known as a “cumulative risk.” For the smaller estimate, with a one-time maximum risk of 0.0087 percent, after 389 condomless sex acts between these couples the maximum cumulative risk of HIV transmission would rise above 1 percent. For the larger estimate, the maximum one-time risk of 0.013 percent would translate to a maximum cumulative risk of more than 1 percent after 195 sex acts. But again, these are the upper-bound risks, so the reality could actually be that there is no risk of transmission in these circumstances—ultimately the estimate reflects a range between zero and the upper bound.

Consider also the two-year interim results of the PARTNER study announced this spring, in which there was no transmission within serodiscordant gay male and straight couples who were at least sometimes not using condoms. Although the researchers famously stated that the ultimate risk of transmission “might be zero,” they still calculated a ten-year confidence interval of zero to 4 percent risk of transmission overall, and zero to 9 percent for condomless anal sex.

The French paper stresses that there are simply too many other variables that can play into the risk of transmission in any one circumstance to apply these estimates to any individual person’s risk of acquiring HIV, and that the estimates cannot be applied to men who have sex with men since no MSM were included in the review.

“The value of models is often to point you in directions,” notes Susan Buchbinder, MD, an assistant clinical professor at the University of California, San Francisco (UCSF), who was one of the investigators of the iPrEX trial that proved the efficacy of Truvada (tenofovir/emtricitabine) as pre-exposure prophylaxis (PrEP) among MSM and transgender women. “It’s not to give you an absolute number. It’s to say, ‘In optimal circumstances what would this look like?’”

Virginie Supervie, PhD, a researcher at the Institute Pierre Louis d’Epidémiologie et de Santé Publique at INSERM in Paris, who is the French study’s lead author, notes that her research only included studies in which participants’ viral loads were checked every three to six months. Considering this, she says that in order to mitigate the risk of transmitting HIV when someone living with the virus is taking ARVs, “I think it’s important that [HIV-positive] people are in care and have their viral load checked. And if the treatment doesn’t work, they have to change [HIV regimens].”**CDC Looks at Risk-Reduction Strategies**

Researchers at the CDC recently released their own study in the journal AIDS in which they’ve used models to estimate the cumulative risk of transmission within both heterosexual and gay male serodiscordant couples after one- and ten-year periods of anal or vaginal sex performed six times a month. They’ve also crunched the numbers to show how risk-reduction strategies mitigate this risk and how a combination of two or more strategies is more effective than one.

The model’s results are useful for helping to conceive of how cumulative risk progresses over time. As better estimates of risk reduction strategies’ efficacy become available, they can be put into the model to come up with more accurate and up-to-date estimates of such cumulative risk.

For a gay male serodiscordant couple in which the HIV-positive partner is not taking ARVs, the paper estimates that when they each are having both insertive and receptive intercourse without a condom, there is a 52 percent chance HIV will transmit after a year, and a 99.9 percent chance after 10 years. If the couple uses condoms consistently, however, the respective chances are reduced to 13 percent and 76 percent.

The paper weighs a small laundry list of risk-reduction strategies, including: Truvada (tenofovir/emtricitabine) as pre-exposure prophylaxis (PrEP); having the HIV-negative man refrain from receptive anal intercourse and always play the insertive role in sex (being the top), also called seropositioning; condoms; and treating the HIV-positive partner with ARVs. Circumcision is also considered as a possible risk-reduction strategy, although this would only reduce the risk of transmission if the HIV-negative partner were always the top, a restriction of sexual roles that research suggests is rare among gay couples. The calculations find that combining these risk-reduction strategies is a more effective way to reduce risk than simply relying on one method, and that using three strategies is more effective than only relying on two. So, for example, if one risk reduction strategy cuts the risk by say 95 percent and a different one also cuts the risk by 95 percent, combining the two does not yield the same 95 percent efficacy, it actually efficacy the efficacy above that figure.

According to Susan Buchbinder, the CDC study “raises to the forefront the issue that condoms aren’t necessarily 100 percent protective. And so when everybody says, ‘Just use condoms,’ that isn’t enough for everybody—and that using other things like PrEP can augment, but doesn’t necessarily need to replace [condoms]. I think the reason that condoms aren’t 100-percent effective is both because people don’t use them all the time even if they say that they are, but also because they break and slip. And I think that that is under recognized.”

One element making the study’s central findings rather tricky to apply to the real-world scenarios is the fact that the researchers opted to use the most pessimistic estimate of PrEP’s efficacy among men who have sex with men (MSM)—44 percent—in order to make their main calculations and to create a list rating the comparative success rates of various strategies. The 44 percent figure, which derives from the December 2010 iPrEx trial that first proved PrEP’s efficacy, is considered overly gloomy because it included in its calculations those who adhered poorly to Truvada.

In a subsequent analysis, the CDC researchers did tinker with the numbers to estimate how factoring in a 92 percent risk reduction for PrEP improved the relative chances of remaining HIV negative over time. A 44 percent efficacy for PrEP translated into a 34 percent likelihood of transmission within a gay serodiscordant couple after a year if no other risk reduction strategies are used, while a 92 percent efficacy would slash the one-year transmission likelihood to 6 percent. It is arguably unfortunate, however, that the investigators buried this particular analysis further back in the paper. Consequently, the journal article’s main abstract—the summary of its conclusions that acts as a marquee to the paper—sends a perhaps skewed message that PrEP is not much of a reliable arsenal over time. This is particularly problematic considering that many estimate that PrEP in fact lowers the risk by 99 percent if taken as directed.

All of this number crunching is not to say that these estimates are perfectly relevant to any particular person’s own navigation through safer-sex choices, cautions study co-author Richard Wolitski, PhD, the senior advisor for strategic indicators in the Division of HIV/AIDS Prevention at the CDC.

“One of the things that’s important to understand with any study that’s estimating transmission risk is that per-contact risks or cumulative risks are really average risks, and those risks are affected by a lot of different things,” Wolitski says. “So for transmission risk, the number of times that people are having sex or the status of the positive partner in terms of their viral load is going to dramatically affect the probability of HIV transmission.” Sexually transmitted infections, he says, can also affect risk.

Robert M. Grant, MD, MPH, a professor of medicine at UCSF and a senior investigator at Gladstone Institutes who headed up the iPrEX trial, explains another way that such mathematical models have significant limitations: “This kind of analysis really doesn’t take into account how people move in and out of seasons of risk. What we observe is that people go through periods when they have a lot of partners and a lot of sex, and they go through other periods when they may have no partners for a period of time.”

In order to better apply the overall lessons of these two studies to the real world, Grant says, “I think if we can get people to recognize when they’re moving into a period where they need more support, where they need to be using condoms more frequently, where they need to be on PrEP, where they need to be more vigilant about asking about suppressive [ARV] therapy [in their HIV-positive partners], then we could get them through those periods. And then in other periods in their lives—which can last weeks, months or years—they don’t need all those extra things.”

To read the French study abstract, click here.

To read the CDC study abstract, click here.

Editor’s note: a previous version of this article incorrectly cited the CDC’s Richard Wolitski as the lead author of the study in question. He is a co-author.

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# What’s Your Long-term Risk of Transmitting HIV?

How mathematical models can help us better understand both the long-term probability of HIV transmission and the benefit of combining risk-reduction strategies.

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