# HIV question: risk of infection

• Medical
• daniel6874
In summary: This is a reasonable assumption, but not the only one possible.In summary, one website gives the risk of infection by HIV for a woman during unprotected vaginal intercourse with an infected male partner as "between 1/1000 and 1/100,000." The CDC estimated the number of undiagnosed persons in the greater U.S. with HIV in 2009 at a conference as 230,000. Using a very rough estimate of the number of males over the age of 18 in the U.S. (150 M--it is of course smaller), one might give a ballpark estimate of the risk of unprotected sex (per event) for a woman as [using 1/1000 times 230,000/150M] about 2/million.
daniel6874
One website gives the risk of infection by HIV for a woman during unprotected vaginal intercourse with an infected male partner as "between 1/1000 and 1/100,000." The CDC estimated the number of undiagnosed persons in the greater U.S. with HIV in 2009 at a conference as 230,000. Using a very rough estimate of the number of males over the age of 18 in the U.S. (150 M--it is of course smaller), one might give a ballpark estimate of the risk of unprotected sex (per event) for a woman as [using 1/1000 times 230,000/150M] about 2/million.

Finding the annual risk for such behavior, with the many simplifications above, one could calculate Probability(one or more encounters that lead to infection) as 1-Probability(no infectious encounters). The probability of no infectious encounters is
----
N = (1 - 2/1000000)^365.
----
The probability of at least one adverse event in a year is then 1 - N = 0.00073 or roughly 7/10,000. I notice that one non-scholarly article gives the annual probability of being murdered as about 1/16,500.

I don't think statistics help much in this area, but as a back-of-envelope calculation, it seems low. Can anyone suggest a factor that would change the order of magnitude of the risk? Thanks.

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daniel6874 said:
One website gives the risk of infection by HIV for a woman during unprotected vaginal intercourse with an infected male partner as "between 1/1000 and 1/100,000." The CDC estimated the number of undiagnosed persons in the greater U.S. with HIV in 2009 at a conference as 230,000. Using a very rough estimate of the number of males over the age of 18 in the U.S. (150 M--it is of course smaller), one might give a ballpark estimate of the risk of unprotected sex (per event) for a woman as [using 1/1000 times 230,000/150M] about 2/million.

Finding the annual risk for such behavior, with the many simplifications above, one could calculate Probability(one or more encounters that lead to infection) as 1-Probability(no infectious encounters). The probability of no infectious encounters is
----
N = (1 - 2/1000000)^365.
----
The probability of at least one adverse event in a year is then 1 - N = 0.00073 or roughly 7/10,000. I notice that one non-scholarly article gives the annual probability of being murdered as about 1/16,500.

I don't think statistics help much in this area, but as a back-of-envelope calculation, it seems low. Can anyone suggest a factor that would change the order of magnitude of the risk? Thanks.
Please post the links to the studies to which you are referring. We only accept mainstream science and acceptable peer reviewed journals as sources. Anything else is anecdotal and we can't work with anecdotes.

Once we are all on the same page we will be able to discuss.

http://aids.about.com/od/hivaidsstats/f/infectionrisk.htm. The content of this site is checked and approved by, among 12 other licensed MDs, Meredith Shur, M.D., of Sinai Hospital, NYC, whose specialty is OB-GYN. This is the source of my risk number (between 1/1000 and 1/100,000). The credentials of the doctors on the review board make it clear it is mainstream.

http://www.cdc.gov/hiv/resources/factsheets/us.htm . This is the CDC's fact site, in which they estimate that 1M people are living with AIDS in the US, of whom 21% are unaware of the infection. The CDC is also a mainstream source.

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http://www.cdc.gov/nchs/data/dvs/LCWK10_2005.pdf gives the homicide statistic, which is ancillary to the question but given for perspective. Out of 2,448,017 deaths in 2005, 8770 were due to homicide, which is about 0.00358. So about 36/10000. Again the source is CDC's site. In my post I may have used a figure from another year.

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Some of the simplifications I used: 1) all undiagnosed infections [230,000 in the OP, 210,000 per the CDC site] are men--this gives an overestimate; 2) the use of 1/1000 is the highest risk in the cited forum, so would give a higher risk; 3) the exponent 365 raises the risk--I doubt anyone actually incurs this much risk; the estimate of number of men over 18 is high. This tends to dilute the risk but the preceding factors would seem to compensate.

There is one factor that could be hard to model, which is that the sexual promiscuity of the men in the population is not homogeneous. That is, some men in the population will have very few partners while some men will have very many partners. Since the most promiscuous individuals are both the most likely to be sexual partners and are at highest risk for HIV infection, this heterogeneity in promiscuity would tend to elevate the risk from calculations where promiscuity is assumed to be homogeneous.

That's an interesting point. A 'randomly selected partner' is really a fiction.

Also, the annual probability of death by (say) homicide assumes one is going to die in a given year, and that probability [from actuarial tables] must be accounted for. It would lower the number and perhaps put it in line with the number [1/16,500] in OP. An interesting coincidence--*death* by homicide and HIV both contribute 0.5 % to the annual deaths for 2005. So we know without further calculation that the probability of *contracting* HIV is much higher (annually) than of dying by homicide.

Unprotected vaginal intercourse isn't the only way a woman can contract HIV.

Intravenous drug use and other types of sex are just two of several possibilities.

enigma said:
Unprotected vaginal intercourse isn't the only way a woman can contract HIV.

Intravenous drug use and other types of sex are just two of several possibilities.

________________________________________

True, but the HIV risk cited (1/1000) speaks to vaginal sex. The origin of the undiagnosed cases is not specified. So I don't think this affects the probabilities calculated. If we threw in other types of sex, it would perhaps affect the calculation, but I wonder whether there is a research incentive to find HIV infection risk for sexual encounters of an unspecified nature.

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daniel6874 said:
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True, but the HIV risk cited (1/1000) speaks to vaginal sex. The origin of the undiagnosed cases is not specified. So I don't think this affects the probabilities calculated. If we threw in other types of sex, it would perhaps affect the calculation, but I wonder whether there is a research incentive to find HIV infection risk for sexual encounters of an unspecified nature.

receptive anal intercourse is the easiest way to get it. this is not rare heterosexual behavior. i suspect it is also not rare for some bisexual (situational or otherwise - note the category is called MSM) men to not inform female partners of past encounters. some are also never going to admit to healthcare providers how they contracted a disease. some may barely be able to admit it to themselves. and... a lot of unwise sexual choices happen under the influence of drugs and alcohol. some may literally have no idea of what happened.

as for teasing out info from reluctant people, there is an indirect method from psychology that uses a little statistical trick, but i can't remember what it's called.

Proton Soup said:
receptive anal intercourse is the easiest way to get it. this is not rare heterosexual behavior. i suspect it is also not rare for some bisexual (situational or otherwise - note the category is called MSM) men to not inform female partners of past encounters. some are also never going to admit to healthcare providers how they contracted a disease. some may barely be able to admit it to themselves. and... a lot of unwise sexual choices happen under the influence of drugs and alcohol. some may literally have no idea of what happened.

as for teasing out info from reluctant people, there is an indirect method from psychology that uses a little statistical trick, but i can't remember what it's called.
____________
Agreed, especially about the difficulty of getting data. So if I understand you correctly, instead of focusing on the "randomly selected partner," who as Ygggdrasil suggested may be drawn from a smaller pool than we imagined, you are saying that the risk appears small with vaginal intercourse because it is only a component of a greater overall risk. I think this is a good answer, although I do think it's important to assess each component. To the extent people are sober, relative risk is still something to be weighed.

nice very unique post i don't thing before this i saw any this type of comparison about the HIV.

For what it's worth, the CDC estimates that the yearly incidence of new infections per year in the US is 56,300, 31% of which are due to heterosexual contact (http://www.cdc.gov/hiv/topics/surveillance/incidence.htm ). If we can get an estimate of the number of sexually active heterosexual individuals in the population, we can compare daniel6874's back-of-the-envelope risk estimate to the actual incidence rate.

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Ygggdrasil said:
For what it's worth, the CDC estimates that the yearly incidence of new infections per year in the US is 56,300, 31% of which are due to heterosexual contact (http://www.cdc.gov/hiv/topics/surveillance/incidence.htm ). If we can get an estimate of the number of sexually active heterosexual individuals in the population, we can compare daniel6874's back-of-the-envelope risk estimate to the actual incidence rate.

Sort of agreed, but I think the earlier observation that needle-sharing and anal sex potentially dwarf the contribution of vaginal intercourse (for women, obviously) make it a hard call. Assuming some continuity of figures year over year, if 20,000 (men and women) are newly HIV+ (roughly your figure), we would need about 28.5 million active heterosexuals (men and women, and we would include bisexuals) to get a similar risk (for both men and women).

There may be this many. It's about 10% of the population.

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daniel6874 said:
Sort of agreed, but I think the earlier observation that needle-sharing and anal sex potentially dwarf the contribution of vaginal intercourse make it a hard call. Assuming some continuity of figures year over year, if 20,000 (men and women) are newly HIV+ (roughly your figure), we would need about 28.5 million active heterosexuals (men and women, and we would include bisexuals) to get a similar risk.

It's very fuzzy at this point. There may be this many. It's about 10% of the population.
Injection drug users come in third.

In 2007, injection-drug use was the third most frequently reported risk factor for HIV infection in the United States, after male-to-male sexual contact and high-risk heterosexual contact

http://www.cdc.gov/mmwr/preview/mmwrhtml/mm5846a2.htm

Yes, and I missed that the infections in Ygggdrasil's statistic are already due to heterosexual sexual encounters. So I guess the question of how many active heterosexuals there are would give a statistic for comparison, bearing in mind the comparison is between annual risk for the general heterosexual population and that for women alone due to vaginal intercourse (the OP), just to check that the risks are of the same order of magnitude. If there are studies estimating that number, I'd be interested.

daniel6874 said:
Yes, and I missed that the infections in Ygggdrasil's statistic are already due to heterosexual sexual encounters. So I guess the question of how many active heterosexuals there are would give a statistic for comparison, bearing in mind the comparison is between annual risk for the general heterosexual population and that for women alone due to vaginal intercourse (the OP), just to check that the risks are of the same order of magnitude. If there are studies estimating that number, I'd be interested.
What exactly are you looking for? Just numbers? And why?

Risk of infection has to do with the risky behaviour you or people you are involved with take.

A gay or heterosexual couple that are monogamous, not infected and not used syringe injection drug users or partners of same, are virtually at no risk, (except for the rare chance that they get a contaminated blood transfusion, etc...)

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Evo said:
What exactly are you looking for? Just numbers? And why?

The question is in the OP. The CDC published the numbers. I respectfully do not understand your question(s).

daniel6874 said:
The question is in the OP. The CDC published the numbers. I respectfully do not understand your question(s).
If this is your question (it's the only one I see), it's too vague. You need to be specific, if you could answer my questions, that would help.

daniel6874 said:
Can anyone suggest a factor that would change the order of magnitude of the risk? Thanks.
Which risk? Sharing needles with injected drug users? Having sex with these users? Having sex with already infected partners?

I explained in my post above how you can choose to be in an extremely low risk group.

Perhaps this will help.

http://www.cdc.gov/hiv/topics/surveillance/resources/reports/

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Evo, in any science, the ultimate goal is to be able to quantitatively explain phenomena observed in nature from first principles. Here, we're trying to quantitatively understand the rate of incidence of new HIV infections.

In the first post of the tread, daniel6874 attempted to estimate the incidence of new HIV infections among heterosexual from a simple mathematical model involving a number of defined assumptions. That his estimate seems to underestimate the actual incidence of new HIV cases points to some of these assumptions are wrong. What we're trying to do in this thread is understand which of these assumptions are wrong. This thread is not specifically about under the factors that affect an individuals risk of HIV infection although the information is very relevant to the discussion.

So far the discussion has illuminated a number of important points that affect daniel's initial estimate. For example, heterosexuals may participate in anal sex which entails a higher risk of HIV transmission, and daniel's calculation likely overestimates the population of sexually active individuals who would be at risk of HIV infection.

It is important to note that these calculations are basically just a thought exercise and should not be taken to be particularly relevant to anyone individual. Risk of HIV infection is definitely a variable that exhibits much heterogeneity among the population.

Ygggdrasil said:
Evo, in any science, the ultimate goal is to be able to quantitatively explain phenomena observed in nature from first principles. Here, we're trying to quantitatively understand the rate of incidence of new HIV infections.

In the first post of the tread, daniel6874 attempted to estimate the incidence of new HIV infections among heterosexual from a simple mathematical model involving a number of defined assumptions. That his estimate seems to underestimate the actual incidence of new HIV cases points to some of these assumptions are wrong. What we're trying to do in this thread is understand which of these assumptions are wrong. This thread is not specifically about under the factors that affect an individuals risk of HIV infection although the information is very relevant to the discussion.

So far the discussion has illuminated a number of important points that affect daniel's initial estimate. For example, heterosexuals may participate in anal sex which entails a higher risk of HIV transmission, and daniel's calculation likely overestimates the population of sexually active individuals who would be at risk of HIV infection.

It is important to note that these calculations are basically just a thought exercise and should not be taken to be particularly relevant to anyone individual. Risk of HIV infection is definitely a variable that exhibits much heterogeneity among the population.
That's why the CDC says that it depends on the risk factors involved. I'm sure you would agree with them that you cannot just pull numbers out of the air if you intend to obtain meaningful information.

For example, heterosexuals may participate in anal sex which entails a higher risk of HIV transmission
Anal sex would be a risk factor ONLY if your partner is infected. Again, *risk factor*.

If the OP just wants a thought exersise, it's not appropriate for this forum, this is for hard science.

Thank you for pointing out what I am trying to get across to the OP, that we need more specifics in order to get to something meaningful.

I'm at a complete loss for why the OP can't respond to my request. All I asked was
What exactly are you looking for? Just numbers? And why?

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Evo said:
That's why the CDC says that it depends on the risk factors involved. I'm sure you would agree with them that you cannot just pull numbers out of the air if you intend to obtain meaningful information.

Anal sex would be a risk factor ONLY if your partner is infected. Again, *risk factor*.

If the OP just wants a thought exersise, it's not appropriate for this forum, this is for hard science.

Thank you for pointing out what I am trying to get across to the OP, that we need more specifics in order to get to something meaningful.

I'm at a complete loss for why the OP can't respond to my request. All I asked was And he came unglued.

The phrase "thought exercise" or "thought experiment" is a term of art in the hard sciences. It refers to inductive reasoning based on data.

You ask why I would be interested in "just numbers." Results in hard science typically involve numbers. The CDC was interested in the numbers and so am I.

My original question is the entire OP. You snipped everything but the last sentence. It is very specific.

I asked Ygggdrasil to reply for me because s/he appears to be a highly qualified professional in the hard sciences who understood the OP. I defer to that note, which expressed my response better than I myself could have done.

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Evo does bring up an important point of this discussion. While we can calculate a value for the risk of HIV infection for the entire population, this value is meaningless. Risk is spread very unevenly throughout the population such that the distribution of risk cannot be characterized by a single number like the mean (consider, for example, a bimodal distribution; the mean of a bimodal distribution is neither representative of any individual point in that distribution nor representative of the distribution as a whole).

However, if we look at a subset of the population where we expect the risk to be much less heterogeneous, we can calculate an incidence rate that does represent the risk of infection for that specific population. For example, we can look at the population of individuals engaging in high-risk heterosexual activity (e.g. unprotected sex with multiple partners). The distribution of risk in this population is probably much less heterogeneous (it is probably has a unimodal distribution), allowing us to calculate a meaningful estimate of their risk.

Assuming that nearly all HIV infections among heterosexuals (excluding those caused by intravenous drug use) are driven by high-risk heterosexual activity, we can estimate the incidence rate for this population. First we need a measure of the new cases of HIV among heterosexuals per year. This number has been measured by the CDC (http://www.cdc.gov/hiv/topics/surveillance/incidence.htm ). Now, we need an estimate of the number of individuals engaging in high-risk heterosexual activity.

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Ygggdrasil said:
Evo does bring up an important point of this discussion. While we can calculate a value for the risk of HIV infection for the entire population, this value is meaningless.
...
Now, we need an estimate of the number of individuals engaging in high-risk heterosexual activity.

Yes, her point about specificity is absolutely correct here. Your narrowing the focus resolves that.

As an aside, the phrase "high-risk" is technically a petit principio here. It's the question we are trying to answer! I think "unprotected" avoids that?

Another factor is that HIV transmission risk is not necessarily the same for all people.

Polymorphisms in the HLA gene affect likelihood of transmission, probably through effects on viral load.

http://www.ncbi.nlm.nih.gov/pubmed/20588164

Ygggdrasil said:
Evo does bring up an important point of this discussion. While we can calculate a value for the risk of HIV infection for the entire population, this value is meaningless. Risk is spread very unevenly throughout the population such that the distribution of risk cannot be characterized by a single number like the mean (consider, for example, a bimodal distribution; the mean of a bimodal distribution is neither representative of any individual point in that distribution nor representative of the distribution as a whole).

However, if we look at a subset of the population where we expect the risk to be much less heterogeneous, we can calculate an incidence rate that does represent the risk of infection for that specific population. For example, we can look at the population of individuals engaging in high-risk heterosexual activity (e.g. unprotected sex with multiple partners). The distribution of risk in this population is probably much less heterogeneous (it is probably has a unimodal distribution), allowing us to calculate a meaningful estimate of their risk.

Assuming that nearly all HIV infections among heterosexuals (excluding those caused by intravenous drug use) are driven by high-risk heterosexual activity, we can estimate the incidence rate for this population. First we need a measure of the new cases of HIV among heterosexuals per year. This number has been measured by the CDC (http://www.cdc.gov/hiv/topics/surveillance/incidence.htm ). Now, we need an estimate of the number of individuals engaging in high-risk heterosexual activity.

IV drug use does not seem to be insignificant enough to discard.

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## 1. What is HIV?

HIV (Human Immunodeficiency Virus) is a virus that attacks the immune system, specifically the CD4 cells which are responsible for fighting off infections. Over time, HIV can weaken the immune system and make it harder for the body to fight off infections and diseases.

## 2. How is HIV transmitted?

HIV is transmitted through the exchange of certain bodily fluids, including blood, semen, vaginal fluids, and breast milk. This can happen through unprotected sexual activity, sharing needles or syringes, or from mother to child during pregnancy, childbirth, or breastfeeding.

## 3. What are the risk factors for HIV infection?

The main risk factors for HIV infection are unprotected sexual activity and sharing needles or syringes. Other risk factors may include having multiple sexual partners, having a sexually transmitted infection, and receiving blood transfusions or organ transplants from an infected donor (although this is rare in developed countries).

## 4. How can I protect myself from HIV?

The best way to protect yourself from HIV is by practicing safe sex, including using condoms and engaging in monogamous relationships. It is also important to never share needles or syringes and to use clean, sterile equipment if injecting drugs. Additionally, pre-exposure prophylaxis (PrEP) medication can be taken by individuals at high risk for HIV to prevent infection.

## 5. Is there a cure for HIV?

Currently, there is no cure for HIV. However, there are highly effective treatments available that can control the virus and allow people living with HIV to live long and healthy lives. These treatments, known as antiretroviral therapy (ART), work by reducing the amount of HIV in the body and preventing it from damaging the immune system.

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