Monday, May 26, 2014

Lies, Damn Lies, and STD Risk Statistics, Part 2

Continued from Part 1.

If you've just joined us, we're giving a good fisking to the Mayo Clinic's worthless list of STD risk factors, namely:
Having unprotected sex. 
Having sexual contact with multiple partners. 
Abusing alcohol or using recreational drugs. 
Injecting drugs. 
Being an adolescent female 
The biggest proof that their advice is completely worthless comes from the full description of the first point, 'having unprotected sex'. At a very minimum, they don't make the most minimal distinction between vaginal, anal and oral intercourse. But even within that, the whole thing is basically a ridiculous scare campaign:
Vaginal or anal penetration by an infected partner who is not wearing a latex condom transmits some diseases with particular efficiency. Without a condom, a man who has gonorrhea has a 70 to 80 percent chance of infecting his female partner in a single act of vaginal intercourse. Improper or inconsistent use of condoms can also increase your risk. Oral sex is less risky but may still transmit infection without a latex condom or dental dam. Dental dams — thin, square pieces of rubber made with latex or silicone — prevent skin-to-skin contact.
This one I know is in the 'deliberately misleading to fool the public' category. You know why? Because they use the weasel words 'some diseases'. They then back it up with the gonorrhea example, where one-off unprotected vaginal transmission rates are high. But people don't generally stay up late at night freaking out about getting gonorrhea, do they? As a matter fact, you don't hear about it much, because it can be treated with antibiotics. What people actually worry about the most is HIV. Why not tell them about that instead?

So what are the chances of HIV transmission from unprotected vaginal intercourse with someone who is HIV positive? This is such a classic that I want to put the answer (and the rest of the post, which gets even more awesome by the way, though you may not believe it's possible) below the jump. Suppose a man and a woman have unprotected vaginal intercourse once. 
a) If the man is HIV positive, what is the chance the women contracts HIV?
b) If the woman is HIV positive, what is the chance the man contracts HIV?

If you're in a high-income country, the answers are:

a) The women has a 0.08% chance, or roughly 1 in 1250
b) The man has a 0.04% chance, or 1 in 2500.

Not exactly what you were expecting, was it? Bear in mind, this is assuming the other person is HIV positive.

What are the unconditional probabilities from the same?

Well, among the USA's 318 million people, there are around 1.1 million HIV infections in total, giving a completely unconditional probability of a randomly chosen person in the US having HIV of 0.35%. Let's assume for the sake of the exercise that all HIV infections are limited to people aged between 18 and 65, thus cutting out 37.2% of the populace. Assuming we're sleeping with a randomly chosen person between 18 and 65, the chances of them having HIV would be 1.1/(318*0.628) = 0.55%. In other words, not many people have HIV.

If we split it out into the sexes, 24% of infections are in women, giving an overall rate under our assumptions of a randomly chosen 18 to 65 year old woman having HIV of  (1.1*0.24)/(0.628*318/2) = 0.26%. For men, the unconditional probability is (1.1*0.76)/(0.628*318/2)=0.84%.

Let's also assume for the sake of the exercise that the male HIV rate is the same when we limit the pool to men likely to be having vaginal sex in the first place, although clearly it's not. The rate is definitely going to be lower, making the risk assessment for women overstated.

From this, our unconditional probability as a  man of contracting HIV from one round of unprotected vaginal intercourse among a randomly chosen 18-65 woman is 0.0026*0.0004=0.0000011,or 0.00011%. In other words, on average we expect one HIV infection for every 945,568 such sex acts. In language that's easy to remember, your chances of contracting HIV are approximately 1 in a million, which is just too hilariously poetic for words. For women, the probability is 0.0084*0.0008=0.0000067, or 0.00067%.We expect one HIV infection per 149,300 such acts.

Are you starting to see why the numbers they sell you seem totally bogus in terms of answering the questions that people might actually be interested in knowing? Assuming that condoms were completely effective in preventing transmission, your chances of getting AIDS per round of sex have only gone down by 0.00011% or 0.00067% by wearing a condom. If you were forced to choose between that and not text messaging someone while driving on the freeway as a way of improving life expectancy, I'd wager on the latter being quite a bit more important.

This doesn't mean you should just throw away condoms, of course. In case my views are unclear, yes, you should all still use them, because the cost of using them is also very low, making it an NPV positive choice. But it does put their scare campaign in a bit of a different light, no? 'You should use them anyway, but it probably doesn't make much of a difference to your HIV risk if all you have is vaginal sex' is a considerably different takeway. People might get the wrong (right) idea, better spin them more $#!& on a stick and call it fairy floss!

Okay, so what are some materially relevant relative risks of catching HIV, given the Mayo clinic seems uninterested in enlightening us?

Let's start with anal sex. What's the transmission rate from rceiving unprotected anal sex, conditional on the other person having HIV?

It turns out from this meta-study I found that it's 1.7%. I didn't actually know this until now, I assumed it would be much higher. You see what I mean about how little people know about this stuff?

But since it's relative risk we're after, for the female comparison, the relative risk of unprotected anal sex to unprotected vaginal sex with the same person is 0.017/0.0008 = 21.5. So anal sex is a lot riskier than vaginal sex. The comparison for men is less straightforward because comparing vaginal sex to anal sex necessitates the joint shift of different populations (gay and bisexual men versus women) and different acts (vaginal versus anal), but even ignoring population prevalence, the transmission rate difference conditional on HIV positive male and female partners is 0.017/0.0004=42.5. Add in some plausible estimates of difference in prevalence of HIV and the overall risk rate is going through the roof.

So it seems that at least for HIV, the advice 'don't have unprotected anal sex' is much more relevant than just 'don't have unprotected sex', with more specific formulations being available for men. If you need an explanation of why this distinction didn't make the Mayo clinic brochure, let me suggest to you to a crash course in the last 20 years of US political history. 

Secondly, the most glaring omission from the Mayo clinic advice is the importance of not sleeping with prostitutes. Again, forget prevalence. On transmission rates alone (mostly because of the presence of other STDs), from the same meta-study your probability of HIV transmission is 2.44%. Compare this to the non-sex worker rate of 0.164% (higher than our 0.08% number, because these studies included the developing world) and the relative risk is 14.9 times higher. Add in prevalence effects, and that number is going way up too. This kind of thing used to be common sense. Perhaps it still is, but not in certain circles.

In terms of other risky behaviour, the study notes that if the other person has genial ulcers then the risk is 5.3 times higher. Although I imagine there's probably other reasons to avoid sleeping with these people, such as, ooh, I don't know, that they have genital ulcers

For a large number of reasons, it is worth pondering the significance of when the powers that be refuse to do simple arithmetic.

Let's take one that the government reports, but not in a useful fashion. How much should you worry about sleeping with someone from a different state? Everything you need to know is contained in this report (which gives you number of people living with HIV by state) and Wikipedia (which gives you state populations), but of course the government would never report something so inflammatory as dividing X by Y.

In case you feel like being inflamed, here's the rankings and percentages of states, as well as a relative risk ratio compared with the median, which is Arkansas. Come on, how much difference could it possibly make?

A lot, as it turns out.

StateHIV RateRankRatio to Median (AK)
 District of Columbia2.87%116.36
 New York0.68%23.86
 New Jersey0.41%52.32
 South Carolina0.32%101.81
 Rhode Island0.27%151.53
 North Carolina0.26%161.51
 New Mexico0.12%360.71
 New Hampshire0.09%410.50
 West Virginia0.08%440.48
 South Dakota0.05%470.30
 North Dakota0.03%510.16

Be honest, I bet you didn't think before today that sleeping with a randomly chosen person from Washington DC was literally 100 times more likely to give you HIV than sleeping with a randomly chosen person from North Dakota.

But I've saved perhaps the most surprising one for last. Another statement I hadn't come across much until reading the CDC pages on this stuff was the following:
Blacks/African Americans continue to experience the most severe burden of HIV, compared with other races and ethnicities.
How big, exactly is this disparity?
Blacks represent approximately 12% of the U.S. population, but accounted for an estimated 44% of new HIV infections in 2010. They also accounted for 44% of people living with HIV infection in 2009
That 12% of population being black number seems strangely wrong (the census says Black or African American alone in 2013 is 13.1%). Using the census number gives us an unconditional probability of HIV among blacks of (1.1*0.44)/(318*0.131) = 1.16%. Among non-blacks, we calculated the unconditional probability of HIV as (1.1*0.56)/(318*(1-0.131)) =0.22%. The relative ratio of these two numbers is 5.21. If you need an explanation of why I have absolutely no comment to make about that number, let me suggest to you to a crash course in the last 200 years of US political history. 

No comments:

Post a Comment