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Thursday, 30 April 2009

Absolute VS Relative Risk Reduction


I've noticed a definite trend with pro circumcisers and statistics. Now as we all know, you can twist statistics to mean pretty much anything you want, and one way to do it is by using absolute and relative risks when it suits you. So, with circumcision, use absolute risk when you're talking about complications of circumcision (and take the smallest possible figure) Then when talking about the potential benefits, use relative risks. Because, when you're talking about a very, very small number, using relative risk makes your gain look MUCH bigger.

Take HIV, as the press is really pushing the alleged link with circumcision at the moment after the 3 Africa studies.  Apparently, the studies showed a 60% reduction in HIV acquisition in the 2 years after voluntary, adult circumcision. Note the latter part, as that is all it does show, since the studies were halted early we do not yet know if circumcision has an effect beyond that, and it is quite possible that the effect becomes lesser as time goes on (Observation of country prevalence of HIV certainly does not bear out that circumcision affects HIV, see the CIA Factbook for that. Note that the United States is right up there as one of the most HIV ridden countries despite around 80% of adult males currently being circumcised there)

The important point is though in terms of absolute vs relative risk reduction is what is the actual risk of catching HIV? Now, I'll admit that I always thought if you had sex with an HIV positive person you had a nigh on 100% chance of catching it. So, I'd forgive people for taking these figures as - 100% chance with unprotected sex, 40% chance with circumcision with the 60% risk reduction, and around 1% with a condom. Schoen touches on the actual risk factor mentioning a figure of 1 in 300, but does not elaborate on what this actually means.

First off where does this figure actually come from? Is he referring to the chance of contracting HIV when having sex with an HIV positive person, or the risk overall of a heterosexual male contracting the disease? It isn't at all clear, and it really seems to me that he simply cherry picked the best possible stat to meet his needs.   A blanket "1 in 300" means very little, because risk of transmission varies by country due to HIV prevalence, and of course viral load in the individual can vary. Some conditions like genital ulcers can make the risk of transmission higher. 

I've heard a lot of parents who circumcise their children state that they want their child to have an extra layer of protection for the "just in case" scenario if a condom breaks or whatever.  Sounds very reasonable, until you look at the actual probability of this occurring. 

This excellent post by Fellow Traveller at Mothering.com spells it out rather well. Quote:

"We'll start the estimate that the chance of infection is 0.06% a bit higher than published in the Lancet article. That means a male having unprotected sex with an HIV positive woman has about a bit more than 1 in 1800 chance of being infected. Base line risk intact men vs circumcised men 1 heterosexual contact with an HIV+ partner.

[1 - 0.0006]^1 99.94% ~= 0.06%
[1 - 0.0006 * 0.5]^1 ~= 99.97% ~= 0.03%

But the HIV distribution in the US population is about 5 in 1000 or 1/200 so, in general, there is only a 1 in 200 chance that one will encounter someone who is HIV positive. Actually, the risk is much lower but we'll discuss that in a bit. Given that the HIV prevalence in the general population is about 1/200, a closer estimate of the risk of becoming HIV infected after the 1 random heterosexual encounters is more like:

The chance of event A (encountering an HIV positive individual in the general population) * the chance of event B the likely hood of getting infected during that encounter.

1/200 * 0.0006 = 0.000003 --- 1 - 0.000003 = 99.9997% = 0.0003%
1/200 * 0.0003 = 0.000006 --- 1 - 0.0000015 = 99.99985% = 0.00015%

Now, the number of sexual encounters is important too. For 1,000 encounters, the difference is 1.5 hundredths of a percent. That's is what circumcision bought you, big deal. Over the course of 1,000 random encounters, on average, an intact guy in the US has 1.5 hundredths of a percent larger chance of becoming HIV positive. Circumcised guys, party on!"

So - parents are being given the information that circumcision will reduce their child's risk of HIV acquisition by 60%, but fail to mention that the actual risk of their child a) coming into contact with an HIV positive partner b) condom failing and c) contracting the virus is a tiny, tiny, fraction.  A 60% reduction of a miniscule base is still miniscule. 

It's also worth looking at the British response to this article here:

"Dr Colm O'Mahony, a sexual health expert from the Countess of Chester Foundation Trust Hospital in Chester, said the US had an "obsession" with circumcision being the answer to controlling sexually transmitted infections. 

He said: "Sure, a dry skinned penis is a bit less likely to contract HIV, herpes and possibly genital warts but it will get infected eventually."

4 comments:

  1. This is very well stated. I would add one thing, just to further clarify the topic. You write:

    "Apparently, the studies showed a 60% reduction in HIV acquisition in the 2 years after circumcision."

    I would state this:

    "Apparently, the studies showed a 60% reduction in HIV acquisition in the 2 years after voluntary, adult circumcision."

    I think it's a critical point to point out that the studies used adult volunteers, which is how they would get through any ethical hurdle. That's not how these studies are being used, which is the problem.

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  2. Good point, Tony, I will amend.

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  3. Tony wow yes, that's a huge difference...

    Claire, thank you so much this is an excellent blog!

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