Relative risk; absolute risk


Howard White of 3ie discusses some of the problems we often see in how people handle data in this post, “Using the Causal Chain to Make Sense of the Numbers“.  The essay makes many excellent points which are relevant both to how programmes are designed and how they are evaluated.

However, I have to take issue with one section:

And different ways of presenting regression models can give a misleading sense of impact. A large reduction in relative risk – a ‘good odds ratio’ – can reflect quite a small change in absolute risk. Three randomised controlled trials have found circumcision reduces the risk of transmission during unprotected sex by around 50 percent. The reduction in risk was from around 3.5 percent to 1.5 percent. Just a 2 percentage point absolute reduction, so 50 men need to be circumcised to avoid one new case of HIV/AIDS.

This is a bit misleading. In assessing effects we are interested both in relative and absolute effects, yes.  But White fails to acknowledge here that the absolute risk at the outset (3.5% in the case of the pooled results of the three trials) is a characteristic of the people being researched.  And indeed the absolute risk in the populations in the three studies (Kenya, South Africa, Uganda) was different. The 3.5% and 1.5% figures come from pooling the results of the three trials.  If study subjects had come from a population where the pre-existing HIV prevalence was higher, and risk factors (including unprotected sex) were higher, then the baseline absolute risk would have been more than 3.5%.  If the risk factors had been lower, the baseline risk would have been lower. White’s estimate that 50 men need to be circumcised to avert one infection is not universally valid. In some places it will be many more; in others it will be fewer. This is one of the reasons male circumcision is primarily promoted in higher HIV prevalence settings.

Having said that, “just” a 2% absolute reduction is actually pretty good when compared to other HIV prevention interventions. Especially when you consider that once a man is circumcised, he stays circumcised, so the risk reduction is permanent. Look at it another way: if the intervention being tested led to a 100% risk reduction, then (according to White’s post), that would be “only” a 3.5% reduction in absolute terms. Still doesn’t look very impressive, does it? Except in this case there would be no new infections whatsoever.

The reason the results of these trials (and any trials) are reported as relative risks is because if you want to estimate what the effects of the intervention might be in another population, you have to apply the relative risk reduction to the absolute risk in each and every population. Reporting it any other way is misleading.  White is of course correct that absolute risk reduction is what matters when looking at the overall effect of an intervention or policy, but absolute risk reduction is a function not just of the relative risk reduction of that intervention, but of all the other relevant factors.


Thought experiment


If I offered you a vaccine against a serious infectious disease, and told you it would reduce your chances of being infected by 60%, would you take it?

If I told you there was an alternative that would reduce your chances of being infected by 95%, would you choose the vaccine or the alternative?

The disease is AIDS, caused by the HIV virus. The vaccine is not really a vaccine. It is male circumcision. So I admit my thought experiment may seem a little bit irrelevant to readers without a penis.  In fact, whether your penised sexual partner is circumcised or not, if they are HIV positive it makes no difference to how likely you are to get infected by them.  Circumcision is not protective for either partner during anal sex.

The alternative described above is condom use. You’ve got to use them properly. They’ll protect you whatever your gender and whatever type of intercourse you are having, though you might want to consider using lubricant as well.

There are other alternatives too. You could just not have penetrative sex at all, or you could stick to sex with one non-infected partner (assuming it is someone you can talk openly with about their infection status and other partners). Circumcision won’t make any difference to you if you take these other alternatives.

There’s more. If you are having sex with someone infected who is on antiretroviral treatment, that will go a long way to protecting you.  You can even take ARVs to protect yourself, but like circumcision it will cut down your risk by something like 60%.

Now put yourself in a policy maker’s shoes. You don’t feel you are making inroads on HIV prevention.  People aren’t using condoms or abstaining enough – you’re more or less giving up on the idea that risky sex will ever reduce enough to make a difference. You aren’t getting people on to treatment quickly enough, and the treatment bills are skyrocketing. You figure that if you circumcise a lot of men, you’ll win a major reduction in overall susceptibility to HIV in the population, irrespective of what happens to condom use and treatment.  How to convince men to get circumcised though? What’s in it for them?

What’s worrying me is that it often seems like policy makers are framing male circumcision as something an individual man can opt for to reduce their risk of HIV.  Here is Michel Kazatchkine, head of the Global Fund to Fight AIDS, Tuberculosis and Malaria, talking about the role of treatment in HIV prevention:

This does not mean that we should tell everyone living with HIV or at risk of being infected to go on antiretroviral treatment and to drop established approaches such as male circumcision, using condoms and encouraging people to avoid risky sexual behaviour.”

This may be just a case of clumsy wording.  However, I recently read a national strategy on male circumcision from sub-saharan Africa, which stated that men undergoing the procedure should be told to use condoms until the wound heals.  It also said men should be advised to use condoms during anal sex “since circumcision does not protect during anal sex”.  As if those are the only circumstances under which condom use is still necessary for circumcised men.

And in this promotional video, the young men getting circumcised say they are becoming “real men”. Condom use is mentioned, but barely. Here’s another.

Circumcision is a big deal.  Male circumcision has certainly spared many countries from serious HIV epidemics.  It is relatively cheap and it is permanent. Policy makers want incremental results at population level, and can live with an approach that reduces susceptibility in a population even if it is not fully protective.  If men are consenting to the procedure then isn’t it fair enough? 

Can men be convinced to get circumcised and to use condoms? Maybe, and there are studies that have shown that, men who get circumcised don’t necessarily “risk compensate” by having more unprotected sex.  But if voluntary circumcision starts being sold to men as an alternative to condom use, that won’t do.  It won’t do because it’s not fully protective of those men. It won’t do because it won’t help people who have anal sex, or women whether they have anal sex or not. It won’t do because sex workers already find it hard enough to convince men to use condoms. It won’t do because millions of people still need treatment, and getting them on treatment in itself could have a huge impact on HIV transmission.  It won’t do because HIV has brought into relief myriad other social problems and human rights violations, and the people that will continue to be at risk if we give up on other means of preventing HIV, are also the most vulnerable.  This is demonstrated by the fact that in countries where most men are circumcised, such as in West Africa, population rates of HIV may be lower than 5% but the percentage of sex workers and men who have sex with men who are infected is often in the ten, twenty, and even thirty percent range.  

This is not a manifesto against male circumcision. As I said above, male circumcision has certainly spared many countries from serious HIV epidemics. But for it to work, it needs to be done in context with other interventions. A lot of policy documents acknowledge this, but I’m not sure we’ve figured out how to do it in practice yet.