Understanding uncertainty : A 113% chance of death?

A recent study from Harvard reported that people who ate more red meat died at a greater rate. This provoked some wonderful media coverage: the Daily Express interpreted the study as saying that "if people cut down the amount of red meat they ate — say from steaks and beef burgers — to less than half a serving a day, 10 per cent of all deaths could be avoided". 

Well it would be nice to find something that would avoid 10% of all deaths, but sadly this is not what the study says. Their main conclusion is that an extra portion of red meat a day, where a portion is 85g or 3 oz — a lump of meat around the size of a pack of cards or slightly smaller than a standard quarter-pound burger — is associated with a hazard ratio of 1.13, that is a 13% increased risk of death. But what does this mean? Surely our risk of death is already 100%, and a risk of 113% does not seem very sensible? To really interpret this number we need to use some maths.

Let's consider two friends — Mike and Sam, both aged 40, with the same average weight, alcohol consumption, amount of exercise, family history of disease, but not necessarily exactly the same income, education and standard of living. Meaty Mike eats a quarter-pound burger for lunch Monday to Friday, while Standard Sam does not eat meat for weekday lunches, but otherwise has a similar diet to Mike (we are not concerned here with their friend Veggie Vern, who doesn't eat meat at all.)

Each one faces an annual risk of death, whose technical name is their hazard. A hazard ratio of 1.13 means that for two people like Mike and Sam, who are similar apart from the extra meat, the one with the risk factor — Mike — has a 13% increased annual risk of death over the follow-up period (around 20 years).However, this does not mean that he is going to live 13% less, although this is how some people interpreted this figure. So how does it affect how long they each might live? For this we have to go to the life tables provided by the Office of National Statistics.

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