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".

Yummy.

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.

The row of the life table corresponding to age 40 is shown below.

*cohort*life tables, rather than the standard

*period*life table, and according to the current cohort life table for England and Wales, a 40-year-old can expect to live another 46 years. Since we assume Sam is consuming an average amount of red meat, we shall take him as an average man. We can see the effect of a hazard-ratio of 1.13 for Mike by multiplying all the $q_x$ columns by 1.13 and recalculating $d_x$ and the life expectancy from age 40, which gives us 39 extra years for Mike. So the extra meat is associated with (but did not necessarily cause) the loss of one year in life expectancy.

Over 40 years this is 1/40th difference, or roughly one week a year or half hour per day. So a life-long habit of eating burgers for lunch is associated with a loss of half an hour a day, considerably more than it takes to eat the burger. As we showed in our discussion of microlives a half-hour a day off your life expectancy is also associated with two cigarettes a day and each day of being 5 Kg overweight.

Of course we cannot say that precisely this time will be lost, and we cannot even be very confident that Mike will die first. An extremely elegant mathematical result says that if we assume a hazard ratio $h$ is kept up throughout their lives, the odds that Mike dies before Sam is precisely $h$. Now odds is defined as $p/(1-p)$, where p is the chance that Mike dies before Sam. Hence $$p=h/(1+h)=0.53.$$ So there is only a 53\% chance that Mike dies first, rather than a 50:50 chance. Not a big effect.(The elegant result is proved here.)

Finally, neither can we say the meat is directly causing the loss in life expectancy, in the sense that if Mike changed his lunch habits and stopped stuffing his face with a burger, his life expectancy would definitely increase. Maybe there's some other factor that both encourages Mike to eat more meat and leads to a shorter life.

It is quite plausible that income could be such a factor — lower income in the US is associated with both eating more red meat and reduced life expectancy, even allowing for measurable risk factors. But the Harvard study does not adjust for income, arguing that the people in the study — health professionals and nurses — are broadly doing the same job. But, judging from the heated discussion that seems to accompany this topic, the argument will go on.

### About the author

David Spiegelhalter

David Spiegelhalter is Winton Professor of the Public Understanding of Risk at the University of Cambridge. David and his team run the *Understanding uncertainty* website, which informs the public about issues involving risk and uncertainty.