# Divide and rule: getting rates in a mess

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https://understandinguncertainty.org was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

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I've been a bit inactive in here for a few weeks, because I've temporarily moved to Berlin. But it turns out that one can find bad presentations of risk in the German media too, and here's one, pointed out to me by my new colleague Jan Multmeier. The topic is a serious one: suicide rates in German troops serving abroad, and the error involves dividing by the wrong thing when calculating rates. This featured in an article on the website of the main German TV evening news programme, where the headline originally said *High suicide rate in German forces serving abroad - every fifth soldier takes his own life*. (My translation.)

That would be terrible, if it were true. But it isn't. Indeed the headline was changed in short order to remove the part about "every fifth soldier". That was based on data, provided by the army authorities, saying that, over the twenty years or so since German troops having been serving abroad, there had been 99 deaths in total, and 19 of these were suicides. So indeed, about a fifth of all the soldiers *who had died* had committed suicide - but the headline made it sound as if about a fifth of *all* soldiers serving abroad had committed suicide. That is, the headline was comparing the number of suicides to the wrong reference population - to all soldiers who died, not to all soldiers. In calculating the rate as a fifth, they had divided the number of suicide cases by the wrong denominator.

The rest of the headline still remained, though, saying that the suicide rate in German soldiers serving abroad is high. But is that true? It would be good if no soldiers ever committed suicide, of course, but soldiers are human and that's a vain hope. So perhaps a better question is: is the rate high, compared to what happens in the general population in Germany?

It isn't entirely straightforward to answer that, though. You have to work out what the rate actually is for the troops, and then you have to find an appropriate national rate to compare it with. One commentator, Thomas Wiegold had a try. He worked out the rate for the soldiers by dividing, not by the total number of deaths amongst soldiers, but by the total number of German soldiers who have served overseas in the past twenty years, which is about 300,000. This gives a rate of 6.3 suicides per 100,000 soldiers, which the author then compared to the average suicide rate in the whole population of Germany, which was 11.4 per 100,000 inhabitants in 2007 according to his source (the German edition of Wikipedia). He concluded that the rate amongst the soldiers is relatively low.

Unfortunately, though, that isn't right either. Rates like death rates and suicide rates are usually given as so many per 1,000 people, or so many per 100,000 people, but it isn't always explicitly stated that they are rates *per year* as well. The national rates take this into account. But Wiegold's calculation did not take into account how long the 300,000 soldiers had been stationed abroad. If each of them was there for a year, the calculation would have been fine, but they (probably) weren't. I don't know how long each was abroad, but as a rough guess, let's assume they were there for half a year on average. Then 300,000 soldiers, each there for half a year, is like having 150,000 soldiers there for a full year, in terms of the time they were exposed to the risk of committing suicide. (In the jargon, we say there are 150,000 person-years of exposure.) The suicide rate per 100,000 soldiers per year is then found by dividing the number of suicides, 19, by the number of person-years at risk, 150,000, and then multiplying by 100,000. This gives a rate of 12.7 per 100,000 per year.

Alternatively, the original news article says that the number of German soldiers currently serving abroad is 7,100. If we assume, as a rough estimate, that that is the average number serving abroad over the last 20 years, then the number of person years at risk is 7,100 x 20, or 142,000. This is a bit lower than my previous rough estimate, and gives a suicide rate for the soldiers of 13.4 per 100,000 per year.

To get a more precise figure, we'd need to get better data on numbers of soldiers over time. But it's at least plausible that the suicide rate for German soldiers serving abroad is somewhere round 13 per 100,000 per year.

But how does that compare to the national rate? Well, which national rate? The German Wikipedia page, that I referred to, conveniently gives a chart showing suicide rates for Germany in 2007, for different age and sex groups. (The text is in German, but the meaning is pretty obvious - rates for men are shown in blue, and those for women are in red.) This shows that, as is generally true in industrialised countries, suicide rates are much higher for males than for females, and increase generally with age.

So it's not completely sensible to compare the rate for the soldiers with the national average rate of 11.4 per 100,000 per year. I don't have data on the age and sex of German soldiers abroad, but they will be considerably more likely to be male than is the case in the total population, and they will be from a much more limited age range. The diagram shows that the suicide rates for males in the general population, at ages between 20 and 39, are around 12 or 13 per 100,000 per year. The rate for the soldiers is similar. So it doesn't look, on the basis of fairly crude calculations, as if the suicide rate for German soldiers abroad is much different from the rate for the general population, if we allow for age and gender. (Given a lot of data on the age and gender of the soldiers serving abroad, one could be a bit more precise.)

Tricky things, rates.

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## Comments

Tim (not verified)

Wed, 28/09/2011 - 4:30pm

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