Go Figure: How can you explain cancer clusters?

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After 25 years, cancer clusters near nuclear power plants are still being investigated. It's a battle with the forces of chance.

This is an experiment. No real cancers are involved. But that's the point. We're going to see if we can make a game of pure chance look like something real and meaningful.

Why? Because this week an official report in the UK stated that radiation from nuclear power stations does not cause increased levels of childhood leukaemia.

A conspiracy, allege critics. Statistical lies, say others. The problem is obvious, they argue.

The Committee on Medical Aspects of Radiation in the Environment (COMARE), first investigated the question 25 years ago. It's still at it.

And the reason, both for some people's scepticism and for COMARE's 25-year struggle to find a definitive answer, is the role of chance.

Can we recreate the problem? Here goes.

First, make some random dots for a graph. You can do this in Excel or similar by typing the formula for a random-ish number and copying it, say 100 times. Do this for the two axes of the chart and you have the coordinates for a random-ish scattering of 100 dots.

Basic spreadsheets will turn this into a chart in one click or two. Remove the grid lines and the axes and it looks like this.

What we see are some big spaces, small patterns or lines and - hey presto - clusters, and all by chance. Now imagine that each of those dots is a case of cancer dropped into the population. So let's superimpose them on any old bit of map.

And then note, for example, those suspicious concentrations on one side of Wolverhampton, while the other side is strangely unaffected.

In other words, how easy it is to take chance distributions and start to speculate about meaning in them. Our experiment is crude. It takes no account of population density, for example, but the principle is straightforward - chance often appears like something meaningful.

If that sounds like a dismissal of people's fears about cancer around nuclear power plants, well, it's not meant to be. For the acute difficulty, still - after 25-years of investigations - is how to be sure what kind of cluster we see at two sites in particular. A cluster of chances with mixed causes, a bit like our dots? Or a cluster from one cause, such as radiation. And if from one cause, which one?

Those who think this an idiotic question are locked in another argument over chance.

For even if it is concluded that a cluster is bigger than we'd expect from chance and mixed causes alone - as indeed it is in a couple of cases - we have to reconcile this with the fact that there were similar clusters at sites that had been identified for plants that were not subsequently built.

That is, maybe the clusters are real clusters, but maybe the cause is not radiation, but a virus, for example. Perhaps this is caused, according to one hypothesis, by population movement of the type we see when lots of people come together for a big construction project.

So it may all be down to population movement, and simply a matter of chance that this movement happened in some cases to be linked to a nuclear power station.

Maybe. Because the report recommends continued monitoring of the data. Until we have an accepted explanation, the case isn't closed.

COMARE's 14th report, called "Further consideration of the incidence of childhood leukaemia around nuclear power plants in Great Britain" is long and complicated. But if you want to see what the slog of statistical sleuthing looks like, it's well worth reading.

Unrelated, but also worth a good look, are a set of animated graphical storyboards from the Office for National Statistics (ONS), which now has an ONS YouTube channel.

The expertise in the ONS is one of the most untapped resources in public argument. But maybe it's beginning to see more daylight.

Image caption The ONS now has a YouTube channel

Stick with it during the small print at the beginning and follow the charts, for example, on jobs and the recession, here.

Others include graduate earnings, the effect of bad weather on GDP, and savings for retirement. Exemplary briefings all.

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