Are there dangers in breast cancer screening?

Critics say screening can lead to unnecessary treatment

GO FIGURE Different ways of seeing stats

Women going for routine breast cancer screening are being misled about the risks of false positives and unnecessary treatment, a recent report suggested. But it's vital to get the numbers in context, says Michael Blastland in his regular column.

Go for a scan and you might end up with surgery you don't need.

It's been argued, with some merit, that NHS information leaflets state the benefits, but ignore the biggest risks.

The latest news shifts the emphasis to what might go wrong. But that can also go too far. We need both sides of the story - how big are the risks compared with the benefits?

Many of us hate uncertainty - doubt mixed with fear is a horrible combination Breast screening info 'misleads'

There are two steps to seeing them in proportion. The first is that a test can be wrong. There's evidence that many doctors don't understand the simple maths of this.

Say that routine screening is 90% accurate. Say you have a positive test. What's the chance that your positive test is accurate and you really have cancer?

The surprise is that it's impossible to answer that question correctly with the information given. But many doctors think otherwise. They think a positive test that's 90% accurate means it's 90% likely to mean cancer. Not so.

It sounds puzzling, but a picture makes it clear. First, let's stop talking percentages, and talk about a real number of women. And let's give more information - that if you take 1,000 women randomly, of mixed ages, very roughly 10 will have breast cancer. These numbers are not intended to be precise, but are not far off. We've rounded everything to make it easier. Now for the chart.

Suddenly, we see how most of the positives from routine screening are false alarms, occurring among women who don't have cancer. Of all the women who have positive tests, only about one in ten will truly have cancer, but they won't yet know which.

That's how a test with 90% accuracy can result in only about 10% certainty, and why thinking about it in percentages can leave some people muddled. Our advice is - don't. Think in people instead.

So one risk of screening is anxiety - thinking a positive test means you're almost sure to have it, when in fact you're not - an anxiety that could be lessened if people knew these facts. That they often aren't told this is odd, to say the least.

The NHS advocates screening

But don't stop there. Because screening has narrowed the doubt. If you have a positive test, you now have a one in ten chance of cancer instead of one in 100. And if you have a negative test, the chance is now even lower than before.

The next step is similar but more serious. Almost all false positives are cleared up - though sometimes it takes a biopsy to find out - but not all, and some lead to unnecessary treatment.

A small number of cases show an unusual cellular state that might develop into full-blown cancer, but some won't - and again we don't know which. Those that were destined to be harmless but are removed anyway are another kind of false alarm.

And there's a third kind. Some people, even though they really do have cancer, would die of something else before the cancer finally struck. Again, we seldom know which.

Put the doubts together and, according to the critics, the picture is now roughly this for a group of 2,000 women.

We start with 2,000 women this time in order to show up the one case of unambiguous benefit. We've also shown all the uncertain cell states as among the false positives. But all this might be too pessimistic.

For example, screening's critics judge it on the number of people invited to attend, not on the number who do. So some deaths - among people who don't attend - are set against screening's success rate when arguably they ought not to be. According to the NHS, the true picture is better.

And there are two other important caveats. First, judging screening by one measure, survival or death, is crude. There are other benefits of being diagnosed early that don't show up in this analysis.

Second, the older you are, the greater the likely benefit of screening. On these figures, given the number of women who go for screening, the NHS says about 1,400 lives are saved each year.

One statistical campaigner, Professor Gerd Gigerenzer of the Max Planck Institute, has been arguing for the information to be shown this way for years. It's not obvious why it isn't. What the technique mostly helps us see is the element of uncertainty.

But perhaps that is part of the explanation. Many of us hate uncertainty. Doubt mixed with fear is a horrible combination, "give me a test and tell me the correct answer", a justifiable hope.

But it is also often an impossible expectation. We can narrow the doubts, sometimes by a large margin, but we can't eliminate them. Should the NHS strive to explain that, or to offer the reassurance most people crave? And what if doctors offer advice having misunderstood the degree of uncertainty?

The decisions are painful enough, all the more reason to be as clear as we can about the balance of risks and benefits.

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• Someone has to say it, but it doesn't half get boring trying to change this habit.

Reports this week of the effect of drinking on breast cancer - and other cancers - failed miserably - again - to say how many people are affected. They all simply give percentage increases. A drink every day increases your chance of breast cancer by 12%.

But here's a simple fact that everyone knows - except journalists, apparently. When playing Who Wants to Be A Millionaire, a 100% increase in your money can be worth next to nothing, or a fortune, depending where you start.

A 12% increase can similarly mean a lot, or a little. Did the news reports tell us where any of the cancers starts?

Of course not. Nothing so helpful. The answer, as we learnt above, is that a bit less than 10 women in 100 have breast cancer in a lifetime. So a 12% increase if they all consume one extra drink ever day, takes us to