It was announced this week that, between 2009 and 2018, a computer error meant that 450,000 women aged around 70 in the UK were not sent their final breast screening appointment letter. These women were mistakenly not offered screening that may have picked up a cancer that had developed since their last check three years before. Secretary of State for Health Jeremy Hunt that “there may be between 135 and 270 women who had their lives shortened”. This has been reported as “”.

Presumably this is an estimate of the number of women who would have been diagnosed at this final screen, and would subsequently have benefited from the screening. There are three reasons why this claim is misleading.

First, Hunt said this was the number of women who “had” their lives shortened. But this is not strictly accurate  -  few of these women will have actually died of their breast cancer yet, as only around 15 per cent of 70-year-olds diagnosed with breast cancer die of their disease within .

But they may have benefited from being diagnosed earlier, and this estimate is presumably based on a statistical model of what might happen in the future. Hunt might better have said “there may be between 135 and 270 women who have had their life expectancy shortened”, although this probably would not have prevented the exaggerated headlines.

Second, even a claim of reduced life expectancy would be questionable, as Hunt made clear in his announcement but which remained unreported. There is only weak evidence that screening , particularly for older women –  there is a reason that the screening programme ends at age 70.

Administrative error

Of course, all these statistical statements about life expectancy are about large groups of people and may sound rather cold. It’s a tragedy for any particular woman to have missed her cancer being detected earlier because of an administrative error, and so Hunt is right to be abject with his apology.

But the third issue is that, contrary to popular belief, screening also does harm . The states that, for every 200 women attending screening between the ages of 50 and 70, we would expect one to have her early death from breast cancer prevented, but three to be unnecessarily treated for a harmless cancer that would not have troubled them. It might be worth pointing out that these women (or their doctors) would never know this – they would forever be grateful, thinking that their lives had been saved by the harrowing treatment process. So, it is an invisible harm, difficult to quantify or take into consideration.

But it means that up to 800 women may have been saved from harm by not sending them their final screening appointment letter, as they avoided possible reduction in their life expectancy through unnecessary treatment.

I feel very sorry for the women who missed getting a screening letter and have subsequently been diagnosed with cancer, or even died. Their situation is bad enough without them, and their families and friends, feeling they could have been helped if only they had received that letter. But this will only be true for a small proportion, and nothing will be said to the far larger number of (unidentifiable) women who would otherwise have faced diagnosis and treatment for a condition that would never have harmed them.

There is a complex story behind these headlines, but there is no doubting that Hunt needed to make a strong apology: there was a policy to offer women this screening choice and 450,000 were denied it by a mistake. It may have done harm to some and benefit to others  –  we will never know who, or how many, had which. Unfortunately, this will probably become known as the scandal that caused “up to 270 deaths”.

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IT’S bad, yes, but not that bad. At least, not in the UK. Headline unemployment, the great plughole in economic fortunes, is less gaping than predicted. Yet, contrary to the figures, , which is eroding consumer confidence and stifling recovery.

The country’s unemployment levels have certainly set no records despite the 2008 financial crash sparking a . In fact, UK unemployment rates are so out of line with other economic indicators and what happened in previous recessions – improving even as the economy idles – that economists have been scratching their heads for an explanation.

The is now only 2.5 points higher than the 30-year low that was seen just before the recession began in 2008. So are the British irrationally afraid of a problem which by this measure seems to leave 97.5 per cent of the labour force as it was?

Possibly. But risk is a psychological phenomenon, not just a question of odds, and 2.5 per cent more of the workforce unemployed doesn’t necessarily equal 2.5 per cent more fear – whatever that might mean. Not least because plenty of people might legitimately fear that they could be next.

“2.5 per cent more of the workforce unemployed doesn’t necessarily equal 2.5 per cent more fear”

What’s more, the headline rate of 7.8 per cent may be far from the whole picture, and not for the usual arguments about whether it hides underemployment. Here’s a telling fact: that 2.5 per cent rise in unemployment is equal to about 1 million people in a working population of about 38 million. But the number of jobs that have been lost to unemployment or inactivity since the start of the recession is probably closer to 16 million.

How so? Simply because the headline figures measure the stock of jobless people. The 16 million jobs lost are not the stock, but the . Think of the job market as a revolving door, into and out of work. The stock of unemployment is the number outside at any one time. The flow, on the other hand, is the number who pass through to find themselves outside long enough to be counted as unemployed or inactive, before some get back in (note that the same person can go round more than once).

It can be cold outside, so even if you aren’t out for long that experience matters. To understand the fear of job loss, we should pay more attention to the flow figure. “It could be me” makes more sense in that context.

In both the UK and the US, flow is vastly greater than stock, meaning that experience of unemployment is more common than it appears from the headline figures. In European countries that share the euro common currency, unemployment varies widely but on average it is 12.2 per cent – worse than in the UK – and above a quarter in Greece and Spain. Imagine the still greater proportions who have felt the chill of being on the wrong side of the door.

In the US, the Bureau of Labor Statistics surveys what it calls, appropriately, JOLTs (job openings and labour turnover), of which “layoffs and discharges” are about 1.6 million every month, even as headline unemployment figures fall.

This hints at another striking phenomenon: experience of unemployment is common in good times as well as bad. Labour market churn can be vast at all points of the economic cycle. To change the metaphor, worsening unemployment is a rise in the waves on top of an always turbulent ocean.

Indeed, the difference in job-loss churn between good times and bad is surprisingly small. Before the recession, the average risk of becoming unemployed in the UK – what the UK’s Office for National Statistics calls the “hazard of unemployment” – was about 1.2 per cent every three months. It briefly spiked in late 2008 and early 2009 at 1.9 per cent then fell back. It’s now about 1.4 per cent. So the difference pre-crash to today equals 0.2 per cent, or 1 extra person in every 500 becoming unemployed every three months. Enough to explain the difference between irrational exuberance and gloom? Hardly.

Except that this leads us to one last piece of the combination of job-risk psychology with the data: the difference that it makes to be outside that door.

One measure of this is the chance of getting back inside. Before the recession, about 1 in 3 unemployed people found a job every quarter, but this dropped to about 1 in 4 after the recession began. In early 2008, about 400,000 people had been unemployed for more than 12 months in the UK. By early 2013, this was up to 900,000.

Another measure of life on the outside is to say that the risk is misery. For the young, especially, it can leave a permanent scar on job prospects and wages.

Unemployed people are also more likely to be sick, stressed and depressed, to divorce, commit crime and die early – and research suggests that unemployment makes the difference. Suicide is often said to be one factor in this rising mortality rate; others are heart disease and alcohol.

Estimates of the extra annual risk of death vary. , others put it at around , while one said around . If true, the latter is huge, similar to the average extra risk from smoking 12 cigarettes a day. It’s as if every 24 hours out of work left you 27 hours older.

Look hard at many risks about which people worry and you often find less to fear in the numbers than headlines suggest. Is unemployment an exception? The odds of becoming jobless are both worse than they might appear and subject to potentially huge consequential multipliers. To be sensitive to this seems perfectly rational.