Don't react: think

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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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DJS New Scientist, July 2009

The actors in the unfolding swine-flu drama are providing a riveting case study of different responses to risk. The government try to stay coolly controlled and consistent, parts of the media search for sensational stories (with the mainland European press revelling in their portrayal of Britain as a land gripped by pestilence), and individuals express the usual range of responses from nervous anxiety to stoic acceptance.

History should warn us about the unintended consequences of over-reacting to events. Individuals may be fearful and make things worse for themselves: in the year after 9/11 people avoided airline travel in the US and this led to 1500 additional deaths on the roads – more than 6 times the number of air passengers that died on 9/11. Officials can panic: the classic example is the 1995 urgent fax sent out to UK general practitioners warning that 3rd generation oral contraceptives were associated with a doubling of the risk of deep-vein thromboses – women stopped taking the pill, there were thousands of subsequent additional abortions, and all because of an over-reaction to a 1/7000 risk being doubled to 2/7000.

There is a wide diversity of opinion about which official responses to risk have been similarly over-zealous. Claimed candidates include GM foods, car seats for children, restrictions on dangerous dogs, BSE, passive smoking, food safety, fire hazards, ecstasy, the millennium bug, asbestos, children’s adventure holidays, electro-magnetic fields from power lines or mobile phones, climate change and so on and so on – try ticking off which risks you feel have been blown out of proportion.

Perhaps the greatest danger is in a government feeling they must respond to popular clamour following a high-profile event with an innocent and vulnerable victim. When a baby is killed, or there is a murder by someone who has been identified as mentally ill or is on probation, people are quite reasonably shocked and feel that ‘something must be done’ to stop such things happening again. But will additional bureaucracy help? While the causes of individual tragedies may be apparently clear, this does not mean similar events can be easily prevented in the future, since there is an essential lack of predictability. A basic problem is that most ‘bad’ things happen to, or are done by, low-risk people, and so attempts to prevent all ‘bad’ things may well have a high negative impact with little apparent gain. This is quite a tricky idea and is best explained using a fictitious, but not unrealistic, example.

Suppose 1 in 1600 of people on probation commit a serious further offence, but some are more likely to offend than others. These high-risk people offend at 3 times the rate of the low-risk. Suppose 7.5 per cent of probationers are classified as high-risk. If you locked them all up, what might be the consequences?

Counterintuitively, you’d make very little impact but impose considerable cost and loss of liberty.

How so? Imagine you had 8000 people on probation. Of these, 600 (7.5%) are high-risk, and 1 of them commits an offence. The other 7400 are low-risk and 4 commit an offence, that’s 3 times the rate of the low-risk probationers. Overall, by locking up all high-risk cases you will only prevent 1 out of the total of 5 offences, so still leave 80 per cent of offences occurring.

So what might at first seem a reasonable policy can be revealed by careful analysis to be an over-reaction. For example, when a UK TV personality, Jade Goody, died of cervical cancer aged only 27, there were strident newspaper campaigns to lower the age of cervix screening. This was resisted by the national screening programme on the basis of statistical modelling.

A group of deaths provokes additional concern and expectation of action, and so for example vast sums are spent on rail safety after high-profile accidents. This has had a substantial impact: in 2008 not a single passenger was killed in a train accident in the UK, compared to 60 years ago when there were at least 50 every year. However it is easy to overlook the fact that 279 members of the public were killed on UK railways in 2008, around the same number as 60 years ago - they were nearly all trespassers and suicides, but one can imagine the public reaction had their deaths all occurred together. posed a very limited risk”

Contrary to popular opinion, the powers that be are well aware of the tendency to overreact to risk. The UK has even had a series of semi-official bodies specifically to identify official over-reaction and discourage excessive interference in people’s lives, including the recently-disbanded Risk and Regulation Advisory Council (RRAC). They identified, for example, a proposed british standard for tree inspection that had “been put together by a rather narrow group led by arboriculturalists who stand to gain from its adoption”, but which threatened to lead to large-scale felling of trees that posed little danger. The RRAC declared itself as “fighting zero-tolerance of risk”, but its successor to continue the battle has yet to be established.

Meanwhile the slow increase in swine-flu deaths is encouraging claims that there has been an over-reaction by government and the media. The worst-case planning scenario by the UK Department of Health projects 65000 deaths, while a more optimistic and possibly more reasonable set of assumptions projects 6000 deaths, 1 in 10,000 of the population, below the number expected from seasonal flu. But it’s the age distribution of these deaths that is crucial – young people are apparently least resilient, and if that mortality rate occurred for all ages in England and Wales it would double the annual number of deaths of 5-14 year-olds from around 700 to 1400.

Why does this appear alarming, when for oral contraceptives we were happy to say that a doubling of a very low risk of thrombosis was no reason for panic? Perhaps because we are so unused to child deaths? Perhaps it’s because the 700 extra deaths should not be compared to the current total of 700, but to the much smaller number that occur unexpectedly to previously well children? In any case it shows that reacting to risk is a constant juggle between the emotional and the analytic parts of our mind, and that although looking coolly at the numbers can help, it is only part of the story.