I  have just delivered an intensive and demanding weekend refresher course of lectures and demonstrations on radiological safety for a group of chiropractors. Why?

The law and the professions demand that anyone using medical x-ray equipment should have a thorough understanding of x-ray physics and engineering, radiobiology, quality assurance, and the law itself, in addition to their professional  training in anatomy and pathology - and continuing professional education, of course. Before attending my lectures, the students had already received a minimum of five years' academic and clinical training, including hundreds of hours' tuition in radiology, and had on-call access to a specialist radiation protection adviser throughout their professional careers. As a result, they take the same radiographs, with about the same radiation dose, as they could by blindly following the World Health Organisation's Basic X-ray System manual, which takes about an hour to read.

We taught our students how to obtain and record the patient's informed consent to an examination that would  at worst subject him to a 1 in 20,000 risk of developing a fatal tumour in the next 20 years (the natural risk is about 1 in 5). I drove to and from the university. As a sober middle-aged professional, I subject other road users to a 1 in 10,000 risk of  fatal injury each year, but I don't need their signed consent before driving.

We dined in a local hotel. Teenage bar staff were selling alcohol (directly implicated in about 4000 accidental deaths each year in this country, and with probably ten times that number accelerated by chronic consumption of alcohol) and cigarettes (about 100,000 early deaths per year). Staff training? Qualifications? Hazard assessment? Customer dose records? Informed consent? Contingency plans? Employer's liability?

We were not offered beef on the bone[1] (acute hazard nil, risk of long-term effects from chronic consumption known to be less than 1 in 2,000,000) by our trained and certificated chef.  He was under no obligation to tell us which of his products contained peanuts (1 in 200 people are allergic, and press reports suggest about one life-threatening allergic reaction per week in the UK).

It seems to me that the degree of regulation of a hazard is mostly determined by the precision with which it can be measured and controlled, and the smallness of the group responsible for dispensing it. Public perception, and thence the law, has very little to do with the actual probability or impact of a hazard. What can be done to reduce irrational regulation, and promote effective public spending on safety?

I want to propose a condensed, rational and publicly understandable scale of risk.

Define the "absolute risk index" of an event as  R = 10 + log P where P is the probability of  the event occuring at all. The "annual risk index" r = 10 + log p where p is the probability of the event occuring within the next year.

Most human activities with uncertain outcomes, such as business decisions, gambling, and warfare, take place in the region where R lies between 9 and 10. Backing a horse

to win at odds of greater than 20/1 (R = 8.7) is considered entertainment rather than investment, and buying a lottery ticket in order to win  first prize (R = 2.8) is clearly insane. The annual risk index of my dying from any cause is about r = 8.5 and will increase to about r = 9.5 over the next 20 years.

The lifetime risk index of contracting CJD from beef seems to be less than 2.7. Government statistics also suggest that r {death|road accident} = 6.0 [2] and

r {death|work accident} = 5.3. We can distinguish between clearly perceived "safe" industries with r below the mean (including retailing, and work with ionising radiations) and those considered hazardous (r{death|deepsea fishing} = 7.1). Turning to a fashionable hazard, it seems that r {devastation|cometary impact} = 0.1[3]

What I propose is thus a short scale with clear reference levels of public perception, rather like Beaufort wind scales (0 – 5 is “normal” weather, 6 is distinctly uncomfortable, 8 – 10 is hazardous to shipping) and Richter earthquake magnitudes (0 – 2 barely perceptible, 5 – 6 damages buildings, 8 – 9 disastrous, 10 is an irremediable catastrophe).

A hazard with r less than 5, and some concomitant benefit, is likely to be acceptable. You would probably be content to expose your children to individual hazards of

R < 4 in the course of education or entertainment. If the cumulative R (summed over all hazards and exposures) of their first 16 years of life was less than 5, you would be considered a diligent but not overprotective parent. So you might send them on a sailing holiday, but you probably wouldn't persuade them to attempt a solo transatlantic crossing (to date, R {drowning|solo transaltlantic crossing} = 7.5) or join a trawler crew.

R = 10 is inevitable, and if r < 1, it is unlikely to happen to anyone on the planet in the next 12 months.

So much for the underpinning maths and psychology. Social "engineering" needs rules of thumb. By all means educate people about risks with r (fatality) 5, and devote public funds to remediate

r (fatality) > 6. The indices are clear, simple, easily communicated to the public, and can be used to underscore proposed legislation or public works. Motorways? yes. Streetlights on motorways? no.

Back to my cosy course dinner. Parliament should ban the supply of tobacco entirely

(r {death | smoking related disease} = 7.2 at 10 cigarettes per day) restrict the sale of alcohol to 1 unit per adult per day (to keep R < 5) put T-bone steak back on the menu immediately, and require restaurants to offer peanut-free meals

(R {serious harm|peanut allergy} = 9.8)[4]

Was there any point in running the course? It is worthwhile taking x-rays, and doing it well, since chiropractic manipulation without radiological examination could yield R{harm|all causes} values of about 7.5. If the students conscientiously apply what we taught them, R{tumor|xrays} for each patient will be around 5.65 but if they were to merely "follow the book" without training, R = 5.7, so there are probably better ways of spending time and money than on continuing professional education in radiation protection. Perhaps all health workers should learn to counsel smokers.