﻿ Statistical concepts > Probability theory > Risks

# Risks

Navigation:  Statistical concepts > Probability theory >

# Risks

The term risk we also associate with probabilities, but again it is often unclear what is meant. In general the concept of risk is the probability that some (adverse) event will occur during a specified time period. For example, the risk of having a fatal car accident in the next 12 months. A widely used guide to the concept of risk to humans is the table produced by Calman (1996, [CAL1]), which we show below.

Calman Chart: Description of risk in relation to risk of an individual dying (D) in any one year or developing an adverse response (A), UK, 1996 [CAL1]

 Term used Risk range Example Risk estimate High >1:100 (A) Transmission to susceptible household contacts of measles and chickenpox 1:1-1:2 (A) Transmission of HIV from mother to child 1:6 (A) Gastrointestinal affects of antibiotics 1:10-1:20 Moderate 1:100-1:1000 (D) Smoking 10 cigarettes/day 1:200 (D) All natural causes, age 40 1:850 Low 1:1000-1:10,000 (D) All kinds of violence and poisoning 1:3300 (D) Influenza 1:5000 (D) Accident on road 1:8000 Very low 1:10,000-1:100,000 (D) Leukemia 1:12,000 (D) Playing soccer 1:25,000 (D) Accident at home 1:26,000 (D) Accident at work 1:43,000 (D) Homicide 1:100,000 Minimal 1:100,000-1:1,000,000 (D) Accident on railway 1:500,000 (A) Vaccination associated Polio 1:1,000,000 Negligible <1:1,000,000 (D) Hit by lightning 1:10,000,000 (D) Release of radiation from Nuclear station 1:10,000,000

Tabulating event data can provide an excellent way of highlighting the relative risks associated with different events. The example shown below was published by Richard Todd in an article for the Huffington Post in December 2017 (results are essentially 10 year averages, some being averages post 9/11):

 Americans killed annually by: Number Islamic jihadist immigrants 2 Far right-wing terrorists 5 All Islamic jihadist terrorists (incl US Citizens) 9 Armed toddlers 21 Lightning 31 Lawnmowers 69 Hit by a bus 264 Falling out of bed 737 Being shot by another American 11,737

The following table provides a somewhat different example of risks, as provided by the UK Health Protection Agency. This shows the estimated risk of death due to lung cancer for different strata of smoker and levels of radioactive radon in the home environment. The overall risks in this case are substantially higher than many other familiar risks, such as death by drink-driving or accidents in the home or at work:

 Indoor radon level (Bq/m3) Non-smoker Ex-smoker, gave up at 30 Ex-smoker, gave up at 50 Current smoker 20 less than 1 in 200 1 in 60 1 in 18 1 in 7 200 1 in 190 1 in 48 1 in 14 1 in 5 800 1 in 100 1 in 28 1 in 8 1 in 3

The figures in the charts above are referred to as absolute risks. If we return to the table in the previous subsection, we can see how such absolute risks might be calculated, and understand a related concept, relative risks:

 Exposed Not exposed Infected A C Not infected B D

From this table we can see that the overall risk of becoming infected is (A+C)/(A+B+C+D), the risk of becoming infected if you are exposed is p=A/(A+B) and if you are not exposed, it is q=C/(C+D). The relative risk of infection is the ratio of the risk if you are exposed to the risk if you are not exposed, so is simply p/q. If this ratio is 1, exposure is not likely to be an important issue, but if it was 20, say, then the risk from exposure would be considered very great. However, the numbers involved matter also. You might (in theory) be 20 times more likely to suffer from blood clots if you take drug X rather than drug Y, but if the probabilities in both cases are close to zero, the relative risks are far less important than the absolute risks, which are negligible. From this we can also see the difference between the risks if exposed versus if not exposed, which is p-q. Likewise, this formulation might be applied to cases where a particular treatment had been applied (e.g. vaccination), and where the differences are very small, the numbers may be inflated by a factor of 1000 or 1,000,000 to provide an indication of increased or reduced risk per 1000 people or per million people.

References

[CAL1] Calman K C (1996) Cancer: Science And Society And The Communication Of Risk. BMJ: British Medical Journal, 313,7060, 799-802