21.2: Describing Risks

We understand risks better when we can describe them in rough numerical terms (e.g., about one person out of every forty-two is killed in an automobile accident). Precise numbers don’t really matter; ballpark figures are enough. It won’t matter to most people whether 37,000 people out of a hundred million or 43,000 people out of a hundred million die each year from lung cancer. But it does make a difference when its 37,000 people out of a hundred million or 370 out of a hundred million.

It will make things more realistic if we work with some actual numbers, so we will use Figure 21.1 below, which gives the leading causes of death among all Americans in 2015 (the most up to date data available at the time of this writing). These figures are based on a report released by the National Center for Health Statistics (the number after each cause of death is the actual number who died; data are based on a review of death certificates).

Risk Ratios

Risks are reported by fractions. They are numbers from 0 to 1, and they can be interpreted as probabilities. We will call these risk ratios. In the case of death rates, the risk ratio is given by a fraction:

Number of Deaths / Number in Target Population

In the case of deaths, the numerator is clear cut; it is simply the number of people who died from a given cause. But the denominator is less clear cut, and in many cases, there will be different ways to express it. For example, in assessing the risk of hang gliding, would we want to express the number of deaths per (over) people who went hang gliding, or the number of hours spent hang gliding? We will return to this important point below. But in the present case we are dealing with conditions that could strike almost anyone, so to keep things simple, we will use the total number of Americans as our denominator.

In the 2010 census the number of Americans tallied just under 309 million. This figure is low, since several million people weren’t counted, and the population has risen since then. If we were aiming to do perfectly accurate risk assessment it would be important to be as precise as possible. Since we

Figure \(\PageIndex{1}\): Causes of Death in America in 2015

are just learning how to do these things we’ll round the population to 300 million to make the math easier. So, we express the death rate for a given medical condition as:

Number of Deaths from Condition / Total Number of Americans

Which is:

Number of Deaths from Condition / 300,000,000

So, for example in 2015 633,842 people died from heart disease, so the death rate for heart disease is:

633,842 / 300,000,000

Numbers with such large denominators are hard to comprehend. It is possible to round such fractions off and reduce them down to more meaningful numbers, but this can take time. We can also use a calculator to divide the numerator by the denominator. This gives a decimal value which is in fact the probability or frequency of a heart attack death. In 2015, this probability number was 0.0021. But this number is so small that it’s hard to comprehend. We need a more user-friendly way to express these numbers.

Deaths per Million

It is often clearest to express risk statistics in terms of number of deaths per million, per hundred thousand or the like. This also makes it easier to compare risks. The general formula for this is just:

(Number of Deaths / Number in Target Population) × c

where c is the common denominator, we use for all of the risks. For example, if we want to express the risk ratio as number of deaths per million, then c is one million (1,000,000). If we want to express them as number of deaths per hundred thousand, then c is one hundred thousand (100,000).

The choice of c is a matter of convenience: select a number that will make the resulting figures as easy to understand as possible. When we are talking about the entire United States, thinking in terms of deaths per one million or even per hundred million makes sense. But if we were thinking about death rates in Norman, OK, a smaller number, like deaths per one thousand, would be easier to understand. The number of heart disease deaths per million people is:

(633,842 / 300,000,000) × 1,000,000

which is approximately 2,113 per one million people. In 2015, 2,113 people out of every one million died from heart disease.

Chapter Exercises

1. Express the death rates for cancer, stroke, diabetes, and suicide:
   1. as a fraction
   2. as a probability
   3. in terms of number of deaths per million people
   4. in terms of number of deaths per hundred million people

Finding a Useful Denominator

Since you probably won’t be compiling risk tables anytime soon, you won’t have to make decisions about the best denominator to use. But you do need to think about the issue, so that you can more easily interpret figures that you read.

If we are thinking about the relative risks of rock climbing and driving a car, it won’t be very useful to express them in terms of the number of deaths (or injuries) out of all 300 million people living in the United States. If we do this, driving a car will look much riskier, since so many more people drive. Instead, we want a denominator that reflects just the actual number of people involved in each activity. We could use the number of people who go rock climbing each year, so that our ratio is number of injuries, say, per number of rock climbers. We could also express the ratio in terms of the number of hours spent rock climbing each year, so that the figure is number of injuries over the total number of hours people spent rock climbing in a given year.

For example, if 700,000 people went rock climbing last year and 150 of them were killed, the relevant ratio would be 150/700,000 = 15\70,000. Alternatively, we could use the number of hours that people spent rock climbing in 2015. Suppose that it is 900,000. If we do this, we would end up with a figure that told us about the number of deaths per 900,000 hours. We could also use a common denominator figure like we did above, to the number of deaths per 100,000 hours (or 1,000 hours, or whatever makes the most sense). It’s useful to try to understand these general ideas, but you won’t need to worry about the details of all of this.

When we think about the riskiness of an occupation (e.g., coal mining), we will probably begin with number of deaths per year over the number of people who were coal miners in that year. But these yearly risks are cumulative. So, if we want to know the risk confronting someone who spends their entire working life as a coal miner, we need to multiply this figure by the number of years the average person works (about 40). This gives the risk that a coal miner will die in the mines at some point in their career.

Choosing an informative denominator is largely a matter of commonsense. For example, suppose we are planning a trip to Anchorage, Alaska and are wondering about the relative risk of driving or taking an airline. We could look at the number of deaths per hour for driving and for flying. But since we are interested in the relative risk of driving or flying for the entire trip, it makes more sense to look at the numbers of deaths per mile. After all, we must travel about the same number of miles with either mode of transportation.

Finding Information about Risks

The United States Census Bureau (https://www.census.gov) has an extensive web site with a huge collection of data (so much that it can be difficult to find what you want). For more data concerning the united states another useful source is the National Safety Council’s Injury Facts page (https://injuryfacts.nsc.org). Internationally the Global Health Observatory out of the World Health Organization (https://www.who.int/data/gho) is an excellent resource. But for specific topics, it is often easiest to do an internet search for the specific information you want. Some of it is reliable, some of it isn’t; as always, the guidelines for evaluating information on the web in 6.3 is relevant here.