# A primer on calculating attributable morbidity and mortality

Quantifying the impact of exposure to environmental hazard on a population is probably easier than you think.  It requires basic math (subtraction, addition, multiplication and division) and data that are often available from public online sources.  Quantifying the impact of exposure to hazard is useful because it helps put the primary consequences of exposure to environmental hazards into proper perspective, which is very important for making decisions about the health information we often encounter in the world.

I am going to use this post to explain the process of quantifying risk in terms of attributable morbidity (but it could be used to calculate attributable mortality as well).  I have demonstrated this simple technique to undergraduate students in my environment and health class for about 6 years, and this example is based on some work of a student from a few years ago.  The data I use in this calculation are from public sources, and I provide links to them in text. This process will give you a sense of how easy it is to approximate the impact of  exposure to some environmental hazard on a community or population.

With this in mind, I would caution that this process should not be viewed as exact; this is a simplification based on data that probably have error.  As such, it is my practice to err on the side of overestimating risks of harm.  In environmental health ‘uncertainty factors’ are often used to accomplish this–they are basically multipliers of risk estimates that ensure human safety is protected whenever the science is unclear.

The example I will use is lung cancer risk due to exposure to radon in the city of Winnipeg, Manitoba Canada.  My intent is to come up with an estimate of the number of cases of lung cancer due to residential radon exposure.  I will refer to this as attributable morbidity (AM).

The basic idea behind attributable risk is to calculate the difference in morbidity between persons in a population who are exposed to an environmental hazard and persons who are not.  For example, consider a population of 1000 people, half of whom are exposed to a hazard.  Now among those who are exposed there are 10 sick people and in the non-exposed there are 5 sick people.  If the exposed and unexposed populations were otherwise the same, it is easy to see 5 cases of illness are attributable to exposure to hazard.

In the real world we very often lack precise measures of incidence and exposure in the settings we’re interested in, so we need to cobble together estimates of AM based on other data.

What data do I need to calculate AM?  At the very least I need:

1. The underlying or baseline incidence of lung cancer
2. The risk of lung cancer due to radon exposure per dose of exposure (a dose-relative risk)
3. Estimate of exposure to radon in the population

1. Baseline incidence

I found baseline lung cancer incidence for Canada from the Canadian Cancer Society, who report cancer incidence at 58 per 100,000 for men and 48 per 100,000 for women.  I’ll use 52 per 100,000 as a weighted half-way point between the two (it’s weighted because there are more women than men, so the population average should be slightly more like the estimate for women than the estimate for men).

Baseline lung cancer incidence is 0.00052

2. Dose-specific risk

The WHO has published a handbook on the cancer risks associated with radon exposure, from which we can obtain a risk of lung cancer per dose of exposure.  In this report they conclude that there is a 16% increase in the risk of lung cancer for every 100 Bq/m3 long-term residential exposure to radon .  I convert this into a measure of relative risk (RR=1.16).

Dose-specific relative risk is 1.16 per 100 Bq/m3

3. Exposure to radon in the population

According to a Health Canada report, 12.1% of Winnipeg homes have a concentration of exposure at or above 200 Bq/m³.  I will assume that 12.1% of the homes is equivalent to 12.1% of the population, so if we multiply Winnipeg’s population (663,000) by 12.1%, we get 80,233 people exposed at the 200 Bq/m³ level.

Population exposed is 80,233 (note that this ignores lower and higher exposure levels)

4. Final calculations

If we assume that risk from exposure is linear and additive (where doubling the dose of exposure results in a doubling of risk), then the relative risk of lung cancer for persons in Winnipeg is 1.32 (16% x 2 and converted into relative risk).  If these 80,233 people had the Canadian average risk of lung cancer, we would expect

80,233 x 0.00052 = 42

cases of lung cancer in this population every year.  The additional risk they experience is

80,233 x 0.00052 x 1.32 = 55

cases of lung cancer every year.  The difference between these values is the lung cancer attributable morbidity (AM) for radon, in this example, 13 cases per year.  Because I like to be conservative, I will multiply this value by an uncertainty factor of 2, resulting in an AM of 26.  I’ll treat this as the upper limit of my AM estimate.  This means that I estimate that Winnipeg has has a radon attributable lung cancer morbidity of somewhere between 13 and 26 per year.  Given that Winnipeg probably has somewhere around 350 lung cancer cases a year, this means that between roughly 5 and 10% of lung cancer cases may be the result of residential radon exposure.

5. Limitations

There are many limitations with this approach.  For one, radon exposures at higher or lower than 200 Bq/m³ may increase risk of lung cancer, so 13 cases might be a low estimate of total AM.  This is partly why I multiplied the calculated AM by 2.  There is also a possible interaction between radon exposure and smoking; some of the risk of lung cancer is due to these factors combined, and this may not be accounted for in these calculations.  Furthermore, the data I used for the calculations are estimated with error, and some of that error propagates–is carried through–my calculations.  But the 13-26 AM I have calculated is probably in the ballpark of correct, and more importantly, I have demonstrated an easy but useful way to quantify the impact of exposure to an environmental hazard on health.