In modules 3 and 4, we learned about two concepts—risk ratios and confounding—that are important in epidemiology for studying the health effects of exposure to drugs. A risk ratio (or relative risk) tells us how much exposure to a certain factor increases one’s risk of a health outcome. In previous lessons, we have examined how living in the U.S. vs. Saudi Arabia puts one at increased risk of alcohol use disorder, and how drinking alcohol in 19th century America put Cartwright’s medical colleagues at increased risk of death over a 30 year period.
We also learned how the increased risk we observe, for example among drinkers vs. abstainers, may result from confounding by another variable, such as cigarette smoking or being prone to other risk behaviors.
Here you will practice both (1) estimating risk ratios and (2) assessing confounding by a third variable using data on alcohol use, cigarette smoking, and lung cancer in participants of the Framingham study (see optional readings in Lesson 4b). The study followed 4973 men and women, asking them about their alcohol and cigarette use, and then tracking who was diagnosed with lung cancer over several decades.
**For this assignment, you should complete the exercises and answer the questions below in this document and submit.**
Calculating Crude Risk Ratio. First we will calculate three risk ratios:
1) the increased risk of lung cancer associated with cigarette smoking
2) the increased risk of cigarette smoking if one drinks
3) the increased risk of lung cancer associated with drinking alcohol
Table 1. Contingency (or 2 x 2) table showing how lung cancer occurred among Framingham participants who were current smokers and those who were not. In the first row, we calculate that the risk of lung cancer among people who are not smokers is 0.009 or less than 1%. In the second row, we calculate that the risk of lung cancer among current smokers is 0.074 or about 7.4%. In the third row, we calculate the risk ratio for the increased risk of lung cancer among current smokers, which is the risk among smokers divided by the risk among non-smokers. We divide the risk of lung cancer among smokers by the risk of lung cancer among non-smokers, because we want to see how much more of a risk smokers have relative to non-smokers.
| | Total participants | Lung cancer cases | Risk of lung cancer |
| :--- | :--- | :--- | :--- |
| Current smoker | 2358 | 176 | 176/2358 = 0.074 |
| Not a current smoker | 1907 | 18 | 18/1907 = 0.009 |
| | | Risk ratio | 0.074/0.009 = 8.22 |
Interpretation: Based on this, we find that current smokers have a 8.22 times greater risk of lung cancer relative to non-smokers. Comparing to results from epidemiological studies about other factors and diseases, this is a very large risk ratio. However, this does not necessarily mean that smoking causes