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. **
**Please give responses to 3 decimal places of precisions (e.g. 0.013)**
Calculating Crude Risk Ratio. First we will calculate three risk ratios:
• the increased risk of lung cancer associated with cigarette smoking
• the increased risk of cigarette smoking if one drinks
• 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 0.013 or 1.3%. In the second row, we calculate that the risk of lung cancer among current smokers is 0.091 or about 9.1%. 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
215
215/2358 = 0.091
Not a current smoker
1907
25
25/1907 = 0.013
Risk ratio
0.091/0.013 = 7.000
Interpretation: Based on this, we find that current smokers have a 7.00 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 lung cancer. It only means that smokers have a much greater risk of lung cancer than non-smokers. In other words, smoking is correlated with lung cancer. Please see lecture 4a for interpretation of risk ratios that are greater than 1, less than one, and about equal to one
Table 2. Contingency (or 2 x 2) table showing how lung cancer occurred among Framingham participants who reported drinking alcohol vs. those who did not. Using the same approach as in Table 1, calculate the: (1) risk of lung cancer among those individuals who reported drinking, (2) the risk of lung cancer among those who did not report drinking and (3) the risk ratio (show your work in the gray box in table 2). Finally, interpret the risk ratio below under Q4.
Total participants
Lung cancer cases
Risk of lung cancer
Reports drinking alcohol
2887
196
Q1
No reported drinking
1378
44
Q2
Risk ratio
Q3
Q4. Interpret the risk ratio from Table 2 here.
Table 3. Contingency (or 2 x 2) table showing how alcohol consumption is related to cigarette smoking among Framingham participants. Using the same approach as in Table 1, calculate the: (1) risk of smoking if one also drinks, (2) the risk of smoking among non-drinkers and (3) the risk ratio (show your work in the gray box in table 2). Finally, interpret the risk ratio below under Q8.
Total participants
Current smoker
Risk of smoking
Reports drinking alcohol
2887
2011
Q5.
No reported drinking
1378
461
Q6.
Risk ratio
Q7.
Q8. Interpret the risk ratio from Table 3 here.
Assessing confounding. In Table 2, you should have found that individuals who drink, have an increased risk of lung cancer. However, you should have also found that people who drink are also more likely to smoke from Table 3. We also know from Table 1 that people who smoke are more likely to have lung cancer. Thus, it is possible that the observed relationship between drinking and lung cancer is due to smoking cigarettes rather than directly due to drinking. To assess this, we can stratify our sample into those individuals who smoke and those who don’t and analyse these samples separately. If the risk ratio between drinking and lung cancer reduces substantially toward 1 (meaning no effect) when we stratify on smoking, this is evidence that smoking confounds the relationship between drinking and lung cancer For simplicity, here we will consider only those individuals who smoke.
Table 4. Contingency (or 2 x 2) table showing how alcohol consumption is related to lung cancer among only those Framingham participants who smoke. Using the same approach as in Table 1, calculate the: (1) risk of lung cancer among smokers who drink alcohol, (2) the risk of lung cancer among smokers who don’t drink and (3) the risk ratio of getting lung cancer comparing smokers who drink versus those who don’t drink (show your work in the gray box in table 2). Finally, interpret the risk ratio below under Q8.
Total participants
Lung cancer cases
Risk of lung cancer
Reports drinking alcohol
1906
212
Q9.
No reported drinking
451
48
Q10.
Risk ratio
Q11.
Q12. Interpret the risk ratio from Table 4 here
Q13. Compare the following two risk ratios for the increased risk of lung cancer from drinking
• The one you calculated in Table 2 with a sample including everyone
• The one you calculated in Table 4 when we only consider smokers.
Does stratifying by smoking change the risk ratio? If so, in what direction and by how much? Based on this data, do you think there is evidence of confounding of the relationship between alcohol consumption and lung cancer by cigarette smoking? Recall, that a risk ratio much greater than one implies increased risk, a risk ratio around one implies no effect, and a risk ratio less than one means a protective effect.
