Assessing Random Error, Confounding, and Effect Modification
Although researchers do their best to reduce error within every study, there will always be error. It is important to identify and report any possible error within the research study in order to accurately interpret the research study’s findings. In epidemiologic research, the focus is on assessing confounding and effect modification along with normal statistical measures (p-values, confidence intervals, etc.).
For this Application Assignment, you will calculate and interpret the effects of confounding, random error, and effect modification within epidemiologic research. Read each of the following questions and answer them appropriately:
• Consider each of the following scenarios and explain whether the variable in question is a confounder:
a. A study of the relationship between exercise and heart attacks that is conducted among women who do not smoke. Explain whether gender is a confounder.
b. A case-control study of the relationship between liver cirrhosis and alcohol use. In this study, smoking is associated with drinking alcohol and is a risk factor for liver cirrhosis among both non-alcoholics and alcoholics. Explain whether smoking is a confounder.
• Interpret the results of the following studies
a. An odds ratio of 1.2 (95% confidence interval: 0.8-1.5) is found for the association of low socioeconomic status and occurrence of obesity.
b. A relative risk of 3.0 is reported for the association between consumption of red meat and the occurrence of colon cancer. The p-value of the association is 0.15.
c. An odds ratio of 7 (95% confidence interval: 3.0 – 11.4) is found for the association of smoking and lung cancer.
• The relationship between cigarette smoking and lung cancer was conducted in a case-control study with 700 cases and 425 controls. Using the results below, calculate the crude odds ratio and explain what the ratio means:
o Heavy Smoking—Cases: 450; Controls: 200
o Not Heavy Smoking—Cases: 250; Controls: 225
• A case-control study looked at the association of alcohol use with the occurrence of coronary heart disease (CHD). There were 300 participants in the study (150 cases and 150 controls). Of the cases, 90 participants drank alcohol; of the controls, 60 participants drank alcohol.
Design the appropriate 2x2 table, calculate and interpret the appropriate measure of association.
You suspect that the association between alcohol use and CHD might be confounded by smoking. You collect the following data:
Smokers Non-Smokers
CHD No CHD CHD No CHD
Alcohol Use 80 40 10 20
No Alcohol Use 20 10 40 80
•
Calculate the appropriate measure of association between alcohol use and CHD in both smokers and non-smokers. Discuss whether smoking was a confounder of the association. What is the relationship of alcohol use to CHD after controlling for confounding?
• A study was conducted in young adults to look at the association between taking a driver’s education class and the risk of being in an automobile accident. 450 participants were included in the study, 150 cases who had been in an accident and 300 controls who had not. Of the 150 cases, 70 reported having taken a driver’s education class. Of the 300 controls, 170 reported having taken a driver’s education class.
Calculate and interpret the appropriate measure of association between driver’s education and accidents.
The question arose as to whether gender might be an effect modifier of this association. When gender was assessed, the data looked like the following:
Women Men
Accident No Accident Accident No Accident
Driver's Ed 10 50 60 120
No Driver's Ed 40 50 40 80
Perform the appropriate calculations to test for effect modification. Interpret your results.
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In order to answer the questions regarding confounding, effect modification, and the interpretation of study results, we need to understand the concepts and calculations involved. Let's go through each question one by one and explain how to approach them.
1. Identify Confounding:
a. In a study of the relationship between exercise and heart attacks among women who do not smoke, the variable in question is gender. To determine if gender is a confounder, we need to consider whether gender is associated with both the exposure (exercise) and the outcome (heart attacks) and if it influences the relationship between exercise and heart attacks. If gender meets these criteria, then it is a confounder.
b. In a case-control study of the relationship between liver cirrhosis and alcohol use, where smoking is associated with drinking alcohol and is a risk factor for liver cirrhosis among both non-alcoholics and alcoholics, smoking is a potential confounder. This is because smoking is related to both the exposure (alcohol use) and the outcome (liver cirrhosis) and can impact the observed relationship between alcohol use and liver cirrhosis.
2. Interpret Study Results:
a. An odds ratio of 1.2 (95% confidence interval: 0.8-1.5) for the association of low socioeconomic status and occurrence of obesity suggests that there is no statistically significant association between the two variables. The confidence interval includes the null value of 1, indicating that the effect is not statistically different from no effect.
b. A relative risk of 3.0 reported for the association between consumption of red meat and the occurrence of colon cancer with a p-value of 0.15 suggests that there is no statistically significant association. The p-value is greater than the commonly used significance level of 0.05, indicating that the association may be due to chance.
c. An odds ratio of 7 (95% confidence interval: 3.0 – 11.4) for the association of smoking and lung cancer indicates a strong positive association between the two variables. The confidence interval does not include the null value of 1, suggesting a statistically significant association.
3. Calculate and Interpret Crude Odds Ratio:
The crude odds ratio can be calculated using the formula:
Crude Odds Ratio = (ad/bc) = (450*225)/(250*200) = 2.25
The calculated crude odds ratio of 2.25 means that heavy smoking is associated with 2.25 times higher odds of having lung cancer compared to not heavy smoking in the study population.
4. Calculate and Interpret Measure of Association between Alcohol Use and CHD:
To assess the measure of association between alcohol use and CHD, we can create a 2x2 table as follows:
CHD No CHD
Alcohol Use 90 40
No Alcohol Use 60 110
Using this table, the appropriate measure of association is the odds ratio. The odds ratio can be calculated as:
Odds Ratio = (ad/bc) = (90*110)/(60*40) ≈ 3.25
The calculated odds ratio of 3.25 indicates that those who drink alcohol have 3.25 times higher odds of having CHD compared to those who do not drink alcohol.
To assess whether smoking is a confounder, we need to calculate the measure of association between alcohol use and CHD within each level of smoking status (smokers and non-smokers) and compare them. If there is a difference in the association between alcohol use and CHD within the levels of smoking, then smoking is a confounder. Similarly, we can calculate the odds ratio for both smokers and non-smokers separately.
5. Calculate and Interpret Measure of Association between Driver's Education and Accidents:
To calculate the measure of association between driver's education and accidents, we can create a 2x2 table as follows:
Accident No Accident
Driver's Ed 10 40
No Driver's Ed 60 150
The appropriate measure of association in this case is the odds ratio. The odds ratio can be calculated as:
Odds Ratio = (ad/bc) = (10*150)/(40*60) ≈ 1.88
The calculated odds ratio of 1.88 indicates that those who have taken a driver's education class have 1.88 times higher odds of being in an automobile accident compared to those who have not taken the class.
6. Test for Effect Modification:
To test for effect modification, we need to compare the measures of association between driver's education and accidents within each level of gender (women and men). If the measures of association differ significantly between the levels of gender, then there is effect modification. To assess this, we can calculate the odds ratio for each level of gender and compare them.
Performing the calculations, the odds ratio for women is (10*120)/(40*50) = 1 and for men is (60*50)/(40*80) = 0.94. Since the odds ratios are similar and there is no significant difference, we can conclude that there is no effect modification by gender.