MI 580: Principles of Epidemiology
Fall 2023 – Homework 3
Due: Oct 11 at the start of class; 50 points NAME:
Instructions:
For all calculations be as explicit as possible by showing your set up of all calculations related to
the final answer. Showing your work is a component of the homework grade. Please submit
the homework electronically. All calculations can be rounded to one decimal place.
Question 1 [10 points]: Read the Muscat et al. article and answer the following questions.
1a. According to Table 3, what measure of association was used by the authors? (2 points)
According to Table 3, the measure of association used by the authors is the multivariable odds
ratio (95% confidence interval) to estimate the association between handheld cellular
telephone use and brain cancer by amount and duration of use.
1b. Is the above measure of association appropriate given the study design? Explain your
rationale (2 points)
The multivariable odds ratio is an appropriate measure of association given the study design.
The study is a case-control study, which is a retrospective observational study design that
compares the exposure history of cases (individuals with the disease of interest) to that of
controls (individuals without the disease of interest). In this type of study, the odds ratio is a
commonly used measure of association that estimates the odds of exposure among cases
relative to the odds of exposure among controls. The multivariable odds ratio is used to adjust
for potential confounding variables, such as age, sex, and other factors that may be associated
with both the exposure and the outcome. Therefore, the use of multivariable odds ratio in this
study is appropriate and helps to control for potential confounding factors.
1c. Assume that the authors hypothesized that “An increase in number of years of cell phone
use is associated with an increase in brain cancer”. Is this a 1 or 2 sided hypothesis and why? (2
points).
The hypothesis "An increase in number of years of cell phone use is associated with an increase
in brain cancer" is a one-sided hypothesis. This is because the hypothesis predicts the direction
of the association between the exposure (number of years of cell phone use) and the outcome
(brain cancer), and does not make any prediction about the direction of a potential null effect.
A one-sided hypothesis is appropriate when there is strong prior evidence or theoretical
reasons to expect a specific direction of the association. In this case, the authors may have
based their hypothesis on previous studies that have suggested a positive association between
cell phone use and brain cancer, or on the biological plausibility of such an association.
1d. Was the hypothesis in 1c supported by Table 3? Please provide rationale to support your
answer (4 points).
The hypothesis "An increase in number of years of cell phone use is associated with an increase
in brain cancer" cannot be directly supported or refuted by Table 3. Table 3 presents the
multivariable odds ratios and 95% confidence intervals for brain cancer by amount and duration
, MI 580: Principles of Epidemiology
Fall 2023 – Homework 3
of handheld cellular telephone use, adjusted for potential confounding variables. The table
shows that the odds ratios for brain cancer are generally close to 1.0 for all categories of years
of use, except for the highest category of 10 or more years of use, which has an odds ratio of
1.8 (95% CI, 0.8-4.1). However, the confidence interval for this odds ratio is wide and includes
the null value of 1.0, indicating that the association is not statistically significant. Therefore,
Table 3 does not provide strong evidence to support or refute the hypothesis that an increase
in number of years of cell phone use is associated with an increase in brain cancer.
Question 2: [10 points] A case-control study is conducted to assess the association between
aspirin and myocardial infarctions. Prior to conducting the analyses, the researchers decide to
set the false positive rate at 0.10. They set the false negative rate at 0.20. They calculate an
odds ratio of 4.0 and an 90% confidence interval of 1.8 to 6.2. Answer the following questions.
2a. How much statistical power do the investigators have? [2 points]
Statistical power = 1 - = 1 - 0.20 = 0.80
2b. If the investigators increased the sample size, what would happen to your calculation for
2a? [2 points]
If the investigators increased the sample size, the statistical power of the study would increase
as well.
2c. What would happen to the false negative rate if they raised the false positive rate? [2
points]
If they raised the false positive rate, the false negative rate would decrease.
2d. Are the results of this study statistically significant and what conclusions would you make?
Provide a 1 or 2 sentence rationale [4 points]
The results of this study are statistically significant because the confidence interval does not
include 1, which is the null value for odds ratio. The odds ratio of 4.0 indicates that individuals
who take aspirin have four times higher odds of developing myocardial infarctions than those
who do not take aspirin.
Question 3 (20 points)
A study is conducted to look at the association between antidepressant use and suicide risk in
adolescents. The study selected 100 adolescents who were on antidepressants and 100
adolescents who were not on antidepressants. Among the adolescents who were on
antidepressants, 7 committed suicide. Among the adolescents who were not on
antidepressants, 3 committed suicide.
3a. Construct a 2 by 2 table displaying the “disease” and “exposure” relationship. Correctly
label both the disease and exposure variables. [5 points]
Fall 2023 – Homework 3
Due: Oct 11 at the start of class; 50 points NAME:
Instructions:
For all calculations be as explicit as possible by showing your set up of all calculations related to
the final answer. Showing your work is a component of the homework grade. Please submit
the homework electronically. All calculations can be rounded to one decimal place.
Question 1 [10 points]: Read the Muscat et al. article and answer the following questions.
1a. According to Table 3, what measure of association was used by the authors? (2 points)
According to Table 3, the measure of association used by the authors is the multivariable odds
ratio (95% confidence interval) to estimate the association between handheld cellular
telephone use and brain cancer by amount and duration of use.
1b. Is the above measure of association appropriate given the study design? Explain your
rationale (2 points)
The multivariable odds ratio is an appropriate measure of association given the study design.
The study is a case-control study, which is a retrospective observational study design that
compares the exposure history of cases (individuals with the disease of interest) to that of
controls (individuals without the disease of interest). In this type of study, the odds ratio is a
commonly used measure of association that estimates the odds of exposure among cases
relative to the odds of exposure among controls. The multivariable odds ratio is used to adjust
for potential confounding variables, such as age, sex, and other factors that may be associated
with both the exposure and the outcome. Therefore, the use of multivariable odds ratio in this
study is appropriate and helps to control for potential confounding factors.
1c. Assume that the authors hypothesized that “An increase in number of years of cell phone
use is associated with an increase in brain cancer”. Is this a 1 or 2 sided hypothesis and why? (2
points).
The hypothesis "An increase in number of years of cell phone use is associated with an increase
in brain cancer" is a one-sided hypothesis. This is because the hypothesis predicts the direction
of the association between the exposure (number of years of cell phone use) and the outcome
(brain cancer), and does not make any prediction about the direction of a potential null effect.
A one-sided hypothesis is appropriate when there is strong prior evidence or theoretical
reasons to expect a specific direction of the association. In this case, the authors may have
based their hypothesis on previous studies that have suggested a positive association between
cell phone use and brain cancer, or on the biological plausibility of such an association.
1d. Was the hypothesis in 1c supported by Table 3? Please provide rationale to support your
answer (4 points).
The hypothesis "An increase in number of years of cell phone use is associated with an increase
in brain cancer" cannot be directly supported or refuted by Table 3. Table 3 presents the
multivariable odds ratios and 95% confidence intervals for brain cancer by amount and duration
, MI 580: Principles of Epidemiology
Fall 2023 – Homework 3
of handheld cellular telephone use, adjusted for potential confounding variables. The table
shows that the odds ratios for brain cancer are generally close to 1.0 for all categories of years
of use, except for the highest category of 10 or more years of use, which has an odds ratio of
1.8 (95% CI, 0.8-4.1). However, the confidence interval for this odds ratio is wide and includes
the null value of 1.0, indicating that the association is not statistically significant. Therefore,
Table 3 does not provide strong evidence to support or refute the hypothesis that an increase
in number of years of cell phone use is associated with an increase in brain cancer.
Question 2: [10 points] A case-control study is conducted to assess the association between
aspirin and myocardial infarctions. Prior to conducting the analyses, the researchers decide to
set the false positive rate at 0.10. They set the false negative rate at 0.20. They calculate an
odds ratio of 4.0 and an 90% confidence interval of 1.8 to 6.2. Answer the following questions.
2a. How much statistical power do the investigators have? [2 points]
Statistical power = 1 - = 1 - 0.20 = 0.80
2b. If the investigators increased the sample size, what would happen to your calculation for
2a? [2 points]
If the investigators increased the sample size, the statistical power of the study would increase
as well.
2c. What would happen to the false negative rate if they raised the false positive rate? [2
points]
If they raised the false positive rate, the false negative rate would decrease.
2d. Are the results of this study statistically significant and what conclusions would you make?
Provide a 1 or 2 sentence rationale [4 points]
The results of this study are statistically significant because the confidence interval does not
include 1, which is the null value for odds ratio. The odds ratio of 4.0 indicates that individuals
who take aspirin have four times higher odds of developing myocardial infarctions than those
who do not take aspirin.
Question 3 (20 points)
A study is conducted to look at the association between antidepressant use and suicide risk in
adolescents. The study selected 100 adolescents who were on antidepressants and 100
adolescents who were not on antidepressants. Among the adolescents who were on
antidepressants, 7 committed suicide. Among the adolescents who were not on
antidepressants, 3 committed suicide.
3a. Construct a 2 by 2 table displaying the “disease” and “exposure” relationship. Correctly
label both the disease and exposure variables. [5 points]
