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Relative Risk and Odds

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1. The following contingency table summarizes the relationship between exposure to a risk factor and development of a disease.
a. Find the relative risk ratio to compare the risk of disease among exposed subjects to that of unexposed subjects.
b. Find the odds ratio to compare the odds of disease among exposed subjects to that of unexposed subjects.
c. What are the consequences of misinterpreting the odds ratio as a ratio of probabilities?
2. In a randomized experiment involving 500 female athletes, 250 received preventative treatment and 250 did not; 100 of the untreated athletes were injured over the next year, whereas only 25 of the treated athletes were injured.
a. Find the relative risk ratio to compare the risk of injury among untreated athletes to that of treated athletes.
b. Find the odds ratio to compare the odds of injury among untreated athletes to that of treated athletes.
c. What are the consequences of misinterpreting the odds ratio as a ratio of probabilities?
3. Consider the data from Question 2 once again.
a. Obtain a point estimate for the probability of remaining uninjured in the Treated group.
Develop Disease
Do Not Develop Disease
Total
Exposed
200
9800
10,000
Unexposed
100
9900
10,000
Total
300
19,700
20,000
Injured
Uninjured
Total
Untreated
100
150
250
Treated
25
225
250
Total
125
375
500
b. Obtain a point estimate for the probability of remaining uninjured in the Untreated group.
c. Find the ratio of these two probability estimates.
d. Is it fair to conclude that the risk (i.e., chance) of injury is 4 times higher in the Untreated group? Is it fair to conclude that the chance of remaining uninjured is 1.5 times higher in the Treated group? Can both of these statements be correct?
e. Compute the odds of remaining uninjured for both groups, and then find the odds ratio. How does this compare to the odds ratio comparing the odds of injury across groups?

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• The following contingency table summarizes the relationship between exposure to a risk factor and development of a disease.
Develop Disease Do Not Develop Disease Exposed 200 9800
Unexposed 100 9900
Total 300 19,700
Total
10,000
10,000
20,000
RR
OR
• Find the relative risk ratio to compare the risk of disease among exposed subjects to that of unexposed subjects.
= P(Disease | Exposed) / P(Develop | Unexposed) = (200 / 10,000) / (100 / 10,000)
= 0.02 / 0.01
= 2 (note: RR is usually greater than 1)
• Find the odds ratio to compare the odds of disease among exposed subjects to that of unexposed subjects.
= (odds Exposed) / (odds Unexposed) = (200 / 9800) / (100 / 9900)
= 0.020408 / 0.010101
= 2.02
• What are the consequences of misinterpreting the odds ratio as a ratio of ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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