Questions: Relative Risk Calculation and Interpretation

Question 1

A case-control study reports an odds ratio of 4.0 for the association between a dietary exposure and a disease. A colleague says this means exposed people have 4 times the risk. Why is this claim potentially incorrect?

• A. The OR should be divided by the baseline prevalence to convert it to a risk ratio
• B. Case-control studies sample participants after disease occurrence, so natural denominators are absent and OR cannot be directly read as RR
• C. An OR of 4.0 always understates the true relative risk due to selection bias
• D. The claim is correct whenever the confidence interval excludes 1.0

Answer: (B)

Relative risk requires knowing how many people in each exposure group were at risk — the denominators. In a case-control study, cases and controls are selected by disease status after the fact, so the natural proportions of exposed and unexposed people who developed disease are not preserved. The OR approximates RR only when disease is rare (rare disease assumption); for common outcomes, OR exaggerates away from 1.0 and cannot be interpreted as 'times the risk.'

Question 2

A cohort study reports RR = 1.8 (95% CI: 1.6–2.0) for an exposure with a baseline (unexposed) disease risk of 0.1%. Which conclusion is most accurate?

• A. The exposure is both statistically and clinically significant because RR exceeds 1.5
• B. The exposure is statistically significant but the absolute risk increase is only 0.08 percentage points — likely clinically negligible
• C. The confidence interval indicates the true RR might be as low as 1.6, suggesting the exposure may be protective
• D. An RR below 2.0 is never clinically meaningful regardless of baseline risk

Answer: (B)

Statistical significance (CI excludes 1.0) and clinical significance are separate judgments. Absolute risk increase = RR × baseline risk − baseline risk = 0.8 × 0.1% = 0.08%. Even though the relative elevation is 80%, adding 0.08 percentage points to an already tiny risk is unlikely to influence clinical decisions. Option C misreads the CI: 1.6 is still above 1.0, indicating increased (not protective) risk throughout the interval.

Question 3

The odds ratio from a case-control study is generally a valid substitute for relative risk, regardless of disease frequency in the population.

• T. True
• F. False

Answer: False

The OR approximates RR only when disease incidence is low (roughly < 10%), under the rare disease assumption. When disease is common, odds and probabilities diverge substantially, and the OR exaggerates the association away from 1.0 compared to RR. An OR of 3.0 for a common outcome overstates the true relative risk — treating it as RR leads to inflated effect size estimates.

Question 4

Relative risk can be calculated from cohort studies but cannot be directly calculated from case-control studies.

• T. True
• F. False

Answer: True

RR = Risk(exposed) / Risk(unexposed) requires knowing the denominators — how many exposed and unexposed people were initially at risk. Cohort studies follow defined groups forward in time, preserving these denominators. Case-control studies select participants based on outcome status after the fact, destroying the natural denominators. The calculable measure from case-control data is the odds ratio, which approximates RR only under the rare disease assumption.

Question 5

Explain why an RR of 2.0 might be clinically important in one context but clinically trivial in another, using the concept of absolute risk.

Model answer: RR is a ratio that says nothing about the baseline level of risk. If baseline risk is 30%, an RR of 2.0 means absolute risk increases by 30 percentage points — a massive, clinically critical difference. If baseline risk is 0.01%, an RR of 2.0 adds only 0.01 percentage points — negligible in practice. Clinical decisions depend on absolute risk change, not relative elevation alone.

This is one of the most important critical appraisal skills in epidemiology. Absolute risk increase (ARI) = (RR − 1) × baseline risk. The same RR can justify urgent intervention in a high-risk population and be irrelevant in a low-risk one. This is also why number needed to treat (NNT = 1/ARI) is often more useful for clinical decision-making than RR alone.