Odds ratio vs. relative risk Practice Questions

Question 1

An investigator presents a forest plot from a meta-analysis of six RCTs examining whether a new anticoagulant reduces stroke in patients with non-valvular atrial fibrillation. The image shows individual study odds ratios with 95% confidence intervals and an overall pooled estimate. Studies 1–4 show confidence intervals entirely to the left of the line of no effect. Study 5 shows a confidence interval of 0.74 (95% CI: 0.51–1.08). Study 6 shows a confidence interval of 0.68 (95% CI: 0.45–0.97). Which of the following conclusions is best supported by these results?

Accepted Answer

The pooled estimate is statistically significant and suggests a protective effect of the anticoagulant across the included trials

Answer

Study 5 demonstrates a statistically significant protective effect because its point estimate is below 1.0

Answer

The pooled result is not clinically meaningful because the odds ratio does not approximate the relative risk in this high-prevalence outcome

Answer

Study 6 is not statistically significant because its confidence interval is wide relative to the other studies

Answer

The p-value of 0.003 confirms clinical superiority of the anticoagulant and eliminates the need for further trials

Question 2

A research fellow proposes a nested case-control study within an existing cohort examining antibiotic exposure and C. difficile infection. The mentor suggests this design wastes the cohort structure and that relative risk should be calculated instead. The fellow argues that odds ratios from nested case-control studies approximate relative risk while being more efficient. Evaluate the validity of each position and synthesize the optimal approach.

Accepted Answer

Use nested case-control with OR since it's mathematically equivalent to cohort RR with proper sampling

Answer

Calculate RR from full cohort since all data are available and RR is more interpretable

Answer

Use nested case-control only if computational resources are limited, otherwise use full cohort

Answer

Perform both analyses and compare results to validate the nested case-control approach

Answer

Calculate hazard ratios using Cox regression as a compromise between efficiency and accuracy

Question 3

Two studies examine statin therapy and stroke prevention. Study A (cohort, n=10,000) reports RR=0.75. Study B (case-control, n=2,000) reports OR=0.68. The absolute stroke rate in the general population is 2% over 5 years. Analyze these findings to determine which study provides more accurate information for clinical decision-making and why.

Accepted Answer

Study A because the cohort design allows calculation of absolute risk reduction

Answer

Study B because case-control designs eliminate confounding

Answer

Study B because odds ratios are more generalizable across populations

Answer

Study A because relative risk is always more accurate than odds ratio

Answer

Both are equally valid since stroke is a rare outcome making OR approximate RR

Question 4

A genetic epidemiology study uses a case-control design to examine BRCA1 mutations and breast cancer risk, reporting an odds ratio of 15.0 (95% CI: 8.2-27.4). A patient with a BRCA1 mutation asks what this means for her actual risk of developing breast cancer. Evaluate how to appropriately counsel this patient regarding the study findings.

Accepted Answer

The odds ratio cannot be directly interpreted as risk; population incidence data are needed

Answer

The confidence interval suggests her risk is between 8-27 times higher

Answer

Convert OR to RR using the formula: RR = OR/(1 + P0(OR-1)) where P0 is baseline risk

Answer

Her risk is 15 times higher than women without the mutation

Answer

She has a 15% absolute risk of developing breast cancer

Question 5

A hospital quality improvement team analyzes surgical site infections (SSI) following colorectal surgery. In Year 1 (pre-intervention), 50 of 500 surgeries resulted in SSI. After implementing a bundle protocol in Year 2, 20 of 500 surgeries resulted in SSI. The team debates whether to report odds ratio or relative risk. Apply your understanding to select the most appropriate measure and calculate it.

Accepted Answer

Relative risk of 0.40, because true incidence rates can be calculated

Answer

Relative risk of 2.50, showing the magnitude of improvement

Answer

Odds ratio of 2.78, comparing Year 1 to Year 2

Answer

Odds ratio of 0.36, because it's more stable with small numbers

Answer

Risk difference of 6%, as it's most clinically meaningful

Odds ratio vs. relative risk — MCQs

Odds ratio vs. relative risk — MCQs

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