When odds ratio approximates relative risk

When odds ratio approximates relative risk

When odds ratio approximates relative risk

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OR vs. RR - Tale of Two Ratios

  • Relative Risk (RR): Compares the risk of an outcome in an exposed group to the risk in an unexposed group. The primary measure for cohort studies.

    • Formula: $RR = [a/(a+b)] / [c/(c+d)]$
  • Odds Ratio (OR): Compares the odds of prior exposure in the disease group to the odds of prior exposure in the control group. The primary measure for case-control studies.

    • Formula: $OR = (a/c) / (b/d) = ad/bc$

2x2 Contingency Table for Exposure and Outcome

  • When OR ≈ RR: The OR approximates RR when the disease prevalence is low (the "rare disease assumption").
    • With low prevalence, the number of cases (a and c) is negligible compared to the non-cases (b and d).

⭐ The Odds Ratio is the primary measure of association in case-control studies, as incidence (and thus Relative Risk) cannot be directly calculated.

The Approximation - When Odds Meet Risk

The Odds Ratio (OR) is a good approximation of the Relative Risk (RR) under the rare disease assumption.

  • Core Principle: When a disease has a low prevalence (or incidence in case-control studies), the OR will closely estimate the RR.
  • Threshold: The approximation holds well when disease prevalence is <10%.

📌 When the disease is RARE, the OR and RR are RELATIVELY the same.

The mathematical basis is that for a rare disease, the number of individuals with the disease (a and c) is negligible compared to those without it.

  • Thus, a+b ≈ b and c+d ≈ d.
  • This simplifies the RR formula: $RR = [a/(a+b)] / [c/(c+d)] ≈ (a/b) / (c/d) = OR$.

⭐ The OR always overestimates the RR when the RR is >1, and underestimates the RR when the RR is <1 (i.e., it's always further from the null value of 1).

Divergence Details - When OR Overstates

  • Primary Condition: OR significantly overestimates RR when the disease is not rare (i.e., common).
  • Mechanism of Divergence:
    • The OR and RR diverge as the disease prevalence ↑.
    • The magnitude of this overestimation increases as the prevalence moves away from 0.
  • Direction of Overestimation: The OR is always further from the null value of 1.0 than the RR.
    • If RR > 1, then OR > RR.
    • If RR < 1, then OR < RR.

⭐ For common diseases, the OR can significantly exaggerate the true measure of association, potentially leading to misinterpretation of a risk factor's importance.

High-Yield Points - ⚡ Biggest Takeaways

  • The Odds Ratio (OR) is a good approximation of the Relative Risk (RR) when the disease is rare.
  • This is often called the rare disease assumption.
  • "Rare" generally means a disease prevalence or incidence of <10%.
  • The OR consistently overestimates the RR, and this divergence worsens as prevalence increases.
  • This approximation is crucial for interpreting case-control studies, where RR cannot be calculated directly.

Practice Questions: When odds ratio approximates relative risk

Test your understanding with these related questions

Recently, clarithromycin was found to have an increased risk of cardiac death in a Danish study. This study analyzed patients who were previously treated with clarithromycin or another antibiotic, and then they were followed over time to ascertain if cardiac death resulted. What type of study design does this represent?

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Flashcards: When odds ratio approximates relative risk

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For rare diseases (low prevalence), _____ approximates relative risk

TAP TO REVEAL ANSWER

For rare diseases (low prevalence), _____ approximates relative risk

odds ratio

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