Common misinterpretations

OR vs. RR - Tale of Two Ratios

• Relative Risk (RR): The standard for cohort studies (prospective).

  • Measures the incidence of disease.
  • Formula: $RR = [a/(a+b)] / [c/(c+d)]$
  • Interpretation: "The risk of developing the disease is X times higher in the exposed group."

• Odds Ratio (OR): The standard for case-control studies (retrospective).

  • Measures the odds of prior exposure.
  • Formula: $OR = ad/bc$
  • Interpretation: "The odds of prior exposure are X times higher among cases than controls."

⭐ The OR approximates the RR when disease prevalence is low (<10%). A common misinterpretation is treating them as equal in all scenarios.

📌 COhort → Relative Risk. Case-COntrol → Odds Ratio.

Common Misinterpretations - Deceptive Doppelgangers

• The Odds Ratio (OR) is often confused with Relative Risk (RR). The OR consistently overestimates the RR, and this divergence ↑ as disease prevalence ↑.
  • 📌 Mnemonic: Think 'O-R-E' for 'Odds Ratio Estimates-over'.
• Rare Disease Assumption: When disease prevalence is low (a rule of thumb is < 10%), the OR provides a good approximation of the RR ($OR \approx RR$). This is the primary scenario where they can be considered interchangeable.
• Study Design Context: ORs typically arise from case-control studies (measuring odds of past exposure), whereas RRs are calculated from cohort studies (measuring incidence/risk). Applying an OR as a direct measure of absolute risk is a frequent error.
• Confounding: Both OR and RR are susceptible to distortion by confounding variables, which can create a misleading association between an exposure and an outcome.

⭐ The OR is always further from 1.0 than the RR. If the RR is > 1, the OR will be even greater. If the RR is < 1, the OR will be even smaller, thus exaggerating the strength of the association.

The 2x2 Table - Crunching the Numbers

The 2x2 contingency table is the foundational tool for analyzing the association between an exposure and an outcome. It organizes subjects into four distinct groups based on their status for both variables, forming the basis for calculating odds ratios and relative risks.

• Cell a (True Positive): Exposed individuals who develop the outcome.
• Cell b (False Positive): Exposed individuals who do not develop the outcome.
• Cell c (False Negative): Unexposed individuals who develop the outcome.
• Cell d (True Negative): Unexposed individuals who do not develop the outcome.

⭐ By convention, exposure status (e.g., risk factor) defines the rows, and outcome status (disease) defines the columns. This standard orientation is the critical first step for correctly calculating risk.

• Odds ratio (OR) significantly overestimates Relative Risk (RR) when disease prevalence is high (>10%).
• A key error is interpreting the OR as the RR; they are only similar when a disease is rare.
• RR cannot be calculated from case-control studies because there is no true denominator of the total exposed population.
• Neither OR nor RR implies causation; they only quantify the strength of an association.
• If the 95% CI for an OR or RR includes 1.0, the result is not statistically significant.