Common misinterpretations

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OR vs. RR - Tale of Two Ratios

2x2 Contingency Table for Biostatistics

  • 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.

Practice Questions: Common misinterpretations

Test your understanding with these related questions

A study is funded by the tobacco industry to examine the association between smoking and lung cancer. They design a study with a prospective cohort of 1,000 smokers between the ages of 20-30. The length of the study is five years. After the study period ends, they conclude that there is no relationship between smoking and lung cancer. Which of the following study features is the most likely reason for the failure of the study to note an association between tobacco use and cancer?

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Flashcards: Common misinterpretations

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_____ studies are observational studies that compare a group of people with disease to a group without disease

TAP TO REVEAL ANSWER

_____ studies are observational studies that compare a group of people with disease to a group without disease

Case-control

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