Number needed to treat relation

Odds Ratio vs. Relative Risk - Dueling Ratios

• Contingency Table (2x2):

  	Disease +	Disease -
  Exposed	a	b
  Unexposed	c	d

• Odds Ratio (OR): Ratio of odds of disease in exposed vs. unexposed.

  • Primarily for case-control studies.
  • Formula: $OR = (a/b) / (c/d) = ad/bc$

• Relative Risk (RR): Ratio of risk (incidence) in exposed vs. unexposed.

  • Requires cohort studies.
  • Formula: $RR = [a/(a+b)] / [c/(c+d)]$
  • For rare diseases, OR ≈ RR.

• Number Needed to Treat (NNT):

  • Inverse of the absolute risk reduction (ARR).
  • Formula: $NNT = 1 / ARR$
  • $ARR = [c/(c+d)] - [a/(a+b)]$

⭐ High-Yield Pearl: NNT is the number of patients who must receive a specific treatment for one to benefit. A low NNT is ideal. For harmful events (NNH), a high NNH is ideal.

Number Needed to Treat - Treatment Scorecard

• Number Needed to Treat (NNT): The number of patients that need to be treated to prevent one additional bad outcome. A measure of treatment effectiveness.

  • Formula: $NNT = 1 / ARR$
  • ARR (Absolute Risk Reduction): $|CER - EER|$
  • Interpretation: A lower NNT indicates a more effective intervention. The ideal NNT is 1.

• Number Needed to Harm (NNH): The number of patients that need to be treated for one patient to experience an additional adverse event.

  • Formula: $NNH = 1 / ARI$
  • ARI (Absolute Risk Increase): $|EER_{harm} - CER_{harm}|$
  • Interpretation: A higher NNH is desirable.

⭐ When comparing treatments, the one with the lower NNT is generally preferred. An NNT of infinity (∞) means the treatment has no effect, as the ARR is zero.

Key Relationships - Formula Face-Off

• Relative Risk (RR): Risk in exposed / Risk in unexposed
  • $RR = [a/(a+b)] / [c/(c+d)]$
• Odds Ratio (OR): Odds of exposure in cases / Odds of exposure in controls
  • $OR = (a/b) / (c/d) = ad/bc$
• Absolute Risk Reduction (ARR): The real difference in risk.
  • $ARR = CER - EER$
• Number Needed to Treat (NNT): Patients to treat to prevent 1 bad outcome.
  • $NNT = 1 / ARR$

⭐ For rare diseases (low prevalence), the Odds Ratio (OR) closely approximates the Relative Risk (RR).

High‑Yield Points - ⚡ Biggest Takeaways

• The Odds Ratio (OR) approximates Relative Risk (RR) when disease prevalence is low.
• RR is calculated from cohort studies; OR is from case-control studies.
• Number Needed to Treat (NNT) is the reciprocal of the Absolute Risk Reduction (ARR).
• NNT = 1 / ARR
• ARR = Control Event Rate (CER) - Experimental Event Rate (EER).
• A higher NNT value indicates a less effective clinical intervention.