U01.06.005 Quantifying risk

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1. Odds Ratio (OR)

  • Definition: Used in case-control studies. Represents the odds of exposure among cases vs. controls.
  • Interpretation:
    • OR = 1 → no association
    • OR > 1 → exposure ↑ odds of disease
    • OR < 1 → exposure ↓ odds of disease
  • Example: In a case-control study, 20/30 lung cancer patients and 5/25 controls smoked → OR = 8.
  • Formula: OR = \frac{a/c}{b/d} = \frac{ad}{bc}

2. Relative Risk (RR)

  • Definition: Used in cohort studies. Risk of disease in exposed ÷ unexposed.
  • Interpretation:
    • RR = 1 → no association
    • RR > 1 → exposure ↑ disease risk
    • RR < 1 → exposure ↓ disease risk
  • Example: 5/10 exposed get cancer, 1/10 unexposed get cancer → RR = 5.
  • Formula: RR = \frac{a/(a+b)}{c/(c+d)}

3. Relative Risk Reduction (RRR)

  • Definition: Proportion of risk reduction attributable to intervention vs. control.
  • Example: Flu shot → 2% risk vs. 8% without vaccine. RR = 0.25, so RRR = 0.75 (75%).
  • Formula: RRR = 1 - RR = \frac{ARC - ART}{ARC}

4. Attributable Risk (AR)

  • Definition: Difference in risk between exposed and unexposed.
  • Example: Lung cancer risk in smokers = 21%, in nonsmokers = 1%. AR = 20%.
  • Formula: AR = \frac{a}{a+b} - \frac{c}{c+d}

5. Absolute Risk Reduction (ARR)

  • Definition: Difference in risk (not proportion) due to intervention vs. control.
  • Example: Flu vaccine → 8% placebo vs. 2% vaccinated. ARR = 6% = 0.06.
  • Formula: ARR = \frac{c}{c+d} - \frac{a}{a+b}

6. Number Needed to Treat (NNT)

  • Definition: Number of patients needed to treat to benefit 1 patient.
  • Interpretation: Lower = better.
  • Formula: NNT = \frac{1}{ARR}

7. Number Needed to Harm (NNH)

  • Definition: Number of patients needed to be exposed for 1 patient to be harmed.
  • Interpretation: Higher = safer.
  • Formula: NNH = \frac{1}{AR}

8. Case Fatality Rate (CFR)

  • Definition: % of deaths among patients with a disease.
  • Example: 4 deaths among 10 meningitis cases → CFR = 40%.
  • Formula: CFR(%) = \frac{\text{deaths}}{\text{cases}} \times 100

9. Mortality Rate

  • Definition: Number of deaths in a population over a defined period.
  • Example: 80 deaths in 10,000 people over 2 years → 4/1000 per year.
  • Formula: Mortality \ Rate = \frac{\text{deaths in a period}}{\text{population}}

10. Attack Rate

  • Definition: Proportion of exposed individuals who become ill.
  • Example: 60/80 exposed become ill → Attack rate = 75%.
  • Formula: Attack \ Rate = \frac{\text{ill individuals}}{\text{total exposed}}

Summary Table

Term Definition Example Formula
Odds Ratio (OR) Odds of exposure among cases vs controls (case-control) OR = 8 for smoking & lung cancer OR = \frac{ad}{bc}
Relative Risk (RR) Risk of disease in exposed ÷ unexposed (cohort) Radiation → RR = 5 RR = \frac{a/(a+b)}{c/(c+d)}
Relative Risk Reduction (RRR) Proportion of risk reduction from intervention Flu vaccine RRR = 75% RRR = 1 - RR
Attributable Risk (AR) Risk difference between exposed & unexposed Smokers vs nonsmokers = 20% AR = \frac{a}{a+b} - \frac{c}{c+d}
Absolute Risk Reduction (ARR) Risk difference between intervention & control Flu vaccine ARR = 6% ARR = \frac{c}{c+d} - \frac{a}{a+b}
NNT Patients needed to be treated for 1 benefit Lower = better NNT = \frac{1}{ARR}
NNH Patients needed to be exposed for 1 harmed. Higher = safer NNH = \frac{1}{AR}
CFR % deaths among cases 4/10 meningitis → 40% CFR(%) = \frac{\text{deaths}}{\text{cases}} \times 100
Mortality Rate Deaths in the population per time 80/10,000 → 4/1000 per yr \frac{\text{deaths}}{\text{population}}
Attack Rate Proportion of exposed who get sick 60/80 = 75% \frac{\text{ill}}{\text{exposed}}

Learning Objective

By the end of this section, you should be able to:

  • Define and distinguish epidemiological measures (OR, RR, AR, ARR, RRR, NNT, NNH, CFR, Mortality Rate, Attack Rate).
  • Apply formulas to clinical or research-based questions.
  • Interpret results in terms of public health significance for USMLE Step 1.

Activity:

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