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Updated: Aug 20 2022

Measures of Association

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  • Overview
    • Measures of association quantify relationships between variables
    • In medicine and public health, measures of association most often quantify the association of exposure with disease
    • Measures of association can be presented and framed in different ways for diverse purposes
    • 2x2 tables can be helpful in calculating these measures
      • note: these tables are slightly different from 2x2 tables used to calculate diagnostic testing parameters
  • Relative Risk, Odds Ratio,Attributable Risk, and Absolute Risk Reduction
    • Relative risk (RR)
      • risk of disease in exposed group/risk of disease in unexposed group
      • = [a/(a+b)] / [c/(c+d)]
      • used in cohort studies or other studies where total population is known
      • RR > 1
        • exposure is associated with increased risk of disease
      • RR < 1
        • exposure is associated with decreased risk of disease
      • RR = 1
        • no association between exposure and disease
    • Odds ratio (OR)
      • odds of having disease in exposed group/odds of having disease in unexposed group
      • = ad/bc
      • primarily used in case control studies
      • can be used in cohort studies when outcome is rare
        • OR approximates RR for rare outcomes
      • OR > 1
        • odds of developing disease are greater in exposed group
      • OR < 1 
        • odds of developing disease are reduced in exposed group
      • OR = 1
        • odds of developing disease are equal in exposed and unexposed group
    • Attributable risk (AR)
      • "How much greater risk is present in the exposed group than the unexposed?"risk of disease in exposed group - risk in unexposed group= a/(a+b) - c/(c+d)
    • Attributable risk percent (ARP)
      • "What percent greater risk is present in the exposed group than the unexposed?"(risk of disease in exposed group - risk in unexposed group)/risk in exposed group= [a/(a+b) - c/(c+d)] / [a/(a+b)]
    • Absolute risk reduction (ARR)
      • "How much risk is reduced by the intervention (or exposure)?"
      • risk in control group - risk in intervention group
        • = c/(c+d) - a/(a+b)
  • Number Needed to Treat and Number Needed to Harm
    • Number needed to treat (NNT)
      • "How many patients needed to be treated before 1 patient will benefit?"
        • e.g.,if a treatment affords a 25% ARR, generally 4 people will have to be treated for every 1 that benefits
      • NNT calculation is the inverse of ARR
        • =1/[c/(c+d) - a/(a+b)]
      • Number needed to harm (NNH)
        • "How many patients need to be exposed before one patient will be harmed?"
        • NNH calculation is the inverse of AR
          • = 1/[a/(a+b) - c/(c+d)]
  • Population-Level Measures of Association
    • Used to make public health decisions and allocate resources
    • Population attributable risk (PAR)
      • "What amount of the risk of disease in a population is attributable to a specific exposure?" (as opposed to baseline population risk)
      • total population incidence of disease - incidence of disease amongst unexposed
      • = [(a+c)/(a+b+c+d) - (c/c+d)]
      • unit is per person
        • e.g., if your PAR for obesity on heart disease is 0.004, the risk of heart disease for the total population that is likely due to obesity is 4 cases per 1,000 people
          • if obesity was eliminated from the population, 4 cases of cardiac disease per every 1,000 people would be eliminated
    • Population attributable risk percent (PAR%)
      • "What percent of disease cases amongst a population can be attributed to a specific exposure?" (as opposed to baseline population risk)
      • [(total population incidence of disease - incidence of disease amongst unexposed)/total population incidence of disease] * 100
      • = [(a+c)/(a+b+c+d) - (c/c+d)]/[(a+c)/(a+b+c+d)] * 100
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