Updated: 9/2/2020

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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