Measures of Association

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
• 2×2 tables can be helpful in calculating these measures 
• note: these tables are slightly different from 2×2 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