Measures of Association

We will learn

  • Attributable risk
  • Attributable risk percent
  • Relative Risk
  • Odds and Odds Ratio
  • Population Attributable risk%

Attributable Risk

  • Risk in exposed = Incidence among exposed
  • Risk in non-exposed = Incidence among non-exposed
  • Attributable Risk = Risk in exposed - Risk in non-exposed
  • Excess Risk attributable to exposure
  • Similarly Excess Risk attributable to interventions

Illustration

  • Incidence of asthma among those exposed to air pollution: 19 per 1000 person-years
  • Incidence of asthma among those NOT exposed to air pollution: 10 per 1000 person-years
  • Attributable risk of asthma with air pollution: 9 per 1000 person-years

Why is attributable risk important?

  • Helps the provider to plan interventions
  • Excess risk helps us to understand how much actual difference exists
  • 10% change for a rare disease and a common disease carry different meanings

Illustration of excess risk, low frequency

  • Disease incidence 1 in 1000 person-years at baseline
  • With exposure, say there is a 20% jump in the incidence
  • With exposure, the disease would be 1.2 per 1000 person-years

Illustration of excess risk, high freq

  • Disease risk 10 in 1000 person-years at baseline
  • Exposure leads to 20% jump in the incidence
  • Post exposure, disease risk 12 per 1000 person-years

Attributable risk percent

  • What percent of asthma among those who are exposed is attributed to air pollution?
  • 9/19 = 47.3% of all exposed cases are due to air pollution
  • Proportion of disease among exposed attributed to an exposure

Relative Risk (RR)

  • Risk in exposed / Risk in non-exposed
  • Measure used for causal inference
  • Rate Ratio (ratio of incidences)
  • Odds Ratio (ratio of two odds)

Illustration of Relative Risk

  • Risk of asthma with air pollution 19 per 1000 person-years
  • Risk of asthma without air pollution 10 per 1000 person-years
  • Risk Ratio is 19 / 10 or 1.9
  • Those exposed to air pollution are 1.9 times
  • Risk Ratio same as Rate Ratio (same thing)

Concept of Odds and Odds Ratio

  • Odds is a ratio of two probabiities
  • Probability that an event E will occur is p(E)
  • Probability that event E will not occur is (1 - p(E))
  • Odds = p(E) / (1 - p(E))

Illustration of Odds

  • Say there is a 10% chance of rain tomorrow
  • Rain is an event
  • Probability of rain is p(Rain) = 10%
  • Probability of no rain tomorrow is 90%
  • We say p(NO Rain) = 90%
  • Odds of Rain = 10: 90 (ten against 90)

Odds Ratio

  • Ratio of two odds
  • Odds of Exposure IF Diseased
  • Written as Odds(Exposure | Disease)
  • Odds of Exposure IF Non Diseased
  • Written as Odds(Exposure | No Disease)
  • Odds Ratio = Odds(E | D) / Odds(E | No D)

Illustration of Odds Ratio

Smoking Lung Cancer No Cancer
Smoker 200 40
Non-smoker 20 180
Total 220 220

Odds of Smoking for those with cancer

  • Out of 220 with cancer,
  • 200 were smokers
  • Probability of smoking = 200/220
  • Probability of NOT smoking = (1 - 200/220) = 20/ 220
  • Odds of smoking = (200/220) / (1 - 200/220)
  • Odds of Smoking IF CANCER = 200 / 20

Odds of Smoking for those with NO Cancer

  • Out of 220 with NO Cancer,
  • 40 were smokers
  • Probability of smoking = 40 / 220
  • Probability of NOT smoking = 180 / 220
  • Odds of Smoking IF NO Cancer = 40 / 180

Odds Ratio of Smoking and Cancer

  • Odds of Smoking IF CANCER
  • Divided by
  • Odds of Smoking IF NO CANCER
  • (200 / 20 ) DIVIDED BY (40 / 180)
  • (200 * 180) / (40 * 20) = 45
  • Smokers are 45 times at risk of Cancer compared with Non-smokers

Meaning of RR and OR

  • OR and RR are essentially same
  • particularly for rare disease conditions
  • If RR or OR > 1, indicates risk
  • If RR or OR < 1, indicates protective effect

How to use RR and OR

  • RR or OR helps to indicate strength of association
  • Using prevalence of exposure,
  • RR and OR can be used to estimate PAR%
  • PAR% = Population attributable risk %
  • How much of the disease can be reduced
  • If the risk factor can be completely eliminated
  • Assuming a cause and effect association exists

Theory of PAR%

  • In a study, we can have
  • Everyone in the exposed group to be exposed
  • Everyone in the non-exposed group to be not exposed
  • This does not happen in real life
  • In real life only some in the population are exposed
  • Prevalence of exposure can be plugged in a formula
  • Also called Population Attributable Fraction

Formula of PAR%

  • ((pE * (RR - 1)) / (1 + pE * (RR - 1))) * 100
  • Where pE = prevalence of exposure
  • RR = Relative Risk (also could be OR)

Illustration with air pollution example

  • In the society about 20% were exposed to high air pollution
  • pE = 0.20
  • RR = 1.9
  • PAR% = ((0.20 * 0.90) / (1 + 0.20 * 0.90)) * 100
  • PAR% = (0.18 / 1.8) * 100 = 10%
  • If air pollution were to be completely eliminated, it would reduce asthma by 10%

Illustration with smoking and lung cancer

  • In a community, about 20% people smoke
  • pE = 0.20
  • RR = 45
  • PAR% = (0.20 * 44 / (1 + 0.20 * 44)) * 100
  • PAR% = 89.8%
  • If smoking could be eliminated, it would reduce lung cancer by 89.8% or roughly by 90%!

Summary

  • We learned about AR, RR, OR, PAR%
  • Attributable Risk is the risk difference
  • Attributable risk % tells us how much of the risk is accounted for by the exposure
  • RR is a relative risk estimate, it can be expressed in two ways:
  • Rate Ratio or Odds Ratio
  • PAR% tells us how much we would be able to reduce the health effect if we are able to eliminate the risk factor
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