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( E xposure | D isease) Odds of Exposure IF Non Diseased Written as Odds( E xposure | No D isease) 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
Resume presentation
Measures of Association
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