# 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(**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