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- 1. COMMON MEASURES OF ASSOCIATION IN MEDICAL AND EPIDEMIOLOGIC RESEARCH: ODDS, RISK, &THE 2X2TABLE Patrick Barlow University ofTennessee Graduate School of Medicine
- 2. ON THE AGENDA Part I Odds, risk, rate, & proportion, what’s the difference? The 2x2 table explained Part II Calculating measures of association
- 3. SOME TERMS FOR PART I Proportion Risk Odds Rate The Basics
- 4. PART I: THE BASICS Comparing probability, risk, rates, & odds
- 5. WHAT IS PROBABILITY? The probability of a favorable event is the fraction of times you expect to see that event in many trials. Always range between 0 and 1 For example… You record 25 heads on 50 flips of a coin, what is the probability of a heads? A “risk” is simply the proportion of individuals in a certain group who had the outcome divided by the total number in that group.
- 6. WHAT ARE ODDS? An “odds” is a probability of a favorable event occurring vs. not occurring. For example… What are the odds you will get a heads when flipping a fair coin? Odds of heads = Probability of heads / (1-Probability of heads) = .5 / (1-.5) = 1 “The odds of flipping heads to flipping tails is 1:1”
- 7. WHAT IS A RATE? The term “Rate” is often misused in medical literature as well as in everyday conversation. Technically, a rate is a measure of occurrence per unit of time such as… Miles Per Hour Words Per Minute OR
- 8. WHAT IS A RATE? In the health sciences, rates are generally expressed as the number of deaths, cases, etc. per “person time”. • For example: a study looking at the incidence of COPD exacerbations following a clinic-wide intervention had five participants… Time in the study (months) COPD Exacerbation Patient 1 3 Yes Patient 2 11 Yes Patient 3 12 No Patient 4 12 No Patient 5 4 No Total 42 2
- 9. WHAT IS A RATE? What is the rate of COPD Exacerbation in this sample? Time in the study (months) COPD Exacerbation Patient 1 3 Yes Patient 2 11 Yes Patient 3 12 No Patient 4 12 No Patient 5 4 No Total 42 2
- 10. THE BOTTOM LINE Proportions & risks are synonymous with one another as the number of “occurrences” or the number at risk to develop the outcome (i.e. sample) An “odds” is a probability of a favorable event occurring vs. not occurring. It is expressed as a ratio, for example, an odds of 1.00 means there is a 1:1 (1 to 1) odds of the event occurring vs. not occurring. A rate differs from both proportions and odds because it is always expressed per a unit of time such as miles per hour. Health sciences usually express rates in terms of “person-time.”
- 11. PART II: CALCULATING COMMON MEASURES OF ASSOCIATION ON A 2X2 TABLE Odds Ratio (OR) Relative Risk Ratio (RR) Attributable Risk (AR) Absolute Risk Reduction (ARR) Number Needed to Treat (NNT) Number Needed to Harm (NNH)
- 12. SOME TERMS FOR PART II Common Measures of Association Odds Ratio (OR) Relative Risk Ratio (RR) Attributable Risk (AR) Absolute Risk Reduction (ARR) Number Needed toTreat (NNT) Number Needed to Harm (NNH)
- 13. RELATIVE RISK VS. ODDS RATIOS Relative Risk (RR) is a more accurate measure of incidence of an outcome of interest. Used in prospective studies or when the total population are known What study designs would use RR? Mathematically, RR is calculated the same way as an odds where Relative Risk of an event = Odds of event occurring / Odds of event not occurring. An odds ratio (OR) provides researchers with an estimate of RR in situations where the total population is unknown. What study designs would use ORs instead of RRs?
- 14. THE 2X2TABLE The basis of nearly every common measure of association in medical and epidemiologic research can be traced back to a 2x2 contingency table. A B C D
- 15. THE 2X2TABLE For every measure of association using the 2x2 table, your research question comes from the A cell. A B C D
- 16. EXAMPLE What is the risk of myocardial infarction (MI) if a patient is taking aspirin versus a placebo? Had MI No MI Aspirin A B Placebo C D What other research questions could be answered using this same table?
- 17. RELATIVE RISK ON A 2X2TABLE What is the risk of myocardial infarction (MI) if a patient is taking aspirin versus a placebo? Had MI No MI Aspirin 50 1030 Placebo 200 1570
- 18. RELATIVE RISK ON A 2X2TABLE What is the risk of MI if a patient is taking aspirin? What is the risk of MI if a patient is taking placebo? Had MI No MI Aspirin 50 1030 Placebo 200 1570
- 19. RELATIVE RISK ON A 2X2TABLE So… What is the risk of myocardial infarction (MI) if a patient is taking aspirin versus a placebo? Had MI No MI Aspirin 50 1030 Placebo 200 1570
- 20. INTERPRETING ORS AND RRS:THE BASICS Odds/Risk ratio ABOVE 1.0 =Your exposure INCREASES risk of the event occurring For OR/RRs between 1.00 and 1.99, the risk is increased by (OR – 1)%. For OR/RRs 2.00 or higher, the risk is increased OR times. Example: Smoking is found to increase your odds of breast cancer by OR = 1.25.What is the increase in odds? You are 25% more likely to have breast cancer if you are a smoker. Smoking is found to increase your risk of developing lung cancer by RR = 4.8.What is the increase in risk? You are 4.8 times more likely to develop lung cancer if you are a smoker vs. non-smoker.
- 21. INTERPRETING ORS AND RRS:THE BASICS Odds/Risk ratio BELOW 1.0 =Your exposure DECREASES risk of the event occurring The risk is decreased by (1 – OR)% Often called a PROTECTIVE effect Example: Addition of the new guidelines for pacemaker/ICD interrogation produced an OR for device interrogation of OR = .30 versus the old guidelines.What is the reduction in odds? (1 – OR) = (1 – .30) = 70% reduction in odds.
- 22. YOUR TURN Work in pairs to calculate the RRs for each of the 2x2 tables below. RR = (79/79+157) / (100/100+375) = 1.59 1 PE No PE DVT 79 157 No DVT 100 375 RR = (190/(190+450)) / (70/(70+700)) = 3.27 3 Lung Cancer No Lung Cancer Smoking Hx 190 450 No Smoking Hx 70 700 RR = (35/(35+170)) / (52/(52+160)) = .70 2 Glucose Tolerance Improved Tolerance not Improved Lap Band 35 170 Gastric Bypass 52 160 RR = (25/(25+350)) / (65/(65+200)) = .27 4 DM Type II No DM Type II BMI < 30 25 350 BMI > 30 65 200
- 23. ODDS RATIOS AND THE 2X2TABLE Recall… Odds ratios are used to estimate RR when the true population is unknown. For discussion Why can’t we just use RR all the time? Will an OR and RR differ from one another? If so, how? Odds ratios look at prevalence rather than incidence of the event. Remember: OR = “Odds of having the outcome” RR = “Risk of developing the outcome”
- 24. ODDS RATIOS AND THE 2X2TABLE What are the odds of myocardial infarction (MI) if a patient is taking aspirin versus a placebo? OR = A*D / B*C OR = 50*1570 / 1030 * 200 = .38 or 38% Had MI No MI Aspirin 50 1030 Placebo 200 1570
- 25. OR = (25*200) / (350*65) = .21 4 DM Type II No DM Type II BMI < 30 25 350 BMI > 30 65 200 OR = (35*160) / (170*52) = .63 2 Glucose Tolerance Improved Tolerance not Improved Lap Band 35 170 Gastric Bypass 52 160 OR = (190*700) / (450*70) = 4.22 3 Lung Cancer No Lung Cancer Smoking Hx 190 450 No Smoking Hx 70 700 YOUR TURN Work in pairs to calculate the ORs for the same 2x2 tables as before. How do the ORs and RRs differ? OR = (79*375) / (157*100) = 1.89 1 PE No PE DVT 79 157 No DVT 100 375
- 26. INTERPRETING ORS AND RRS:THE BASICS So for our example… OR = .39 What is the reduction in odds? So: “Taking aspirin provides a 61% reduction in the odds of having an MI compared to a placebo.” RR = .41 What is the reduction in risk? So: “Taking aspirin provides a 59% reduction in risk of MI compared to a placebo.”
- 27. INTERPRET THE FOLLOWING OR/RRS OR = 3.00 OR = .39 RR = 1.50 OR = 1.00 RR = .22 RR = 18.99 OR = .78 What does the OR/RR say about the strength of relationship?
- 28. OR/RRAND CONFIDENCE INTERVALS The magnitude of the OR/RR only provides the strength of the relationship, but not the accuracy 95% Confidence intervals are added to any OR/RR calculation to provide an estimate on the accuracy of the estimation. 95% of the time the true value will fall within a given range Wide CI = weaker inference Narrow CI = stronger inference CI crosses over 1.0 = non-significant AnOR/RR is only as important as the confidence interval that comes with it
- 29. INTERPRET THESE 95% CIS OR 2.4 (95% CI 1.7 - 3.3) OR 6.7 (95% CI 1.4 - 107.2) OR 1.2 (95% CI .147 - 1.97) OR .37 (95% CI .22 - .56) OR .57 (95% CI .12 - .99) OR .78 (95% CI .36 – 1.65)
- 30. OTHER COMMON MEASURES OF ASSOCIATION EXAMPLE ONE: ABSOLUTE RISK REDUCTION Absolute Risk Reduction (ARR): This is the difference between the risk (not RR) of the outcome in the control group minus the risk of the outcome in the study group. For Example…Recall the MI & Aspirin study What is the ARR of aspirin vs. the placebo? Had MI No MI Aspirin 50 1030 Placebo 200 1570
- 31. OTHER COMMON MEASURES OF ASSOCIATION EXAMPLE TWO: ATTRIBUTABLE RISK Attributable Risk (AR) is the increase in risk associated with a particular risk factor. It is the incidence in the exposed group minus the incidence in the unexposed group. For Example…a classic example is a 1980s controversy between Aspirin and Rye’s syndrome. What is the AR for Rye’s in children exposed to aspirin vs. not exposed? Ryes (+) Ryes (–) Aspirin (+) 600 9030 Aspirin (–) 150 10000
- 32. OTHER COMMON MEASURES OF ASSOCIATION: NUMBER NEEDED TO TREAT / HARM Number needed to treat (NNT) is the number of patients that would need to be treated in order to prevent a single event. It is the inverse of ARR. Conversely, number need to harm (NNH) is the number of patients that would need to be exposed to the risk factor before someone had an event. It is the inverse of AR. In our aspirin and MI example (Example 1), the ARR for aspirin = 6.2% and the AR = 4.7
- 33. WHAT IS STATISTICAL INFERENCE? Causation, hypothesis testing & what it means to be “statistically significant”

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