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# Common measures of association in medical research handout

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A quick introduction and practice to two of the most common measures of association in epidemiologic and medical research: the odds and risk ratios. The original version has substantially more moving parts for the examples and such, so please feel free to email if you'd like a copy!

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### Common measures of association in medical research handout

1. 1. COMMON MEASURES OFASSOCIATION IN MEDICAL ANDEPIDEMIOLOGIC RESEARCH:ODDS, RISK, & THE 2X2 TABLEPatrick BarlowPhD. Student in Evaluation, Statistics, & MeasurementThe University of Tennessee
2. 2. ON THE AGENDA What are odds/risks? The 2x2 table explained Calculating measures of association  Odds Ratio  Risk Ratio Interpreting measures of association  Magnitude of the relationship  Accuracy of the inference  The P-value fallacy
3. 3. SOME TERMS 2x2 table Proportion Odds Risk Odds Ratio (OR) Relative Risk Ratio (RR)
4. 4. WHAT IS PROBABILITY?The probability of a favorable event is the fraction of times you expect tosee that event in many trials. In epidemiology, a “risk” is considered aprobability. For example… You record 25 heads on 50 flips of a coin, what is the probability of a heads? Remember: a probability should never exceed 1.0 or 100%.
5. 5. WHAT ARE ODDS?An “odds” is a probability of a favorable event occurring vs. notoccurring. For example… What are the odds you will get a heads when flipping a fair coin? “The odds of flipping heads to flipping tails is 1 to 1” In clinical and epidemiologic research, we use a ratio of two odds, or Odds Ratio (OR) and Relative Risk Ratio (RR), to express the strength of relationship between two variables.
6. 6. 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? 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?
7. 7. THE 2X2 TABLE 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
8. 8. THE 2X2 TABLE For every measure of association using the 2x2 table, your research question comes from the A cell. A B C D
9. 9. 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
10. 10. RELATIVE RISK ON A 2X2 TABLE 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
11. 11. RELATIVE RISK ON A 2X2 TABLE Had MI No MI Aspirin 50 1030 Placebo 200 1570 What is the risk of MI if a patient is taking aspirin?  Risk of MI for aspirin = Number with MI / Number on Aspirin = 50 / 1080 = .048 or 4.8% What is the risk of MI if a patient is taking placebo?  Risk of MI for placebo = Number with MI / Number on placebo = 200 / 1770 = .11 or 11%
12. 12. RELATIVE RISK ON A 2X2 TABLE Had MI No MI Aspirin 50 1030 Placebo 200 1570 So… What is the risk of myocardial infarction (MI) if a patient is taking aspirin versus a placebo?  RR = (A / A+B) / (C / C+D)  RR = Risk of MI for Aspirin / Risk of MI for Placebo  RR = .048 / .11 = .41 or 41%
13. 13. YOUR TURN Work in pairs to calculate the RRs for each of the 2x2 tables below. No Lung 1 PE No PE 3 Lung Cancer Cancer DVT 79 157 Smoking Hx 190 450 No Smoking No DVT 100 375 Hx 70 700 Glucose No DM Type 2 Tolerance Improved Tolerance not Improved 4 DM Type II II Lap Band 35 170 BMI < 30 25 350 Gastric Bypass 52 160 BMI > 30 65 200
14. 14. YOUR TURN Work in pairs to calculate the RRs for each of the 2x2 tables below. RR = (79/79+157) / RR = (190/(190+450)) / (100/100+375) = 1.59 (70/(70+700)) = 3.27 RR = (35/(35+170)) / RR = (25/(25+350)) / (52/(52+160)) = .70 (65/(65+200)) = .27
15. 15. ODDS RATIOS AND THE 2X2 TABLE 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”
16. 16. ODDS RATIOS AND THE 2X2 TABLE Had MI No MI Aspirin 50 1030 Placebo 200 1570 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%
17. 17. YOUR TURN Work in pairs to calculate the ORs for the same 2x2 tables as before. How do the ORs and RRs differ? No Lung 1 PE No PE 3 Lung Cancer Cancer OR = (79*375)79(157*100) = / OR = (190*700) / (450*70) = DVT 157 Smoking Hx 190 450 1.89 4.22 No Smoking No DVT 100 375 Hx 70 700 Glucose No DM Type 2 Tolerance Improved Tolerance not Improved 4 DM Type II II OR = (35*160) / (170*52) = .63 OR = (25*200) / (350*65) = .21 Lap Band 35 170 BMI < 30 25 350 Gastric Bypass 52 160 BMI > 30 65 200
18. 18. 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) = OR = (190*700) / (450*70) = 1.89 4.22 OR = (35*160) / (170*52) = .63 OR = (25*200) / (350*65) = .21
19. 19. 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, but you could also still use (OR – 1)%. 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.
20. 20. 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.
21. 21. 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.”
22. 22. 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?
23. 23. OR/RR AND 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 An OR/RR is only as important as the confidence interval that comes with it
24. 24. 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)
25. 25. THE P-VALUE FALLACY What is a p-value?  The probability that the observed statistics would occur due to chance.  Alpha, usually set to .05  Values below .05 indicate a statistically significant relationship exists. What influences p-values?  Sample size  Chance  Effect size  Statistical power Is a p-value of .001 a more significant relationship than a value of .03?
26. 26. GOING BEYOND THE P-VALUE The OR/RR provides a far more vivid description of the magnitude of the relationship.  Can you say an OR of 4.30 is stronger than an OR of 1.50?  What about RR = .25 vs. RR = .56? The 95% CI provides far more information on the accuracy of the inference.  Which is more accurate?  OR = 2.5 (95% CI = 1.2 – 10.0) vs. OR = 2.5 (95% CI = 1.2 – 3.1)