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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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• No matter what the situation, you can easily rearrange the table so that the research question you want is in the A cell. There are 4 different research questions for each 2x2 table, and you can change the values and labels around to answer the question you’re asked.
• The OR consistently OVER-estimates the risk
• Alternatively, the second example could be interpreted as: “Smoking increases your risk of lung cancer by 380% vs. non-smoking”
• Assume (until I can find literature examples) that all of these are for generic “Exposure vs. Non-exposure” and “Disease vs. non-disease”
• What influences p-values?Sample size: Larger sample sizes increases your likelihood of finding a statistically significant difference. Theoretically, the tiniest difference could be shown to be statistically significant if you have enough people. Many public health studies have massive sample sizes, so the statistically significant findings are very small practical differences.Chance: If Alpha is set to .05, then you have a 5% chance of making a Type I error, or, a false positive result. That is, you would conclude that a difference/association is statistically significant when you shouldn’t have.Effect size: Larger effect sizes (i.e. bigger odds ratios or higher correlation coefficients) are easier to find statistically significant because the association is stronger.Statistical power: Large sample sizes increase the “power” of your test to find a statistically significant difference. Low power increases you chance for a Type II error, or, “missing” the significant relationship.Is a p-value of .001 a more significant relationship than a value of .03? There is a lot of discussion about this, and it is more of a debate rather than a certainty, but what is trending now is to favor the effect size (e.g. OR or correlation coefficient) and 95% confidence intervals instead of just a p-value.
• As you can see, it is much easier to claim an OR of 4.3 is HIGHER than one of 1.50, and it makes practical and intuitive sense to see this. Likewise, Saying we’re 95% confidence the difference lies between 1.2 and 3.1 is MORE accurate than between 1.2 and 10.0.
• ### 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)
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