This document discusses common measures of association used in medical and epidemiological research, including odds, risk, odds ratios, and relative risk ratios. It explains how these measures are calculated using a 2x2 contingency table and how to interpret the results, including whether the exposure increases or decreases risk/odds. Confidence intervals are also discussed as they provide accuracy about the estimates. The document cautions about solely relying on p-values and advocates considering the magnitude and confidence in the measures of association.

1. COMMON MEASURES OF
ASSOCIATION IN MEDICAL AND
EPIDEMIOLOGIC RESEARCH:
ODDS, RISK, & THE 2X2 TABLE
Patrick Barlow
PhD. Student in Evaluation, Statistics, & Measurement
The University of Tennessee

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. SOME TERMS
 2x2 table
 Proportion
 Odds
 Risk
 Odds Ratio (OR)
 Relative Risk Ratio (RR)

4. WHAT IS PROBABILITY?
The probability of a favorable event is the fraction of times you expect to
see that event in many trials. In epidemiology, a “risk” is considered a
probability.
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. 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?
“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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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)