This is an updated version of my Common Measures of Association presentation. I've updated it to include (1) more detail on rates, risks, and proportions, (2) Absolute Risk Reduction (ARR), Attributable Risk (AR), Number Needed to Treat (NNT) and Number Needed to Harm (NNH). Feel free to email me for a full version of the slideshow.

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”