2. Measures of Association
• Comparing the frequency of disease
between exposed and unexposed
• Measures of association (effect)
• There are two types of measures of
association
– Absolute measures
– Relative measures
3. Measures of Association
• Show the strength of the relationship
between an exposure and outcome
• Indicate how more or less likely a group is
to develop disease as compared to
another group
4. Absolute Measures of Association
• Based on DIFFERENCE between two
measures of disease frequency
• May range from -1 to 1
– If value of difference measure=0 then no
difference between exposed and unexposed
• Difference measures are useful for
assessing the public health impact of an
exposure
5. Absolute Measures of Association
• Incidence
– Risk difference = Cumulative Incidence in
Exposure – Cumulative Incidence in
Unexposed
– Rate Difference = Incidence Rate in Exposed
– Incidence Rate in Unexposed
• Prevalence
– Prevalence Difference = Prevalence in
Exposed – Prevalence in Unexposed
6. Absolute Measures of Association
• Incidence Differences
– Both differences measure the excess number
of NEW cases among the exposed compared
to the unexposed
• Prevalence Differences
– Measures excess number of EXISTING cases
among exposed compared to unexposed at a
particular point in time
7. Relative Measures of Association
• The RATIO of two disease frequencies
– Risk Ratio (aka Cumulative Incidence Ratio,
aka Relative Risk)
– Rate Ratio
– Prevalence Ratio
• Relative measures may be interpreted as
the excess Risk, Rate, or Prevalence in
exposed relative to the unexposed
8. Relative Measures of Association
• Relative measures may range from 0 to
infinity
• Relative measures assess the strength of
association between exposure and
disease and are useful in identifying risk
factors
9. Data Layouts
• Typically, epidemiologists organize study
data as a 2x2 table
– Column = Disease or Outcome status (Yes or
No)
– Row = Exposure Status (Yes or No)
• Study participants assigned to one of the
four cells according to their individual
exposure and disease state
• Results used to calculate and compare
frequency of disease according to
exposure
10. 2 x 2 Tables
Used to summarize counts of disease and
exposure to calculate measures of association
Outcome
Exposure Yes No Total
Yes a b a + b
No c d c + d
Total a + c b + d a + b + c + d
11. 2 x 2 Tables
a = number exposed with outcome
b = number exposed without outcome
c = number not exposed with outcome
d = number not exposed without outcome
******************************
a + b = total number exposed
c + d = total number not exposed
a + c = total number with outcome
b + d = total number without outcome
a + b + c + d = total study population (N)
a b
c d
Outcome
Yes No
Exposure
Yes
No
16. Interpretation
• Cumulative incidence in the exposed:
-10% of the exposed group developed the
disease in the study period
• Cumulative incidence in the unexposed:
-5% of the unexposed group developed
the disease in the study period
17. Risk difference and ratio
• Risk Difference =
• Risk Ratio (Relative Risk, RR) =
a c
a b c d
a
a b
c
c d
20. Interpretation
• Risk Difference:
In a population of 100 exposed people, there
would be 5 additional cases of disease than
what you would observe if exposure was
absent in the study period
• Risk Ratio:
The risk of developing the disease in the
exposed group is two times the risk of
developing the disease in the unexposed group
in the study period
21. Relative Risk Example
Escherichia coli?
Pink
hamburger Yes No
Total
Yes 23 10 33
No 7 60 67
Total 30 70 100
a / (a + b) 23 / 33
RR = = = 6.67
c / (c + d) 7 / 67
22. Odds Ratio
• Used with case-control studies
• Population at risk is not known (selected
participants by disease status)
• Calculate odds instead of risks
a x d
OR =
b x c
23. 2x2 tables
a b
c d
Diseased Non-diseased
Exposed
Unexposed
a+b
c+d
a+c a+d a+b+c+d = N
* Assume incidence data over 1 year
24. Odds
• Odds of disease in the exposed =
• Odds of disease in the unexposed =
a
b
c
d
29. Interpretation
• Odds Ratio:
(OR as an estimate of RR)
The risk of developing the disease in the
exposed group is 2.11 times the risk of
developing the disease in the unexposed
group during the study period
30. Odds Ratio Example
Increased Blood
Pressure
Caffeine
intake “high”? Yes No
Total
Yes 130 115 245
No 120 135 255
Total 250 250 500
a x d 130 x 135
OR = = = 1.27
b x c 115 x 120
31. Interpreting Risk and Odds
Ratios
RR or OR
< 1
• Exposure
associated
with
decreased
risk of
outcome
RR or OR
= 1
• No
association
between
exposure
and
outcome
RR or OR
> 1
• Exposure
associated
with
increased
risk of
outcome
32. Interpretation
• RR = 5
– People who were exposed are 5 times more likely to
have the outcome when compared with persons who
were not exposed
• RR = 0.5
– People who were exposed are half as likely to have
the outcome when compared with persons who were
not exposed
• RR = 1
– People who were exposed are no more or less likely
to have the outcome when compared to persons who
were not exposed
33. Measures of Association (Effect)
• Prevalence difference
• Prevalence ratio
• Risk difference
• Risk ratio
• Incidence rate difference
• Incidence rate ratio
• Odds ratio
APPROPRIATE MEASURE DEPENDS ON THE
STUDY YOU HAVE CONDUCTED
Editor's Notes
How do we interpret risk and odds ratios? We use the following general rules, which can also be used to interpret any other type of relative measure:A risk ratio of less than 1.0 means that the exposure is associated with a decreased risk of the outcome, or that the exposure is protective. It is also called a negative association.A risk ratio of 1.0 means that there is no association between the exposure and the outcome. This is also called the null value.A risk ratio of greater than 1.0 means that the exposure is associated with an increased risk of developing the outcome. It is also called a positive association.In our high blood pressure example, the odds ratio was 1.27, which is greater than 1, indicating that the exposure, high caffeine intake, is associated with the outcome, high blood pressure.
