Measures of Association
Misrak G. (BSc., MSc., MPH)
2022
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Learning Objectives
♦ At the end of this session learners are expected
to:
– Understand , explain and calculate the
different measures of association
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Measure of association/Impact
♦ Measure of association : a statistic that
quantifies the relationship between an
exposure and a disease
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Definitions…
♦ Exposure (E) : an explanatory factor; any
potential health determinant; the
independent variable
♦ Disease (D) : the response; any health-
related outcome; the dependent variable
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Association
Exposure Outcome
Is there a relationship between the
exposure and outcome of interest?
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“Exposure”
♦ Exposure in usual sense
e.g., ingestion of contaminated food
e.g., droplets from someone with active
pulmonary TB
♦ Behaviors
e.g., sharing needles, drinking alcohol etc
♦ Treatment
e.g., intervention - education program: yes or no
– drug 1 versus drug 2 in a clinical trial
♦ Inherent trait or characterizes 6
“Outcome”
♦ Disease
– e.g., infectious disease: malaria, TB
– e.g., non-infectious disease diabetes, cancer
♦ Event
– e.g., injury from land mine, car accident
♦ Condition
– e.g., blindness, other disabilities
♦ Death
♦ Other
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"Every epidemiologic study
can be summarized
in a 2-by-2 table”
to show association
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Standard Two-by-Two Table =
Contingency Table
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Two-by-Two Table
♦ From the table one can calculate:
• Risk in Exposed,
• Risk in Unexposed,
• Odds of exposure,
• RR,
• OR,
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Description of Relationship
♦ Variables can be Related or Unrelated to one
another
♦ If the two variables are Related, they can be
related either:
– positively or negatively
– strongly or weakly (one variable can have
large or small effect on the other)
– significantly or not significantly
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Relationships between variables —
Related or unrelated?
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2.00
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Dependent variable
Dependent variable
1.50
6
1.00
4
0.50
2
0.00
0
0.00 0.20 0.40 0.60 0.80 1.00 1.20
Independent variable 0.00 20.00 40.00 60.00
Independent Variable
Related unrelated
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Relationships between variables —
Positive & Negative association
10 10
Y Y
0 0
0 X 1 0 X 1
Positive Negative
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Relationships between variables —
Large or Small effect
10 10
Y Y
0 0
0 X 1 0 X 1
Strong/Large Weak/Small
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Significant or non-significant
♦ Statistically significant
The observed association is unlikely to be
due to chance alone
But remember:
• Statistically significant means that the
association is not likely due to chance
• It is dependent on the strength of the
association and sample size
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Measures of Association
– Relative Risk
– Odds Ratio
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RELATIVE RISK [RR]
♦ Is the term we use to describe the comparison of
two risks as a ratio
♦ Estimates the magnitude (size) of an association
between exposure and disease
♦ It indicates the likelihood of the exposed group
developing the disease relative to those not
exposed
♦ Indicates how many more times likely the
exposed are to develop the disease than the
non-exposed
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Relative Risk or Risk Ratio
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Relative Risk or Risk Ratio
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Example 1:
♦ Data from a cohort study of oral contraceptive (OC) use and
Breast Ca. among women aged 16-49 years
B. CA
Yes No Total
Current OC use
Yes 27 455 482
No 77 1831 1908
Total 104 2286 2390
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Example 1: cont…
RR = a/(a+b) =27/482 =1.4
c/(c+d) 77/1908
♦ Interpretation – OC users had 1.4 times the risk
more likely to develop B.Ca than nonusers
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Example 2:
♦ Data from a cohort study of postmenopausal
hormone use and coronary heart disease among
female nurses
Coronary heart disease
Yes No Person-years
Postmenopausal
hormone use
Yes 30 - 54,308.7
No 60 - 51,477.5
Total 90 105,786.2
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Example 2: …
RR = Ie =IDe = a/PY1 = 30/54,308.7 = 0.5
Io IDo c/PYo 60/51,477.5
♦ Interpretation: women who use
postmenopausal hormones had 0.5 times, or
only half, the risk of developing coronary heart
disease compared with nonusers.
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Example 3:
In an outbreak of ♦ Risk of Measles among
Measles in AA in vaccinated children
2002, measles was = 18 ⁄ 152 = 0.118 =
diagnosed in 18 of
152 vaccinated
11.8%
children compared ♦ Risk of measles among
with 3 of 7 unvaccinated children
unvaccinated = 3 ⁄ 7 = 0.429 = 42.9%
children. Calculate
the RR.
♦ RR= 0.118 ⁄ 0.429 =
0.28
Interpretation? 24
Interpreting Relative Risk
If RR = 1 Risk in exposed = Risk in non-exposed
– No association
If RR > 1 Risk in exposed > Risk in non-exposed
– Positive association; ? causal
If RR < 1 Risk in exposed < Risk in non-exposed
– Negative association; ? protective
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Measures of Association
Interpretation
A. RR = 0.87
B. RR = 4.25
C. RR = 1.86
Which RR suggests the strongest association?
Why?
Which RR suggests a protective effect?
Why?
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Odds Ratio
Odds are a measurement of the likelihood of
occurrence of an event
odds are a ratio of the probability that an event
occurs to the probability that the event does not
occur:
Odd = Probability of occurrence
Probability of non-occurrence
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Odds Ratio
Indicates the likelihood of having been exposed
among cases relative to controls
Cases and controls are predetermined and
we are calculating to determine whether
cases or controls are more exposed to a
postulated risk factor.
It is an indirect measure of a risk in a disease of
rare occurrence.
Thus, usually used in a case-control and
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cross-sectional analytic study designs.
Odds Ratio
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Odds ratio= cross product ratio
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Example 1:
♦ Data from a case-control study of current
oral contraceptive (OC) use and MI in
premenopausal women
Myocardial infarction
Yes No Total
Current OC use
Yes 23 304 327
No 133 2816 2949
Total 156 3120 3276
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Example 1 …
OR = ad = (23)(2816) = 1.6
bc (304)(133)
The odds of exposure history among MI
women is 1.6 times that of non- MI women.
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Example 2:
Deep Vein Thrombosis
Yes No
History of OC Yes 40 20
use No 20 30
OR = Odds of exposure in diseased = a/c = 40/20 = 3
odds of exposure in non diseased b/d 20/30
The odds of oral contraceptive use among
women with DVT is three times as likely when
compared to women with out DVT. 33
Attention!
♦ How can we calculate measure of association
when you have multiple levels of exposure?
♦ How can you calculate OR from the following
2x2 table
D- D+
E+
E-
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Interpretation
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Interpretation
RR & OR
1. RR/ OR > 1, the exposure is risk
2. RR/ OR = 1, there is no association
3. RR/ OR < 1, the exposure is Preventive
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THANK YOU
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