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Exposure
(Risk Factor) Outcome
Exposures
“Risk factors”
Preventive measures
Management strategy
Independent variables
Outcomes
Dependent variable
Disease occurrence
Examples:
Lack of exercise Heart disease?
Flu Shot Dystonia Disorder?
Is There An Association?
Hypothesis Testing Scheme
Target Population
Study
Population
• Collect data
• Make comparisons Is there an association?
Are the results valid? Chance
Bias
Confounding
Inference Sample
In analytic studies one enrolls subjects from a population
and groups them in some way to make comparisons that
test association between risk factors and outcomes.
Various Exposure-Disease
Categories
Sorted by Exposure & Disease
Diseased & Exposed
Not exposed,
But diseased
Not exposed and
Non-diseased
Exposed, but
Non-diseased
Did those who were exposed to a
given dish have a higher probability
of disease compared to …
… those who were
not exposed?
All Three Of These Can Be
Summarized by a 2x2 Table
All three analytical studies rely on a comparison of
groups to determine whether there is an association.
Yes No
Yes
No
Outcome
Exposure
• Cohort
• Clinical Trial
• Case-Control
7 124 131
1 78 79
Incidental Appendectomy
and Risk of Wound Infection
How can we quantify the magnitude of association?
Yes No
Yes
No
Wound Infection
A Retrospective
Cohort Study
7 124 131
1 78 79
210 Subjects
Incidental
Appendectomy
Cumulative
Incidence
= 5.3%
= 1.3%
= 7/131
= 1/79
CIe
CI0
Options For Comparing Incidence
1. Calculate the ratio of the incidences for
the two groups. (Divide incidence in
exposed group by the incidence in the
control group).
Or
Ie
I0
Ie- I0
For Cohort Type Studies
2. Calculate the difference in incidence
between the two groups. (Subtract
incidence in control group from the
incidence in the exposed group).
The Risk Ratio
(a measure of association)
Yes No
Yes
No
Wound Infection
A Retrospective
Cohort Study
7 124 131
1 78 79
Incidental
Appendectomy
Cumulative
Incidence
= 5.3%
= 1.3%
= 7/131
= 1/79
Ie
I0
RR = 7/131 = 5.3 = 4.2
1/79 1.3
“Risk Ratio” or
“Relative Risk”
Exposure
(Risk Factor) Outcome
Association A link between antecedent factors and
some outcome –possibly a causal
relationship, but not necessarily.
Exposures
“Risk factors”
Preventive measures
Management strategy
Independent variables
Outcomes
Dependent variable
Disease occurrence
Examples:
Lack of exercise Heart disease?
Flu Shot Dystonia Disorder?
Risk Ratio in the Appendectomy Study
RR = = 5.3%
1.3% = 4.2
Interpretation: “In this study those who had an
incidental appendectomy had 4.2 times the risk
compared to those who did not have appendectomy.”
5.3%
1.3%
Also had appendectomy
No appendectomy
(A simple ratio;
no
dimensions.)
RR = = 5.3%
= 1.0 5.3%
5.3%
5.3%
Exposed group
Unexposed group
What If Risk Ratio = 1.0 ?
The Risk Ratio
(a measure of association)
Yes No
Yes
No
Wound Infection
A Randomized
Clinical Trial
139 10,898 11,037
Incidental
Appendectomy
Cumulative
Incidence
CIe
CI0 = 239/11034
= .0221
RR = .0126 = 0.55
.0221
239 10,795 11,034
= 139/11,037
= .0126
The Risk Ratio
(a measure of association)
Yes No
Yes
No
Heart Attack
139 10,898 11,037 Low Dose
Aspirin
Cumulative
Incidence
CIe
CI0 = 239/11034
= .0221
RR = .0126 = 0.55
.0221
239 10,795 11,034
= 139/11,037
= .0126
Interpretation: “Subjects who used aspirin had
0.55 times the risk of myocardial infarction
compared to those who did not use aspirin.”
A Randomized
Clinical Trial
Comparing Incidence Rates
Yes No
Yes
No
Outcome
Prospective Cohort Study
or
RCT
a - PYe
Exposure
Incidence
Rates
IRe
IR0 = b/PY0 b - PY0
= a/PYe
Disease-free
Obs. Time
Rate Ratio = IRe
IR0 b/PY0
a/PYe =
Comparing Incidence Rates
Yes No
Yes
No
Heart Disease
Prospective Cohort Study
30 - 54,308
Postmenopausal
HRT
Incidence
Rates
IRe
IR0 60 - 51,478
=30/54,308
Disease-free
Obs. Time
=60/51,478
Rate Ratio = 55.2 /100,000 P-Yr. = 0.47
116.6 /100,000 P-Yr.
Best interpretation?
1. Women using hormone replacement therapy had 0.47
times the risk of coronary disease compared to women who
did not use HRT.
2. Women using hormone replacement therapy had 0.47
times more risk of coronary disease compared to women
who did not use HRT.
3. Women using hormone replacement therapy had 0.47
times less risk of coronary disease compared to women
who did not use HRT.
Rate Ratio = 55.2 /100,000 P-Yr. = 0.47
116.6 /100,000 P-Yr.
It is more precise to say that postmenopausal
women on HRT had 0.47 times the rate of coronary
disease, compared to women not taking HRT.
In practice, however, many people interpret it just
like a risk ratio.
Risk Ratios
.0415 / .0336 = 1.33
.0445 / .0336 = 1.23
.0336 / .0336 = 1.00
Cumulative Incidence
30/674 =.0445
61/1,469 =.0415
2,264/67,424=.0336
High
Medium
Low
Magnetic
Field
Exposure
Leukemia
No
Leukemia
Totals
30 644 674
61 1,408 1,469
2,264 65,160 67,424
High
Medium
Low
Lowest exposure group is the reference for comparison.
Multiple Exposure Categories
Data from The Nurses’ Health Study
Obesity Heart Attack ?
# MIs
(non-fatal) 41
57
56
67
85
Person-years
of observation 177,356
194,243
155,717
148,541
99,573
Rate of MI per
100,000 P-Yrs.
(incidence) 23.1
29.3
36.0
45.1
85.4
Rate
Ratio 1.0
1.3
1.6
2.0
3.7
<21
21-23
23-25
25-29
>29
BMI:
wgt kg
hgt m2
?
Multiple Exposure Categories - An “r x c” (row/column) Table
RD = Incidence in exposed - Incidence in unexposed
Risk Difference = Ie - I0
The Risk Difference
(Attributable Risk)
Risk Difference
(another measure of association)
Yes No
Yes
No
Wound Infection
A Retrospective
Cohort Study
7 124 131
1 78 79
Incidental
Appendectomy
Cumulative
Incidence
= 5.3%
= 1.3%
= 7/131
= 1/79
Ie
I0
RD = 5.3%-1.3% = 4 per 100 appendectomies
= 0.053 – 0.013 = 0.04 = 4 per 100
Risk
Difference
1.3/100
Exposed Not Exposed
Excess
risk is
4 per 100
5.3/100
Even if appendectomy is
not done, there is a risk
of wound infection (1.3
per 100).
Assuming there is a cause-effect relationship… the RD is
the excess risk in those who have the “exposure”, i.e., the
risk of wound infection that can be attributed to having had
the incidental appendectomy.
Adding an appendectomy
appears to increase the
risk by (4 per 100
appendectomies), so…
Risk Difference Gives a Different Perspective
Example:
Incidence with appendectomy = 5.3% = 0.053
Incidence without appendectomy = 1.3% = 0.013
Risk Difference = 0.040
= 40/1000
i.e., 4 per 100 incidental appendectomies or
40 per 1,000 incidental appendectomies
#1: Convert decimals into a form so that
you can interpret for a group of people.
Interpretation:
In the group that underwent incidental appendectomy there were
40 excess wound infection per 1000 subjects (or 4 per 100).
#2: The focus is on excess disease in the exposed group.
Tips for Interpretation of Risk Difference
#3 Don’t forget to specify the time period when
you are describing RD for cumulative incidence.
NOTE: In the appendectomy study the time period was very
brief and was implicit (“postoperatively”) it wasn’t necessary
to specify the time frame. However, for most cohort studies it
is important. Remember that with cumulative incidence, the
time interval is described in words.
Interpretation:
In the group that failed to adhere closely to the
Mediterranean diet there were 120 excess deaths per
1,000 men during a two year period of observation.
Tip #3 for Interpretation of Risk Difference
85.4
23.1
# MIs
(non-fatal)
41
57
56
67
85
Person-years
of observation
177,356
194,243
155,717
148,541
99,573
Rate of MI per
100,000 P-Yrs
(incidence rate)
29.3
36.0
45.1
Rate
Ratio
1.0
1.3
1.6
2.0
3.7
Rate Difference = 85.4/100,000 - 23.1/100,000
= 62.3 excess cases / 100,000 P-Y in the heaviest group
<21
21-23
23-25
25-29
>29
BMI:
wgt kg
hgt m2
Rate Differences
Interpretation: Among the heaviest women there were 62
excess cases of heart disease per 100,000 person-years
of follow up that could be attributed to their excess weight.
This suggests that if we followed 50,000 women with BMI
> 29 for 2 years we might expect 62 excess myocardial
infarctions due to their weight. (Or one could prevent 62
deaths by getting them to reduce their weight.)
If 100,000 obese women had remained lean, it
would prevent 62 myocardial infarctions per year.
or
Rate Difference Interpretation
Influenza Vaccination and Reduction in Hospitalizations
for Cardiac Disease and Stroke among the Elderly. Kristin Nichol et al.: NEJM 2003;348:1322-32.
These investigators used the administrative data bases
of three large managed care organizations to study the
impact of vaccination in the elderly on hospitalization
and death. Administrative records were used to whether
subjects had received influenza vaccine and whether
they were hospitalized or died during the year of study.
The table below summarizes findings during the 1998-