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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-
1999 flu season.
Flu Vaccine Study
Vaccinated
subjects
(N=77,738)
Unvaccinated
subjects
(N=62,217)
Hospitalized for pneumonia
or influenza
495 581
Hospitalized for cardiac
disease
888 1026
Death 943 1361
If the exposure is vaccination & outcome of
interest is death, what is the risk difference?
Flu Vaccine Study Data
Vaccinated
subjects
(N=77,738)
Unvaccinated
subjects
(N=62,217)
Hospitalized for pneumonia
or influenza
495 581
Hospitalized for cardiac
disease
888 1026
Death 943 1361
Died Not Dead
Vaccinated 943 (77,738 - 943)
Not Vaccinated 1361 (62,217 – 1,361)
If the exposure is vaccination & outcome of
interest is death, what is the risk difference?
RD = CIe – CIu = (943 / 77,738) - (1,361 / 62,317) = - 0.0097
= - 97/10,000 over a year
77,738
62,217
- 97/10,000 over a year
Sure, instead of calling it ‘excess risk’,
just refer to it as a ‘risk reduction.’
Can a risk difference be a
negative number?
RR & RD: Different Perspectives
Relative Risk: shows the strength of the association.
RR = 1.0 suggests no association
RR close to 1.0 suggests weak association
RR >> 1.0 or RR << 1.0 suggests a strong association
Risk Difference: a better measure of public health impact.
How much impact would prevention have?
How many people would benefit?
Example: A study looked at whether fecal occult blood testing
(FOBT) decreased mortality from colorectal cancer (CRC).
FOBT decreased mortality from 9 per 1,000 people to 6
per 1,000.
Relative Risk Perspective:
RR= 0.006/0.009 = 0.67, so FOBT decreased CRC
mortality by 33%.
Risk Difference Perspective:
The risk difference was 3 per 1,000
people screened.
The ratio of these two numbers is
more impressive than the actual
difference.
FOBT Screening
Coronary Heart Disease
Cigarette smokers 669
Non-smokers 413
Annual Mortality
per 100,000 (CI)
Smoking is a stronger risk factor for …. ? Smoking is a bigger public health problem for …. ?
Lung Cancer
Cigarette smokers 140
Non-smokers 10
Annual Mortality
per 100,000 (CI)
Calculate RR & RD for Two Diseases
Coronary Heart Disease
Cigarette smokers 669
Non-smokers 413
Annual Mortality
per 100,000 (CI)
Smoking is a stronger risk factor for …. ? Smoking is a bigger public health problem for …. ?
Lung Cancer
Cigarette smokers 140
Non-smokers 10
Annual Mortality
per 100,000 (CI)
Calculate RR & RD for Two Diseases
RR= 14
RD= 130 per 100,000
RR= 1.6
RD= 256 per 100,000
0
100
200
300
400
500
600
700
800
Lung Cancer Heart Disease
Non-s
mokers
Sm
okers
Sm
okers
Non-s
mo
ke
rs
MI 125.9 216.6
Aspirin Placebo Risk Ratio (/10,000) (/10,000)
0.59
What should we conclude?
What should we recommend?
Aspirin & Myocardial Infarction
(Heart Attack)
Stroke 107.8 88.8 1.2
Ischemic 82.4 74.3 1.1
Hemorrhagic 20.8 10.9 1.9
Upper GI ulcer 153.1 125.1 1.2
with hemorrhage 34.4 19.9 1.7
Bleeding 2699.1 2037.3 1.3
Transfusion need 43.5 25.4 1.7
Aspirin Placebo Risk
(/10,000) (/10,000) Ratio
MI 125.9 216.6 0.59
What should we conclude?
What should we recommend?
Benefits & Risks
Stroke 107.8 88.8 1.2 19
Ischemic 82.4 74.3 1.1 8
Hemorrhagic 20.8 10.9 1.9 10
Upper GI ulcer 153.1 125.1 1.2 28
with hemorrhage 34.4 19.9 1.7 15
Bleeding 2699.1 2037.3 1.3 690
Transfusion need 43.5 25.4 1.7 18
MI 125.9 216.6 0.59 -100
Aspirin Placebo RR RD (/10,000) (/10,000) (/10,000)
Benefits & Risks
If we are going to discuss rare, but serious possible
complications of influenza vaccine, would it be better
to look at the Risk Ratio or the Risk Difference?
Observed frequency in:
Exposed people: 2 / 100,000
Unexposed people: 1 / 100,000
Risk Ratio = 2; those exposed had two times the risk! (OMG!)
Risk Difference = 1 per 100,000; assuming that the
exposure is a cause of the outcome, the exposed group
had an excess risk of 1 case per 100,000 subjects.
Rare Outcomes – RR or RD?
The proportion (%) of disease in the exposed group
that can be attributed to the exposure, i.e., the
proportion of disease in the exposed group that
could be prevented by eliminating the exposure.
AR% = RD x 100
Ie
.04 x 100 = 75%
.053
Interpretation: 75% of infections occurring in patients who had
the appendectomy could be attributed to the appendectomy.
Exposed Not
Exposed
.013
.053 .04
What % of infections in the exposed group
can be attributed to having had the exposure?
Attributable Risk % - (Attributable Proportion)
Diseased No Disease Totals Cumulative
Incidence
Exposed 500 9,500 10,000 0.050
Not Exposed 900 89,100 90,000 0.010
1,400 98,600 100,000 0.014
1. Total risk in exposed group?
2. Excess risk in exposed group?
3. Attributable proportion in exposed group?
Quiz: A Cohort Study Over One Year
Diseased No Disease Totals Cumulative
Incidence
Exposed 500 9,500 10,000 0.050
Not Exposed 900 89,100 90,000 0.010
1,400 98,600 100,000 0.014
1. Total risk in exposed group?
2. Excess risk in exposed group?
3. Attributable proportion in exposed group?
0.050 = 50/1,000
= 0.050 – 0.10
= 40/1,000 over 1 yr.
40/1,000 = 80%
50/1,000
Quiz: A Cohort Study Over One Year
Quiz: Smoking & Lung CA Death
A prospective cohort study compared lung cancer mortality in
smokers vs. non-smokers.
Among 20,000 non smokers there were 20 deaths from
lung cancer during 5 years of study.
Among 5,000 smokers there were 100 deaths from lung
cancer during the 5 year study period.
1) Organize this information in a 2x2 table.
2) Calculate the cumulative incidence of death (per 1,000) due to lung
cancer in smokers and non-smokers.
3) Calculate the relative risk; interpret it in words.
4) Calculate the risk difference; interpret it in words.
5) Calculate the attributable fraction in the exposed; interpret it in words.
A prospective cohort study compared lung cancer mortality in
smokers vs. non-smokers.
Among 20,000 non smokers there were 20 deaths from
lung cancer during 5 years of study.
Among 5,000 smokers there were 100 deaths from lung
cancer during the 5 year study period.
1) Organize this information in a 2x2 table.
2) Calculate the cumulative incidence of death (per 1,000) due to lung
cancer in smokers and non-smokers.
3) Calculate the relative risk; interpret it in words.
4) Calculate the risk difference; interpret it in words.
5) Calculate the attributable fraction in the exposed; interpret it in words.
100 4900
20 19980
5000
20000
100/5,000=0.02=20/1,000 over 5 yrs.
20/20,000=0.001=1/1,000 over 5 yrs.
RR = 20/1
AF in exposed = 19/20 x 100 = 0.95 = 95%
RD = 19/1,000 over 5 yrs.
Measuring Association in a
Case-Control Study
Cohort & Case-Control Models
Compare
Incidence
X
X X X
Time passes
Case-Control
Studies Compare odds of
exposure to risk factor Compare Prior
Exposures
Exposed
Non-Exposed
Non-Diseased
X X X
X X
X X Diseased
Cohort Type
Studies
But in a case-control study we find diseased & non-diseased
people and compare the frequency of prior exposures.
To calculate incidence, you need to take a group of initially disease-
free people and measure the occurrence of disease over time.
Yes No
Wound Infection
1 78 79
7 124 131 Yes
No
Had Incidental
Appendectomy
Cumulative
Incidence
5.3%
1.3%
How many exposed people did it take to
generate the 7 cases in the 1st cell?
Retrospective
Cohort Study
Yes No
Hepatitis
1 29
18 7 Yes
No
19 36
Ate at
Deli
Case Control
How many people had to eat at the Deli in
order to generate the 18 cases in the 1st cell?
In a true case-control study, you do not know
the denominators for exposure groups!
?
?
Case-Control
Study
Diseased Non-
diseased Total
Exposed 7 1,000 1,007
Non-
exposed 6 5,634 5,640
If I somehow had exposure and outcome information on all
of the subjects in the source population and looked at the
association using a cohort design, it might look like this:
The risk ratio is calculated as (7/1,007) / (6/5,640) =
6.53, i.e., the key information is in the four numbers
in the four highlighted numbers.
A Rare Outcome
Diseased Non-
diseased Total
Exposed 7 1,000 1,007
Non-
exposed 6 5,634 5,640
But RR = (7/1,007) can be rearranged algebraically
(6/5,640)
To (7/6)
(1,007/5,640) = 6.53
In a sense this is comparing the exposure distribution
(odds of exposure) in the diseased people to the
exposure distribution in the overall population.
So all of the information we need in in those 4 numbers.
Diseased Non-
diseased Total
Exposed 7 1,000 1,007
Non-
exposed 6 5,634 5,640
And since the disease is infrequent, the exposure distribution in
non-diseased subjects is similar to that in the total population.
So, if all I need to estimate the risk ratio is the exposure
distribution in in the cases and the exposure distribution in
non-diseased people, why not just take a sample of non-
diseased people?
=
Diseased Non-
diseased Total
Exposed 7 10 ?
Non-exposed 6 56 ?
(7/1007)
(6/5640) = 6.53 = Risk Ratio
(7/6)
(10/56) = 6.53 = Odds Ratio
X X
X X X X X
X If I take a reasonable
sample of non-diseased
people, I can estimate
the exposure distribution
in the overall population.
Diseased Non-
diseased Tot.
Exposed 7 10 ?
Non-
exposed 6 56 ?
So, if I want to estimate a risk ratio for a rare disease, it is
more efficient to find cases, but then just take a sample of
non-diseased “controls” in order to estimate the exposure
distribution in the entire population.
(7/1007)
(6/5640) = 6.53 = Risk Ratio
Diseased Non-
diseased Tot.
Exposed 7 1000 1007
Non-
exposed 6 5634 5640
(7/6)
(10/56) = 6.53 = Odds Ratio
Sick Not Sick
Yes
No
Find diseased people & non-diseased people;
compare their odds of having been exposed.
Odds of exposure = 6/4; odds of exposure =8/24
(Esp. useful for rare outcomes, e.g., birth defects.)
Outcome
Exposure
Status
Case-control Method for Sampling
Hepatitis
1 29
18 7 Yes
No
19 36
Ate at
Rick’s Deli
Cases Controls
X X
X X X X X
X
Yes
No
Odds = 7/29 Odds = 18/1
Odds Ratio =
= 75
18/1
7/29
Literal: Hepatitis cases were 75 times
more likely to have eaten at the Deli.
Better: Those who ate at Rick’s had 75
times the risk of hepatitis.
OR for
Rick’s Deli
An Odds Ratio Is Interpreted
Like a Relative Risk
“Individuals who ate at the Deli had 75 times the risk of hepatitis A compared to those who did not eat at the Deli.”
• An odds ratio is a good estimate of relative risk when the outcome is relatively uncommon.
• The odds ratio exaggerates relative risk when the outcome is more common.
In cohort studies and clinical trials you can
calculate incidence, so you can calculate
either a relative risk or an odds ratio.
In a case-control study, you can only
calculate an odds ratio.
You can always calculate an odds ratio, but…
Odds = 16/14
Ratio 108/341
= 3.6
a/c
b/d
a x d
b x c
16 108
14 341
Kid pool
Not
a b
c d
Odds = 16x341
Ratio 108x14
= 3.6
Odds = 16/108
Ratio 14/341
= 3.6
a/b
c/d
Ratio of Odds
of Disease
Ratio of Odds
of Exposure
Cross Product
Ways to Calculate an Odds Ratio
Ie = 60
168
I0 = 45
386
Yes No
Outcome
45 341 386
unexposed
60 108 168
exposed Yes
No
Risk Factor
60 / (60+108)
45 / (45+341)
RR = 3.06
RR = 60 / 108
45 / 341
OR = 4.21
OR =
With a Common Outcome OR Exaggerates RR
You should be able to calculate these measures of
disease frequency and measures of association
using a simple hand calculator.
Epi_Tools.XLS will also do them, but you need to
be able to do them without Epi_Tools for the exams.
What does one measure and
compare in a case-control study?
1. Cumulative incidence
2. Incidence rate
3. Risk of disease
4. Frequency of past exposures
5. Risk difference
In a cohort study one may measure the degree of
association between an exposure and an outcome by
calculating either a relative risk or an odds ratio?
1. True
2. False
3. I’m not sure
In a case-control study one may measure the degree
of association between an exposure and an outcome
by calculating either a relative risk or an odds ratio.
1. True
2. False
3. I don’t know.
When is an odds ratio a legitimate
estimate of relative risk?
1. Whenever one is conducting a case-control study.
2. When the exposure is relatively uncommon.
3. When the outcome is relatively uncommon.
4. When the sample size is large.
Percent Death By Age Group
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
<25 26-39 40-54 55-69 70+
Age
Perc
en
t D
eath
What measure of disease frequency was used?
MVC in Elderly Drivers
Mean
ISS
Mean
LOS N Deaths Incidence
No Restraint 18.35 13.85 26 8 0.31
Restraint 11.86 9.92 50 5 0.10
Elderly Drivers Admitted to BMC after MVC
Compute risk difference & attributable proportion;
interpret them.
Mean
ISS
Mean
LOS N Deaths Incidence
No Restraint 18.35 13.85 26 8 0.31
Restraint 11.86 9.92 50 5 0.10
Elderly Drivers Admitted to BMC after MVC
Risk Difference = 0.31-0.10
= 0.21
= 21 excess deaths/100 injured drivers
Attributable Proportion = (0.21/0.31) x 100
= 68%
68% of the deaths in unrestrained elderly drivers
could be attributed to their lack of restraint.
Compute risk difference & attributable proportion;
interpret them.
Diseased Non-diseased Total
Exposed 7 1,000 1,007
Non-exposed 6 5,634 5,640
(7/1,000) = Odds Ratio (7/1,007) = Risk Ratio
(6/5,634) (6/5,640)
(7 / 1,000)
(6 / 5,634)
7 x
1,000 6
5,634 (7 /
(1,000
6)
/ 5,634)
7 x
1,000 6
5,634 =
Odds of disease in Exposed Odds of disease in Unexposed
Odds of exposure in Disease Odds of exposure in Non-Disease
But this rearranges
algebraically:
= =
I just need these two ratios of the exposure distribution.
