E3 Measures
A tale of risks, rates and odds
Hein Stigum
Presentation, data and programs at:
http://folk.uio.no/heins/
courses
May-16
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Outcome types
• Weight and Blood pressure
– Continuous outcome:
• How much:
• More if exposed:
mean
difference in mean
• Exposure and Disease
– Binary outcome:
• How much:
• More if exposed:
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?
?
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Epidemiological measures
• Frequency
– prevalence
– incidence
How much disease?
• Association, effect
– Risk difference
– Risk ratio
– Odds ratio
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CONCEPTS
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Disease frequency
New versus existing cases
A
Hospital beds:
existing cases
Disease growth: new cases
B
Comparability:
Large versus small population: cases per population
Long versus short study:
cases per population and time
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Concepts
Risk
(new) cases
p
N
probability, proportion, %
Rate
new cases
r
N t
Km/h, cases/person-time
p N disease
Odds o 
 
1  p N healthy
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risk
0.0100
0.1000
0.3000
Odds
0.0101
0.1111
0.4286
6
Cohorts
Closed cohort
start
Open cohort
start
end
Count persons, risk
May-16
end
Count person-time, rate
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Exercise, Comparability
• 1) Two countries
–
–
–
–
Norway: 50 000 cases, population 5 million
Sweden: 150 000 cases, population 10 million
How would you compare frequencies of disease?
What measure did you use (risk, rate or odds)?
• 2) Two studies
–
–
–
–
A) 1000 subjects followed 2 years, 200 new cases
B) 1000 subjects followed 10 years, 500 new cases
How would you compare frequencies of disease?
What measure did you use (risk, rate or odds)?
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FREQUENCY MEASURES
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Cross-section, Prevalence
Existing
disease
50
Prevalence:
Healthy
Existing disease cases
P
Population
950
start
end
Frequency
Risk
Rate Odds
0 year follow up
+
Disease
50
-
950
N
Risk time
1 000
0.050
0.053
Prevalence risk: 5% with disease
Prevalence odds: 53 with disease per 1000 without
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Exercise
• 2200 subject in total
• 200 of these have disease
• Is this prevalence or incidence?
• Can you calculate risk, rate and odds?
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Cohort, Incidence
(Existing
disease)
New
disease
200
Healthy
Risk time
1700
950
750
2-year risk, incidence proportion:
Healthy
New disease cases
IP 
Healthy
rate, incidence rate:
0
1
IR 
2
Frequency
Risk
Rate Odds
2 year follow up
+
Disease
200
-
750
N
Risk time
950
1 700
New disease cases
RiskTime
0.21
0.12
0.27
Incidence risk: 21% risk of getting disease in 2 years
Incidence rate: 12 new cases per 100 person years
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Convert rate to risk
Use
• Risks only in closed cohorts
Understanding
• Easy
• Rates in all cohorts
• Difficult
• Convert the rate=0.12 to a 2-year risk
IP  1  e  IR  t  IR  t
IP  1  e 0.12 2  0.12  2
2-year risk
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=0.21
H.S.
=0.24
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Exercise, small cohort
• 6 subjects followed
up to 10 years
• 3 new cases of
disease
2
1
2
6
6
9
0
• Can only get
disease once
1
2
3
4
5
6
Time
Follow up
7
Disease
8
9
10
Death
• Can you calculate risk, rate and odds?
10 min
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26
Incidence of hip fracture,
women age 65+
Beijing, Kina (1990-92)
Tottori, Japan (1994)
Wessex, England (1993-95)
Tampare, Finland (1989)
Vaud, Sveits (1991)
Hvite, USA (1988-89)
Göteborg (1989)
København (1989)
Oslo (96/97), sommer
Oslo (1996-97)
Kvinner
0
50
100
150
200
250
Insidensrate
10 000
000 personår
Incidence
rate prpr10
person years
(Lofthus et al. 2001)
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Disease frequency summary
Theoretical concept
Estimator
Prevalence:
Existing Cases
P
Population
The risk of having disease
New Cases
IP 
Healthy
Incidence proportion:
The risk of getting disease
Incidence rate:
New Cases
IR 
RiskTime
The rate of getting disease
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Frequency measures
risk
rate
odds
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Prevalence
Incidence proportion
Incidence rate
existing cases
new cases
Prevalence odds
Incidence odds
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Epidemiological measures
• Frequency
– prevalence
– incidence
How much disease?
• Association, effect
– Risk difference
– Risk ratio
– Odds ratio
May-16
More disease
among exposed?
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ASSOCIATIONor
EFFECT MEASURES
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Association measures
• More disease among exposed?
– Compare frequency among exposed1 and unexposed0
– Difference:
RD=IP1-IP0
0=no effect
– Ratio:
RR=IP1/IP0
1=no effect
Frequency
Association or Effect
Difference
Ratio
Risk
Risk Difference, RD
Risk Ratio, RR
Rate
Rate Difference
Rate Ratio, RR, IRR, (HRR)
Odds
-
Odds Ratio, OR
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Prevalence depicted
Existing
cases
Prevalence risk
Exposed: P1
Unexposed: P0
Healthy
Prevalence odds
Exposed: O1
Unexposed: O0
start
May-16
end
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Cross-sectional example
Smoking
+
300
140
Girls
Boys
Disease freq
22.0 %
Exposure freq
50.0 %
N
Frequency
Risk
Rate Odds
Risk time
-
700
860
1 560
1 000
1 000
2 000
Difference
Ratio
Risk
Difference
Ratio
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16 pp added
risk
2.1 times the
risk
H.S.
0.30
0.43
0.14
0.16
Association
0.16
2.1
2.6
Interpretation
Rate
Odds
2.6 times the
odds
22
Incidence risk, rate and odds depicted
Existing
cases
t
a
Healthy
New
cases
Risk time
Exposed:
Unexposed:
start
R1
R0
end
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Exercise: Cohort study
Disease: lung cancer
Exposure: smoking
Closed cohort
Frequency
Risk
Rate Odds
10 year follow up
Lung cancer
+
Smoking
+
-
200
12
212
N
Risk time
4 000
6 000
10 000
39 000
59 940
98 940
-
3 800
5 988
9 788
Association
Difference
Ratio
Disease freq
Exposure freq
• Calculate frequency measures for lung cancer
• Calculate association measures for smoking on lung cancer
10 min
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Traditional Case-Control
Full cohort:
Lung cancer
+
Smoking
+
-
200
12
212
Disease freq
2.1 %
Exposure freq
40.0 %
Frequency
Risk
Rate Odds
10 year follow up
-
3 800
5 988
9 788
N
Risk time
4 000
6 000
10 000
39 000
59 940
98 940
Difference
Ratio
0.050 0.005 0.053
0.002 0.000 0.002
Association
0.048 0.005
25.00 25.62 26.26
Case-Control:
Sampling fraction 0.1
Lung cancer
+
Smoking
+
-
200
12
212
Risk time
-
380
599
979
Trad. CC
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N
Pseudo Frequency
Risk
Rate Odds
0.526
0.020
Association
Case-Cohort
Nested CC
H.S.
Difference
Ratio
-
26.26
25
Traditional Case-Control
Existing
cases
Healthy
New
cases
Risk time
start
May-16
.
.
.
.
controls
end
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ASSOCIATION MEASURES
COMPARED
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Changing reference group
Expo
sure
+
-
Risk
10 %
1%
RR
10
1
0.1
RR
1
0.10
RD
9pp
0
RD
0
-9pp
10
0
∞
1
More than 2 groups:
Group
a
b
c
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Risk
1%
2%
10 %
RR
1
2.0
10.0
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Cohort 2
• Do infections early in life protect against allergy?
– 166 asthmatic children (high risk of allergy)
– 33 with repeated infections, 11 of these allergic
– 133 without repeated infections, 83 of these allergic
Cohort
Allergy
+
Infections
Frequency
Risk
Rate Odds
3 year follow up
+
-
11
83
94
Disease freq
56.6 %
Exposure freq
19.9 %
N
Risk time
-
0.33
0.62
33
133
166
Difference
Ratio
Difference:
Ratio:
Association
-0.29
0.5
29 pp less risk
half the risk
Conclusion: infections protect against allergy
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Association conversions
Risk Ratio versus Rate Ratio
For small IR*t:
IP1 IR1  t IR1
Incidence Risk Ratio 


 Rate Ratio
IP0 IR0  t IR0
Prevalence Risk Ratio versus Incidence Rate Ratio
Under steady state and no migration:
P1 IR1  D IR1



Prevalence Risk Ratio 
P0 IR0  D IR0
Rate Ratio
All often termed relative risk, RR
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Bullying, OR example
• Bullying in the Nordic countries
17 114 children, 2 584 bullied
2584
Prevalence 
 0.151  15.1%
17114
• Why use OR?
– Traditional Case-Control
– Logistic regression
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Variable
Overall
Study
1984
1996
Country
Sweden
Iceland
Norway
Finland
Denmark
Sex
Female
Male
Age group
13-17 years
2-6 years
7-12 years
Education
> 12 years
12 years
10-11 years
 9 years
Chronic disease
No
Yes
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N
% bullied
17114
15.1
8093
9021
13.7
16.4
3340
2949
3183
4076
3573
7.2
9.7
14.7
22.6
19.4
8409
8605
12.9
17.5
5306
4658
7035
10
16.5
18.3
4963
3892
4221
3172
12.3
16.6
15.3
17.4
14221
1978
13.6
26.8
H.S.
p-value
Adjusted OR
(CI)
<0.001
1
1.3(1.2-1.4)
<0.001
1
1.4(1.1-1.7)
2.2(1.8-2.6)
4.0(3.4-4.7)
3.3(2.8-3.9)
<0.001
1
1.4(1.3-1.6)
<0.001
1
2.0(1.8-2.3)
2.2(1.9-2.5)
<0.001
1
1.3(1.1-1.4)
1.3(1.1-1.4)
1.4(1.2-1.7)
<0.001
1
2.3(2.1-2.6)
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Unexposed
Exposed
RR and OR depicted
N1
N1
aa
bb
aa
N1
N1
RR=
RR:
N0
N0
Exposed
Exposed
start
N1
N1
cc
dd
Unexposed
Unexposed
N0
N0
aa
bb
aa
N1b
RR=
OR=
N0
N0
start
start
RR=2
OR
2.02
2.10
4.67
end
OR:
May-16
cc
Disease
1%
5%
40 %
RR=1.2
risk OR
1.20
1.21
1.38
cc
dd
cc
N0
d
OR=RR
if
rare disease
or
small effect
end
end
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Epidemiological measures
• Frequency
Prevalence
risk
odds
Incidence
risk
rate
odds
How much disease?
• Association, effect
Difference
risk diff
rate diff
-
May-16
Ratio
More disease
among exposed?
risk ratio
rate ratio
odds ratio
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