Constantly forgotten
Hein Stigum
Presentation, data and programs at:
http://folk.uio.no/heins/
Talks, Constantly forgotten
May-16
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Agenda
• Example
• Concepts
– Prevalence, risk and odds
• Methods
– Regression models
• RD
• RR
• OR
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Smoking among 10th graders
Variable
N
%
All
Sex
Boy
Girl
Parents marital status
Living together
Single
Educational plans
Academic
Secondary 3 years
Secondary 1 year
Vocational
Family economy
Well off
Good
Short of mony
10785
14.5
May-16
p-value
<.001
5045
5740
8.7
19.5
Adjusted
Odds Confidence
Ratio interval
?
1.0
3.0
(2.7 - 3.4)
1.0
2.3
(2.1 - 2.6)
1.0
1.7
2.4
2.8
(1.3 - 2.2)
(1.9 - 3.1)
(2.5 - 3.2)
1.0
1.3
1.7
(1.0 - 1.6)
(1.3 - 2.2)
<.001
7165
3564
10.4
22.5
<.001
5157
540
41
2701
9.9
15.4
22.0
23.4
<.001
936
9381
331
14.2
14.0
27.8
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30
40
Constant term, sex
10
20
y  βo  β1sex
βo
0
Constant term, intercept
1, Boys
2, Girls
20
10
βo
0
generate sex1  sex - 1
y  βo  β1sex1
30
40
0
0
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1, Boys
2, Girls
4
20
30
40
Constant term, age
10
y  βo  β1age
-10
0
βo
20
Age
25
30
35
40
20
10
0
βo
-10
generate age30  age  30
y  βo  β1age 30
30
40
0
0
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20
Age
25
30
35
40
5
Prevalence and risk
• Prevalence
– Risk of having disease
• Incidence proportion
– Risk of getting disease
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Generalized linear models, GLM
• Smoking as outcome
– y=0/1, x = covariates
– E(y|x) = P(y=1|x) = p
– family: y|x~Binomial
–
identity
– link: log
–
logit
May-16
RD
RR
OR
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RD versus RR and OR
RD
-1
0
1
RR, OR
0
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1

8
Linear binomial model, RD
p  βo  β1sex   2 age
p  βo  RD1  RD2
Girl, with single parents,
academic plans and well off:
Prevalence=
0.000+0.120+0.104=0.223
=22.3%
May-16
Variable
Risk at reference
Sex
Boy
Girl
Parents marital status
Living together
Single
Educational plans
Academic
Secondary 3 years
Secondary 1 year
Vocational
Family economy
Well off
Short of mony
H.S.
Confidence
RD
interval
0.000
0
0.120
(0.107, 0.132)
0
0.104
(0.088, 0.119)
0
0.057
0.107
0.130
(0.027, 0.088)
(0.069, 0.145)
(0.113, 0.147)
0
0.086
(0.038, 0.134)
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Log binomial model, RR
log( p)  βo  β1sex   2 age
p  e βo  β1sex  2 age
 e  RR1  RR2
βo
Girl, with single parents,
academic plans and well off:
Prevalence=
0.043 * 2.45 * 1.94=0.203
=20.3%
May-16
Variable
Risk at reference
Sex
Boy
Girl
Parents marital status
Living together
Single
Educational plans
Academic
Secondary 3 years
Secondary 1 year
Vocational
Family economy
Well off
Short of mony
H.S.
Confidence
RR
interval
0.043
1
2.45
(2.21, 2.72)
1
1.94
(1.77, 2.12)
1
1.55
2.04
2.26
(1.26, 1.90)
(1.68, 2.46)
(2.05, 2.48)
1
1.45
(1.21, 1.74)
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Odds and probability
p
Disease
Odds 

1  p NotDisease
P
1%
10 %
30 %
Odds
1.01 %
11.11 %
42.86 %
Odds
p
1  Odds
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Disease frequency depicted
100
Existing
Cases
t
a New
Healthy
Healthy*time
0
50
Cases
time
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Logistic model, OR
p
log(
)  βo  β1sex   2 age
1 p
odds  e βo  β1sex  2 age
 e βo  OR1  OR2
Girl, with single parents,
academic plans and well off:
Prevalence odds=
0.039 * 3.01 * 2.30=0.269
Prevalence=21.2%
May-16
Variable
Odds at reference
Sex
Boy
Girl
Parents marital status
Living together
Single
Educational plans
Academic
Secondary 3 years
Secondary 1 year
Vocational
Family economy
Well off
Short of mony
H.S.
Confidence
OR
interval
0.039
1
3.01
(2.65, 3.41)
1
2.30
(2.05, 2.58)
1
1.70
2.44
2.82
(1.31, 2.19)
(1.90, 3.13)
(2.49, 3.19)
1
1.71
(1.31, 2.24)
13
Summing up
• Reporting constant
- Increases information a lot!
• Technical
– 0 must be part of the range
– Not for traditional Case Control
May-16
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