constantly forgotten
DESCRIPTION
Constantly ForgottenTRANSCRIPT
09-11 1 09-11 H.S. 1
Constantly forgotten
Hein Stigum
Presentation, data and programs at:
http://folk.uio.no/heins/ Talks, Constantly forgotten
09-11 2 09-11 H.S. 2
Agenda
• Example
• Concepts – Prevalence, risk and odds
• Methods – Regression models
• RD • RR • OR
09-11 3 09-11 H.S. 3
Smoking among 10th graders
Adjusted Adjusted
Variable N % p-valueOdds Ratio
Confidence interval
All 10785 14.5 Sex <.001
Boy 5045 8.7 1.0 Girl 5740 19.5 3.0 (2.7 - 3.4)
Parents marital status <.001Living together 7165 10.4 1.0 Single 3564 22.5 2.3 (2.1 - 2.6)
Educational plans <.001Academic 5157 9.9 1.0 Secondary 3 years 540 15.4 1.7 (1.3 - 2.2)Secondary 1 year 41 22.0 2.4 (1.9 - 3.1)Vocational 2701 23.4 2.8 (2.5 - 3.2)
Family economy <.001Well off 936 14.2 1.0 Good 9381 14.0 1.3 (1.0 - 1.6)Short of mony 331 27.8 1.7 (1.3 - 2.2)
?
09-11 4 09-11 H.S. 4
Constant term, sex
sexββy 1o +=
010
2030
40
0 1, Boys 2, Girls
oβ
1sexββy1-sexsex1 generate
1o +=
=0
1020
3040
0 1, Boys 2, Girls
oβ
Constant term, intercept
09-11 5 09-11 H.S. 5
Constant term, age
ageββy 1o +=
30ageββy30geaage30 generate
1o +=
−=-10
010
2030
40
0 20 25 30 35 40Age
oβ
-10
010
2030
40
0 20 25 30 35 40Age
oβ
09-11 6 09-11 H.S. 6
Prevalence and risk
• Prevalence – Risk of having disease
• Incidence proportion – Risk of getting disease
09-11 7 09-11 H.S. 7
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 RD – link: log RR – logit OR
09-11 8
RD versus RR and OR
0 1 ∞
RR, OR
0 1
RD
-1
09-11 9
Linear binomial model, RD
09-11 H.S. 9
21
21
RDRDβpagesexββp
o
o
++=
++= βVariable RD
Confidence interval
Risk at reference 0.000 Sex
Boy 0 Girl (0.107 , 0.132)
Parents marital status Living together 0 Single 0.104 (0.088 , 0.119)
Educational plans Academic 0 Secondary 3 years 0.057 (0.027 , 0.088) Secondary 1 year 0.107 (0.069 , 0.145) Vocational 0.130 (0.113 , 0.147)
Family economy Well off 0
Short of mony 0.086 (0.038 , 0.134)
Girl, with single parents, academic plans and well off: Prevalence= 0.000+0.120+0.104=0.223 =22.3%
09-11 10
Variable RR Confidence
interval Risk at reference 0.043 Sex
Boy 1 Girl 2.45 (2.21 , 2.72)
Parents marital status Living together 1 Single 1.94 (1.77 , 2.12)
Educational plans Academic 1 Secondary 3 years 1.55 (1.26 , 1.90) Secondary 1 year 2.04 (1.68 , 2.46) Vocational 2.26 (2.05 , 2.48)
Family economy Well off 1
Short of mony 1.45 (1.21 , 1.74)
Log binomial model, RR
09-11 H.S. 10
21
21
21
)log(
RRRReep
agesexββp
o
o
β
agesexββo
⋅⋅=
=
++=++ β
β
Girl, with single parents, academic plans and well off: Prevalence= 0.043 * 2.45 * 1.94=0.203 =20.3%
09-11 11 09-11 H.S. 11
Odds and probability
NotDiseaseDisease
ppOdds =−
=1
P Odds1 % 1.01 %
10 % 11.11 %30 % 42.86 %
OddsOddsp+
=1
09-11 12 09-11 H.S. 12
Disease frequency depicted
Existing Cases
Healthy
New Cases
Healthy*time
050
100
time
a
t
09-11
Variable OR interval Odds at reference 0.039 Sex
Boy 1 Girl 3.01 (2.65 , 3.41)
Parents marital status Living together 1 Single 2.30 (2.05 , 2.58)
Educational plans Academic 1 Secondary 3 years 1.70 (1.31 , 2.19) Secondary 1 year 2.44 (1.90 , 3.13) Vocational 2.82 (2.49 , 3.19)
Family economy Well off 1
Short of mony 1.71 (1.31 , 2.24)
Logistic model, OR
09-11 H.S. 13
21
21
21
)1
log(
OROReeodds
agesexββpp
o
o
β
agesexββ
o
⋅⋅=
=
++=−
++ β
β
Girl, with single parents, academic plans and well off: Prevalence odds= 0.039 * 3.01 * 2.30=0.269 Prevalence=21.2%
09-11 14 09-11 H.S. 14
Summing up
• Reporting constant - Increases information a lot!
• Technical – 0 must be part of the range
– Not for traditional Case Control