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The risk of disease, given exposure, is:
The risk of disease, given no exposure, is:
The relative risk isP(D | E)
RR =P(D | E' )
P(D | E)
P(D | E’)
LC no LCSmoke
No Smoke
12
3
88
147
100
150
P(LC | Smoke)12
=100 = .12
=3
150P(LC | No Smoke) = .02
RR =P(LC | Smoke)
P(LC | No Smoke).12
= .02
= 6
p1- pIf p = P(event), then odds =
The odds of disease, given exposure:
P(D | E)1 - P(D | E)
P(D | E)=
P(D' | E)
The odds of disease, given no exposure:
P(D | E' )1 - P(D | E' )
P(D | E' )=
P(D' | E' )
Disease Odds Ratio
P(D | E) P(D' | E)/OR =
P(D | E' ) P(D' | E' )/
P(D | E) P(D' | E' )=
P(D | E' ) P(D' | E)
Can calculate as shown only from a cohort study
From a case-control study, we can calculate things like:
P(E | D) , P(E’ | D) , P(E | D’ ) , & P(E’ | D’ )
The odds of exposure, given disease:
P(E | D)1- P(E | D)
P(E | D)=
P(E' | D)
Exposure Odds Ratio
OR
P(E | D) P(E' | D' )=
P(E | D' ) P(E' | D)
Can calculate as shown from a case-control study
P(E | D) P(E' | D)=
P(E | D' ) P(E' | D' )//
P(E' | D' )P(E | D' P(E | D)
= P(E' )) | D
OR
D D’
E
E’
a b
c d
a+c b+d
OR =
aa + c
ca + c
db + d
bb + d
= adbc
= adbc
The disease odds ratio is also OR
OR is used to estimate RR!
OR can be calculated in any study design!
CHD no CHD
HF
not HF
200 300
180
120
50
150
CHD no CHD
HF
not HF
200 600
360
240
50
150
OR = (150)
(50)(180)
(120)= 4.5
OR = (150)
(50)(360)
(240)= 4.5
“RR” = = 2.56150/270
50/230
“RR” = = 3.15150/39050/410
Yes No
Heavy
Light
None
46
33
10
89
39
82
32
153
HN
(46)(32)OR = = 3.77
(39)(10)
Liver Cancer
Alc
ohol
Con
sum
ptio
n