Lesson #11

Relative Risk andthe Odds Ratio

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

D D’

E

E’

Cohort Study

En

E 'n

n

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

Case-Control Study

Dn

D 'n n

D D’

E

E’

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

High Fat

not High Fat

200 300

180

120

50

150

OR =

CHD no CHD

High Fat

not High Fat

200 300

180

120

50

150

OR = (150)

CHD no CHD

High Fat

not High Fat

200 300

180

120

50

150

OR = (150)(180)

CHD no CHD

High Fat

not High Fat

200 300

180

120

50

150

OR = (150)(180)

(120)

CHD no CHD

High Fat

not High Fat

200 300

180

120

50

150

OR = (150)

(50)

(180)

(120)

CHD no CHD

High Fat

not High Fat

200 300

180

120

50

150

OR = (150)

(50)

(180)

(120)= 4.5

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

Liver Cancer

Alc

ohol

Con

sum

ptio

n

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

Yes No

Heavy

Light

None

46

33

10

89

39

82

32

153

HN

(46)(32)OR = = 3.77

(39)(10)

LN

(33)(32)OR = = 1.29

(82)(10)

Liver Cancer

Alc

ohol

Con

sum

ptio

n