ph 241: lecture 4 nicholas p. jewell university of california berkeley january 25-30, 2006
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1
PH 241: Lecture 4
Nicholas P. JewellUniversity of California Berkeley
January 25-30, 2006
2
Measures of Association: Relative Risk
Relative measure
RR = 1 Independence
Note upper bound
RR is not symmetric in roles of D and E
)|(
)|(
EnotDP
EDPRR
3
Non-Symmetry of RR
EDDE RRDnotEP
DEP
EnotDP
EDPRR
)|(
)|(
)|(
)|(
4
1991 US Infant Mortality
Mother’s Marital StatusInfant
MortalityUnmarried Married Total
Death 16,712 18,784 35,496
Live at 1 Year
1,197,142 2,878,421 4,075,563
Total 1,213,854 2,897,205 4,111,059
RR (assoc. with unmarried) = 12.2)205,897,2/784,18
)854,213,1/712,16(
5
Measures of Association: Odds Ratio
Relative measure
OR = 1 Independence
No upper bound
OR is symmetric in roles of D and E
)|()|(
)|()|(
EnotDnotPEnotDP
EDnotPEDP
OR
6
Symmetry of OR
)&()&(
/)&()&(
)(/)&()(/)&(
)(/)&()(/)&(
)|()|(
)|()|(
EnotDnotPEnotDP
EDnotPEDP
EnotPEnotDnotPEnotPEnotDP
EPEDnotPEPEDP
EnotDnotPEnotDP
EDnotPEDP
OR DE
7
Symmetry of OR
ED
DE
OR
DnotEnotPDnotEP
DEnotPDEP
DnotPEnotDnotPDnotPEnotDP
DPEDnotPDPEDP
EnotDnotPEDnotP
EnotDPEDP
OR
)|()|(
)|()|(
)(/)&()(/)&(
)(/)&()(/)&(
)&()&(
/)&()&(
8
1991 US Infant Mortality
Mother’s Marital StatusInfant
MortalityUnmarried Married Total
Death 16,712 18,784 35,496
Live at 1 Year
1,197,142 2,878,421 4,075,563
Total 1,213,854 2,897,205 4,111,059
OR (assoc. with unmarried) )563,075,4/421,878,2/()563,075,4/142,197,1(
)496,35/784,18/()496,35/712,16(
14.2)205,897,2/421,878,2/()205,897,2/784,18(
)854,213,1/142,197,1/()854,213,1/712,16(
9
OR as Approximation to RR
)|()|(
)|()|(
EnotDnotPEnotDP
EDnotPEDP
OR
10
OR as Approximation to RR
)|(
)|(
)|(
)|(
)|()|(
)|()|(
EDnotP
EnotDnotP
EnotDP
EDP
EnotDnotPEnotDP
EDnotPEDP
OR
11
OR as Approximation to RR
)|(
)|(
)|(
)|(
)|(
)|(
)|()|(
)|()|(
EDnotP
EnotDnotPRR
EDnotP
EnotDnotP
EnotDP
EDP
EnotDnotPEnotDP
EDnotPEDP
OR
12
OR as Approximation to RR
)|(
)|(
)|(
)|(
)|(
)|(
)|()|(
)|()|(
EDnotP
EnotDnotPRR
EDnotP
EnotDnotP
EnotDP
EDP
EnotDnotPEnotDP
EDnotPEDP
OR
1if1 RR
13
OR as Approximation to RR
)|(
)|(
)|(
)|(
)|(
)|(
)|()|(
)|()|(
EDnotP
EnotDnotPRR
EDnotP
EnotDnotP
EnotDP
EDP
EnotDnotPEnotDP
EDnotPEDP
OR
1if1 RR
RROR
14
Comparison of RR and OR at Various Risk Levels
P(D|not E) P(D|E) RR OR Relative Difference
0.01
0.01
0.02
0.05
0.10
15
Comparison of RR and OR at Various Risk Levels
P(D|not E) P(D|E) RR OR Relative Difference
0.01
0.01 1.00
0.02 2.00
0.05 5.00
0.10 10.00
16
Comparison of RR and OR at Various Risk Levels
P(D|not E) P(D|E) RR OR Relative Difference
0.01
0.01 1.00 1.00
0.02 2.00 2.02
0.05 5.00 5.21
0.10 10.00 11.00
17
Comparison of RR and OR at Various Risk Levels
P(D|not E) P(D|E) RR OR Relative Difference
0.01
0.01 1.00 1.00 0
0.02 2.00 2.02 1%
0.05 5.00 5.21 4.2%
0.10 10.00 11.00 10%
18
Comparison of RR and OR at Various Risk Levels
P(D|not E) P(D|E) RR OR Relative Difference
0.05
0.05
0.01
0.15
0.20
0.50
19
Comparison of RR and OR at Various Risk Levels
P(D|not E) P(D|E) RR OR Relative Difference
0.05
0.05 1.00 1.00
0.01 2.00 2.11
0.15 3.00 3.35
0.20 4.00 4.75
0.50 10.00 19.00
20
Comparison of RR and OR at Various Risk Levels
P(D|not E) P(D|E) RR OR Relative Difference
0.05
0.05 1.00 1.00 0
0.01 2.00 2.11 5.6%
0.15 3.00 3.35 11.8%
0.20 4.00 4.75 18.8%
0.50 10.00 19.00 90%
21
Comparison of RR and OR at Various Risk Levels
P(D|not E) P(D|E) RR OR Relative Difference
0.10
0.10 1.00 1.00
0.15 1.50 1.59
0.20 2.00 2.25
0.30 3.00 3.86
0.40 4.00 6.00
0.50 5.00 9.00
22
Comparison of RR and OR at Various Risk Levels
P(D|not E) P(D|E) RR OR Relative Difference
0.10
0.10 1.00 1.00 0
0.15 1.50 1.59 5.9%
0.20 2.00 2.25 12.5%
0.30 3.00 3.86 28.6%
0.40 4.00 6.00 50%
0.50 5.00 9.00 80%
23
Comparison of RR and OR at Various Risk Levels
P(D|not E) P(D|E) RR OR Relative Difference
0.20
0.20 1.00 1.00 0
0.30 1.50 1.71 14.3%
0.40 2.00 2.67 33.3%
0.50 2.50 4.00 60%
0.60 3.00 6.00 100%
0.80 4.00 16.00 300%
1.00 5.00 ∞ ∞
24
RH (solid line), RR (dotted line), OR (dash-dotted line) as Risk Period extends in
Time
25
Measures of Association: Odds Ratio
Absolute comparison
ER = 0 Independence
ER is not symmetric in roles of D and E
)|()|( EnotDPEDPER
26
Measures of Association: Attributable Risk
)1)((1
)1)((
)(
)|()(
)(
)|()(
RREP
RREP
DP
EDPDP
DNP
EDNPDNPAR
Number of cases with current exposure distribution
Number of cases with no exposure to E
Population size = N
27
1991 US Infant Mortality
Mother’s Marital StatusInfant
MortalityUnmarried Married Total
Death 16,712 18,784 35,496
Live at 1 Year
1,197,142 2,878,421 4,075,563
Total 1,213,854 2,897,205 4,111,059
AR (assoc. with unmarried)
)112.2()059,111,4/854,213,1(1
)112.2()059,111,4/854,213,1(
25.0)059,111,4/496,35(
)205,897,2/784,18()059,111,4/496,35(
28
Attributable Risk—Caution!
Encourages causal interpretation that may be incorrect
Assumes modification of E doesn’t change other risk factors
"Baseball is 90% mental -- the other half is physical." (Yogi Berra)
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