ph 241: lecture 4 nicholas p. jewell university of california berkeley january 25-30, 2006
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PH 241: Lecture 4 Nicholas P. Jewell University of California Berkeley January 25-30, 2006. Measures of Association: Relative Risk. Relative measure RR = 1 Independence Note upper bound RR is not symmetric in roles of D and E. Non-Symmetry of RR. 1991 US Infant Mortality. - PowerPoint PPT PresentationTRANSCRIPT
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PH 241: Lecture 4
Nicholas P. JewellUniversity of California Berkeley
January 25-30, 2006
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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
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Symmetry of OR
)&()&(
/)&()&(
)(/)&()(/)&(
)(/)&()(/)&(
)|()|(
)|()|(
EnotDnotPEnotDP
EDnotPEDP
EnotPEnotDnotPEnotPEnotDP
EPEDnotPEPEDP
EnotDnotPEnotDP
EDnotPEDP
OR DE
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Symmetry of OR
ED
DE
OR
DnotEnotPDnotEP
DEnotPDEP
DnotPEnotDnotPDnotPEnotDP
DPEDnotPDPEDP
EnotDnotPEDnotP
EnotDPEDP
OR
)|()|(
)|()|(
)(/)&()(/)&(
)(/)&()(/)&(
)&()&(
/)&()&(
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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(
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OR as Approximation to RR
)|()|(
)|()|(
EnotDnotPEnotDP
EDnotPEDP
OR
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OR as Approximation to RR
)|(
)|(
)|(
)|(
)|()|(
)|()|(
EDnotP
EnotDnotP
EnotDP
EDP
EnotDnotPEnotDP
EDnotPEDP
OR
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OR as Approximation to RR
)|(
)|(
)|(
)|(
)|(
)|(
)|()|(
)|()|(
EDnotP
EnotDnotPRR
EDnotP
EnotDnotP
EnotDP
EDP
EnotDnotPEnotDP
EDnotPEDP
OR
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OR as Approximation to RR
)|(
)|(
)|(
)|(
)|(
)|(
)|()|(
)|()|(
EDnotP
EnotDnotPRR
EDnotP
EnotDnotP
EnotDP
EDP
EnotDnotPEnotDP
EDnotPEDP
OR
1if1 RR
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OR as Approximation to RR
)|(
)|(
)|(
)|(
)|(
)|(
)|()|(
)|()|(
EDnotP
EnotDnotPRR
EDnotP
EnotDnotP
EnotDP
EDP
EnotDnotPEnotDP
EDnotPEDP
OR
1if1 RR
RROR
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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
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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
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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
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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%
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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
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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
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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%
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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
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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%
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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 ∞ ∞
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RH (solid line), RR (dotted line), OR (dash-dotted line) as Risk Period extends in
Time
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Measures of Association: Odds Ratio
Absolute comparison
ER = 0 Independence
ER is not symmetric in roles of D and E
)|()|( EnotDPEDPER
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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
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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(
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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)