Download - November 15 H.S.1 Selection Bias Concepts Hein Stigum Presentation, data and programs at:
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*H.S.*Selection Bias ConceptsHein StigumPresentation, data and programs at:http://folk.uio.no/heins/talks
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QuestionsGiven measured appropriate variables:
Can you adjust for confounding?Yes
Can you adjust for selection bias?Depends on the definition*H.S.*
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ContentsBackgroundDefine biasSelection biasas effect modification(old concept)as collider stratification bias(new concept)DAG structureExamplesSize and direction of bias*H.S.*
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Bias definitionBiasFrequency:expected risk true riskEffect:association causal effect*H.S.*
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Selection bias conceptsConceptEffect responders Effect non responders
Differential response biasDifferential loss to follow upHealthy worker biasBerksons bias (case control)
DAG structure
Effectmodification
Colliderstratificationbias*H.S.*
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Selection bias as effect modification*H.S.*
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Selection bias: RiskSelection of responders The prevalence is different amongthe responders compared to the full populationthe responders compared to the non responders
*H.S.*R1R0RpNon respondersRespondersPopulationRp is the weighted mean of R0 and R1
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Effect modificationSelection of responders The effect of E on D is different amongthe responders compared to the full populationthe responders compared to the non responders
*H.S.*RR1RR0RRpNon respondersRespondersPopulation
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ProblemsIs not a bias, RR0 and RR1 are the true effectsIs effect modification by selection variable SLeads to the conclusion that:Biolocical effects are protected from biasThe bias can not be adjusted forRRp is the average of RR0 and RR1*H.S.*EDSDAG structure:Not true for collider stratification bias
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Selection bias as collider stratification bias*H.S.*
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Example with pathsStudyMilk on bone densityExclude Calcium supplements
*H.S.*Lessons learned:Biological effect not protectedMay adjust for selection biasStructure:Collider stratification
PathTypeStatus1EDCausalOpen2E[S]DNoncausalOpen
2E[S][C]DNoncausalClosed
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ExamplesDifferential responseSurvey: Alcohol and CHD
Differential loss to follow upRandomized trial: drug and disease
Healthy worker effectCross-section: Melt hall dust and lung disease*H.S.*Note: no confounding
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Selection bias structure*H.S.*
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Paths1. Causal2. ConfoundingAn open non-causal path without colliders3. Selection biasA non-causal path that is open due to conditioning on a collider BCVs?
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Collider stratification biasSelection bias = Collider stratification biasSelection bias, Path definitionA non causal path that is open due to conditioning on a collider
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Selection bias examples*H.S.*
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Folic acid and cardiac malformationSelection: Study only live bornBias?
*H.S.*Yes, E[C]D is openSelection: Non grieving parents volonteerBias?
Yes, E[C]D is (partially) open
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Education and unfaithfulnessStudy the effect among couples in a relationship (not divorced)?*H.S.*Selection bias
PathTypePopulationSample1EDCausalOpenOpen2ERDNoncausalClosedOpen3ERSDNoncausalClosedOpen
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Size and Direction of bias*H.S.*
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Example 1, full tableProportion responding in 1,1 groupTrue and biased RRs(Adjusted) RRs
Sel Bias
Selection bias examples
Fill inn gray cells
Selection:
Example1ResponseOnly E
N1000DNo bias
% exposed40%10
% disease20%E10.90.93.01.0RR among
RR200.30.3selected=
Response=54%10
PopulationRespondersNon respond2.02.02.0
DDDWeighted average54%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=03.03
1000540460D on S|E=11.0
RR=2.0RR=2.0RR=2.0D on S|E=01.01
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.14RD=0.14E=10.66666666670.33
Selection:
Example2ResponseOnly D
N1000DOR not biased
% exposed40%10
% disease20%E10.90.31.03.0RR among
RR200.90.3selected=
Response=42%10
PopulationRespondersNon respond2.01.62.3
DDDWeighted average42%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=01.01
1000420580D on S|E=13.0
RR=2.0RR=1.6RR=2.3D on S|E=03.03
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.21RD=0.03E=10.66666666670.33
Selection:
Example3ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10Ex 3 to 5 are variants of the same pattern
% disease20%E10.90.92.51.7RR among
RR200.90.3selected=
Response=59%10
PopulationRespondersNon respond2.00.912.3
DDDWeighted average59%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=03.02.5
1000591.4285714286408.5714285714D on S|E=11.0
RR=2.0RR=0.9RR=12.3D on S|E=03.01.6666666667
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.05RD=0.26E=10.66666666670.33
Selection:
Example4ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.90.92.61.4RR among
RR200.70.3selected=
Response=57%10
PopulationRespondersNon respond2.01.04.3
DDDWeighted average57%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.3
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5714285714
1000574.2857142857425.7142857143D on S|E=11.0
RR=2.0RR=1.0RR=4.3D on S|E=02.31.4444444444
OR=2.4OR=1.0OR=5.6D=10.250.75
RD=0.14RD=0.01RD=0.22E=10.66666666670.33
Selection:
Example5ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.70.92.51.3RR among
RR200.70.3selected=
Response=55%10
PopulationRespondersNon respond2.00.88.2
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E180257337.14285714290.2E1342962.85714285710.5E on S|D=11.0
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5
1000551.4285714286448.5714285714D on S|E=10.8
RR=2.0RR=0.8RR=8.2D on S|E=02.31.2962962963
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.04RD=0.48E=10.66666666670.33
Selection:
Example6ResponseBoth E and D through E and D
N1000DPositive association among responders
% exposed40%10
% disease20%E10.90.31.52.3RR among
RR200.30.3selected=
Response=37%10
PopulationRespondersNon respond2.03.80.4
DDDWeighted average37%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=01.01.5
1000368.5714285714631.4285714286D on S|E=13.0
RR=2.0RR=3.8RR=0.4D on S|E=01.02.3333333333
OR=2.4OR=7.2OR=0.3D=10.250.75
RD=0.14RD=0.40RD=-0.09E=10.66666666670.33
Selection:
Example7ResponseBoth E and D through E and D
N1000DBoth strata neg bias
% exposed40%10
% disease20%E10.90.82.51.3RR among
RR200.50.3selected=
Response=53%10
PopulationRespondersNon respond2.01.41.6
DDDWeighted average53%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103229331.42857142860.3E1115768.57142857140.2E on S|D=11.8
0865146000.1043154197.14285714290.2043360402.85714285710.1E on S|D=02.72.45
1000528.5714285714471.4285714286D on S|E=11.1
RR=2.0RR=1.4RR=1.6D on S|E=01.71.3055555556
OR=2.4OR=1.6OR=1.7D=10.250.75
RD=0.14RD=0.09RD=0.06E=10.66666666670.33
Selection:
Example8Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.90.452.02.0RR among
RR100.450.225selected=
Response=38%10
PopulationRespondersNon respond1.01.00.3
DDDWeighted average38%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E1803204000.2E1721442160.3E181761840.0E on S|D=12.0
01204806000.20541081620.30663724380.2E on S|D=02.02
1000378622D on S|E=12.0
RR=1.0RR=1.0RR=0.3D on S|E=02.02
OR=1.0OR=1.0OR=0.3D=10.250.75
RD=0.00RD=0.00RD=-0.11E=10.66666666670.33
Selection:
Example9Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.450.92.00.5RR among
RR200.2250.45selected=
Response=56%10
PopulationRespondersNon respond2.02.23.6
DDDWeighted average56%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E151257308.57142857140.2E1632991.42857142860.7E on S|D=12.0
0865146000.1019231250.71428571430.1066283349.28571428570.2E on S|D=02.02
1000559.2857142857440.7142857143D on S|E=10.5
RR=2.0RR=2.2RR=3.6D on S|E=00.50.5
OR=2.4OR=2.4OR=9.4D=10.250.75
RD=0.14RD=0.09RD=0.50E=10.66666666670.33
Selection:
Example10Response
N1000DStrong opposite effects
% exposed40%10
% disease20%E10.30.60.60.7RR among
RR200.90.8selected=
Response=69%10
PopulationRespondersNon respond2.01.15.4
DDDWeighted average69%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E134171205.71428571430.2E180114194.28571428570.4E on S|D=10.3
0865146000.1077411488.57142857140.209103111.42857142860.1E on S|D=00.80.6458333333
1000694.2857142857305.7142857143D on S|E=10.5
RR=2.0RR=1.1RR=5.4D on S|E=01.1250.7083333333
OR=2.4OR=1.1OR=8.4D=10.250.75
RD=0.14RD=0.01RD=0.33E=10.66666666670.33
Selection:
Example11ResponseThis and next: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.990.661.52.01.5RR among
RR200.4950.33selected=
Response=51%210
PopulationRespondersNon respond2.01.90.1
DDDWeighted average51%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1113189301.71428571430.4E119798.28571428570.0E on S|D=12.0
0865146000.1042170212.14285714290.2043345387.85714285710.1E on S|D=02.02
1000513.8571428571486.1428571429D on S|E=11.5
RR=2.0RR=1.9RR=0.1D on S|E=01.51.5
OR=2.4OR=2.4OR=0.1D=10.250.75
RD=0.14RD=0.18RD=-0.10E=10.66666666670.33
Selection:
Example12ResponseThis and previous: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.50.33333333331.52.01.5RR among
RR200.250.1666666667selected=
Response=26%210
PopulationRespondersNon respond2.01.91.8
DDDWeighted average26%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E15795152.3809523810.4E157190247.6190476190.2E on S|D=12.0
0865146000.102186107.14285714290.2064429492.85714285710.1E on S|D=02.02
1000259.5238095238740.4761904762D on S|E=11.5
RR=2.0RR=1.9RR=1.8D on S|E=01.51.5
OR=2.4OR=2.4OR=2.0D=10.250.75
RD=0.14RD=0.18RD=0.10E=10.66666666670.33
Selection:
Example13Response
N1000D
% exposed40%10
% disease20%E10.90.451.31.7RR among
RR200.450.45selected=
Response=50%10
PopulationRespondersNon respond2.03.10.5
DDDWeighted average50%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103129231.42857142860.4E111157168.57142857140.1E on S|D=12.0
0865146000.10392312700.10472833300.1E on S|D=01.01.25
1000501.4285714286498.5714285714D on S|E=12
RR=2.0RR=3.1RR=0.5D on S|E=011.6666666667
OR=2.4OR=4.8OR=0.4D=10.250.75
RD=0.14RD=0.30RD=-0.08E=10.66666666670.33
ED2
E
D
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D
E
D
D
E+D
E
D
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E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
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E
D
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E
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E
D
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Sel Bias
Selection bias examples
Fill inn gray cells
Selection:
Example1ResponseOnly E
N1000DNo bias
% exposed40%10
% disease20%E10.90.93.01.0RR among
RR200.30.3selected=
Response=54%10
PopulationRespondersNon respond2.02.02.0
DDDWeighted average54%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=03.03
1000540460D on S|E=11.0
RR=2.0RR=2.0RR=2.0D on S|E=01.01
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.14RD=0.14E=10.66666666670.33
Selection:
Example2ResponseOnly D
N1000DOR not biased
% exposed40%10
% disease20%E10.90.31.03.0RR among
RR200.90.3selected=
Response=42%10
PopulationRespondersNon respond2.01.62.3
DDDWeighted average42%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=01.01
1000420580D on S|E=13.0
RR=2.0RR=1.6RR=2.3D on S|E=03.03
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.21RD=0.03E=10.66666666670.33
Selection:
Example3ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10Ex 3 to 5 are variants of the same pattern
% disease20%E10.90.92.51.7RR among
RR200.90.3selected=
Response=59%10
PopulationRespondersNon respond2.00.912.3
DDDWeighted average59%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=03.02.5
1000591.4285714286408.5714285714D on S|E=11.0
RR=2.0RR=0.9RR=12.3D on S|E=03.01.6666666667
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.05RD=0.26E=10.66666666670.33
Selection:
Example4ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.90.92.61.4RR among
RR200.70.3selected=
Response=57%10
PopulationRespondersNon respond2.01.04.3
DDDWeighted average57%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.3
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5714285714
1000574.2857142857425.7142857143D on S|E=11.0
RR=2.0RR=1.0RR=4.3D on S|E=02.31.4444444444
OR=2.4OR=1.0OR=5.6D=10.250.75
RD=0.14RD=0.01RD=0.22E=10.66666666670.33
Selection:
Example5ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.70.92.51.3RR among
RR200.70.3selected=
Response=55%10
PopulationRespondersNon respond2.00.88.2
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E180257337.14285714290.2E1342962.85714285710.5E on S|D=11.0
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5
1000551.4285714286448.5714285714D on S|E=10.8
RR=2.0RR=0.8RR=8.2D on S|E=02.31.2962962963
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.04RD=0.48E=10.66666666670.33
Selection:
Example6ResponseBoth E and D through E and D
N1000DPositive association among responders
% exposed40%10
% disease20%E10.90.31.52.3RR among
RR200.30.3selected=
Response=37%10
PopulationRespondersNon respond2.03.80.4
DDDWeighted average37%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=01.01.5
1000368.5714285714631.4285714286D on S|E=13.0
RR=2.0RR=3.8RR=0.4D on S|E=01.02.3333333333
OR=2.4OR=7.2OR=0.3D=10.250.75
RD=0.14RD=0.40RD=-0.09E=10.66666666670.33
Selection:
Example7ResponseBoth E and D through E and D
N1000DBoth strata neg bias
% exposed40%10
% disease20%E10.90.82.51.3RR among
RR200.50.3selected=
Response=53%10
PopulationRespondersNon respond2.01.41.6
DDDWeighted average53%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103229331.42857142860.3E1115768.57142857140.2E on S|D=11.8
0865146000.1043154197.14285714290.2043360402.85714285710.1E on S|D=02.72.45
1000528.5714285714471.4285714286D on S|E=11.1
RR=2.0RR=1.4RR=1.6D on S|E=01.71.3055555556
OR=2.4OR=1.6OR=1.7D=10.250.75
RD=0.14RD=0.09RD=0.06E=10.66666666670.33
Selection:
Example8Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.90.452.02.0RR among
RR100.450.225selected=
Response=38%10
PopulationRespondersNon respond1.01.00.3
DDDWeighted average38%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E1803204000.2E1721442160.3E181761840.0E on S|D=12.0
01204806000.20541081620.30663724380.2E on S|D=02.02
1000378622D on S|E=12.0
RR=1.0RR=1.0RR=0.3D on S|E=02.02
OR=1.0OR=1.0OR=0.3D=10.250.75
RD=0.00RD=0.00RD=-0.11E=10.66666666670.33
Selection:
Example9Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.450.92.00.5RR among
RR200.2250.45selected=
Response=56%10
PopulationRespondersNon respond2.02.23.6
DDDWeighted average56%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E151257308.57142857140.2E1632991.42857142860.7E on S|D=12.0
0865146000.1019231250.71428571430.1066283349.28571428570.2E on S|D=02.02
1000559.2857142857440.7142857143D on S|E=10.5
RR=2.0RR=2.2RR=3.6D on S|E=00.50.5
OR=2.4OR=2.4OR=9.4D=10.250.75
RD=0.14RD=0.09RD=0.50E=10.66666666670.33
Selection:
Example10Response
N1000DStrong opposite effects
% exposed40%10
% disease20%E10.30.60.60.7RR among
RR200.90.8selected=
Response=69%10
PopulationRespondersNon respond2.01.15.4
DDDWeighted average69%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E134171205.71428571430.2E180114194.28571428570.4E on S|D=10.3
0865146000.1077411488.57142857140.209103111.42857142860.1E on S|D=00.80.6458333333
1000694.2857142857305.7142857143D on S|E=10.5
RR=2.0RR=1.1RR=5.4D on S|E=01.1250.7083333333
OR=2.4OR=1.1OR=8.4D=10.250.75
RD=0.14RD=0.01RD=0.33E=10.66666666670.33
Selection:
Example11ResponseThis and next: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.990.661.52.01.5RR among
RR200.4950.33selected=
Response=51%210
PopulationRespondersNon respond2.01.90.1
DDDWeighted average51%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1113189301.71428571430.4E119798.28571428570.0E on S|D=12.0
0865146000.1042170212.14285714290.2043345387.85714285710.1E on S|D=02.02
1000513.8571428571486.1428571429D on S|E=11.5
RR=2.0RR=1.9RR=0.1D on S|E=01.51.5
OR=2.4OR=2.4OR=0.1D=10.250.75
RD=0.14RD=0.18RD=-0.10E=10.66666666670.33
Selection:
Example12ResponseThis and previous: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.50.33333333331.52.01.5RR among
RR200.250.1666666667selected=
Response=26%210
PopulationRespondersNon respond2.01.91.8
DDDWeighted average26%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E15795152.3809523810.4E157190247.6190476190.2E on S|D=12.0
0865146000.102186107.14285714290.2064429492.85714285710.1E on S|D=02.02
1000259.5238095238740.4761904762D on S|E=11.5
RR=2.0RR=1.9RR=1.8D on S|E=01.51.5
OR=2.4OR=2.4OR=2.0D=10.250.75
RD=0.14RD=0.18RD=0.10E=10.66666666670.33
Selection:
Example13Response
N1000D
% exposed40%10
% disease20%E10.90.451.31.7RR among
RR200.450.45selected=
Response=50%10
PopulationRespondersNon respond2.03.10.5
DDDWeighted average50%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103129231.42857142860.4E111157168.57142857140.1E on S|D=12.0
0865146000.10392312700.10472833300.1E on S|D=01.01.25
1000501.4285714286498.5714285714D on S|E=12
RR=2.0RR=3.1RR=0.5D on S|E=011.6666666667
OR=2.4OR=4.8OR=0.4D=10.250.75
RD=0.14RD=0.30RD=-0.08E=10.66666666670.33
ED2
E
D
S
D
E
D
D
E+D
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
Sel Bias
Selection bias examples
Fill inn gray cells
Selection:
Example1ResponseOnly E
N1000DNo bias
% exposed40%10
% disease20%E10.90.93.01.0RR among
RR200.30.3selected=
Response=54%10
PopulationRespondersNon respond2.02.02.0
DDDWeighted average54%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=03.03
1000540460D on S|E=11.0
RR=2.0RR=2.0RR=2.0D on S|E=01.01
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.14RD=0.14E=10.66666666670.33
Selection:
Example2ResponseOnly D
N1000DOR not biased
% exposed40%10
% disease20%E10.90.31.03.0RR among
RR200.90.3selected=
Response=42%10
PopulationRespondersNon respond2.01.62.3
DDDWeighted average42%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=01.01
1000420580D on S|E=13.0
RR=2.0RR=1.6RR=2.3D on S|E=03.03
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.21RD=0.03E=10.66666666670.33
Selection:
Example3ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10Ex 3 to 5 are variants of the same pattern
% disease20%E10.90.92.51.7RR among
RR200.90.3selected=
Response=59%10
PopulationRespondersNon respond2.00.912.3
DDDWeighted average59%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=03.02.5
1000591.4285714286408.5714285714D on S|E=11.0
RR=2.0RR=0.9RR=12.3D on S|E=03.01.6666666667
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.05RD=0.26E=10.66666666670.33
Selection:
Example4ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.90.92.61.4RR among
RR200.70.3selected=
Response=57%10
PopulationRespondersNon respond2.01.04.3
DDDWeighted average57%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.3
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5714285714
1000574.2857142857425.7142857143D on S|E=11.0
RR=2.0RR=1.0RR=4.3D on S|E=02.31.4444444444
OR=2.4OR=1.0OR=5.6D=10.250.75
RD=0.14RD=0.01RD=0.22E=10.66666666670.33
Selection:
Example5ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.70.92.51.3RR among
RR200.70.3selected=
Response=55%10
PopulationRespondersNon respond2.00.88.2
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E180257337.14285714290.2E1342962.85714285710.5E on S|D=11.0
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5
1000551.4285714286448.5714285714D on S|E=10.8
RR=2.0RR=0.8RR=8.2D on S|E=02.31.2962962963
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.04RD=0.48E=10.66666666670.33
Selection:
Example6ResponseBoth E and D through E and D
N1000DPositive association among responders
% exposed40%10
% disease20%E10.90.31.52.3RR among
RR200.30.3selected=
Response=37%10
PopulationRespondersNon respond2.03.80.4
DDDWeighted average37%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=01.01.5
1000368.5714285714631.4285714286D on S|E=13.0
RR=2.0RR=3.8RR=0.4D on S|E=01.02.3333333333
OR=2.4OR=7.2OR=0.3D=10.250.75
RD=0.14RD=0.40RD=-0.09E=10.66666666670.33
Selection:
Example7ResponseBoth E and D through E and D
N1000DBoth strata neg bias
% exposed40%10
% disease20%E10.90.82.51.3RR among
RR200.50.3selected=
Response=53%10
PopulationRespondersNon respond2.01.41.6
DDDWeighted average53%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103229331.42857142860.3E1115768.57142857140.2E on S|D=11.8
0865146000.1043154197.14285714290.2043360402.85714285710.1E on S|D=02.72.45
1000528.5714285714471.4285714286D on S|E=11.1
RR=2.0RR=1.4RR=1.6D on S|E=01.71.3055555556
OR=2.4OR=1.6OR=1.7D=10.250.75
RD=0.14RD=0.09RD=0.06E=10.66666666670.33
Selection:
Example8Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.90.452.02.0RR among
RR100.450.225selected=
Response=38%10
PopulationRespondersNon respond1.01.00.3
DDDWeighted average38%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E1803204000.2E1721442160.3E181761840.0E on S|D=12.0
01204806000.20541081620.30663724380.2E on S|D=02.02
1000378622D on S|E=12.0
RR=1.0RR=1.0RR=0.3D on S|E=02.02
OR=1.0OR=1.0OR=0.3D=10.250.75
RD=0.00RD=0.00RD=-0.11E=10.66666666670.33
Selection:
Example9Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.450.92.00.5RR among
RR200.2250.45selected=
Response=56%10
PopulationRespondersNon respond2.02.23.6
DDDWeighted average56%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E151257308.57142857140.2E1632991.42857142860.7E on S|D=12.0
0865146000.1019231250.71428571430.1066283349.28571428570.2E on S|D=02.02
1000559.2857142857440.7142857143D on S|E=10.5
RR=2.0RR=2.2RR=3.6D on S|E=00.50.5
OR=2.4OR=2.4OR=9.4D=10.250.75
RD=0.14RD=0.09RD=0.50E=10.66666666670.33
Selection:
Example10Response
N1000DStrong opposite effects
% exposed40%10
% disease20%E10.30.60.60.7RR among
RR200.90.8selected=
Response=69%10
PopulationRespondersNon respond2.01.15.4
DDDWeighted average69%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E134171205.71428571430.2E180114194.28571428570.4E on S|D=10.3
0865146000.1077411488.57142857140.209103111.42857142860.1E on S|D=00.80.6458333333
1000694.2857142857305.7142857143D on S|E=10.5
RR=2.0RR=1.1RR=5.4D on S|E=01.1250.7083333333
OR=2.4OR=1.1OR=8.4D=10.250.75
RD=0.14RD=0.01RD=0.33E=10.66666666670.33
Selection:
Example11ResponseThis and next: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.990.661.52.01.5RR among
RR200.4950.33selected=
Response=51%210
PopulationRespondersNon respond2.01.90.1
DDDWeighted average51%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1113189301.71428571430.4E119798.28571428570.0E on S|D=12.0
0865146000.1042170212.14285714290.2043345387.85714285710.1E on S|D=02.02
1000513.8571428571486.1428571429D on S|E=11.5
RR=2.0RR=1.9RR=0.1D on S|E=01.51.5
OR=2.4OR=2.4OR=0.1D=10.250.75
RD=0.14RD=0.18RD=-0.10E=10.66666666670.33
Selection:
Example12ResponseThis and previous: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.50.33333333331.52.01.5RR among
RR200.250.1666666667selected=
Response=26%210
PopulationRespondersNon respond2.01.91.8
DDDWeighted average26%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E15795152.3809523810.4E157190247.6190476190.2E on S|D=12.0
0865146000.102186107.14285714290.2064429492.85714285710.1E on S|D=02.02
1000259.5238095238740.4761904762D on S|E=11.5
RR=2.0RR=1.9RR=1.8D on S|E=01.51.5
OR=2.4OR=2.4OR=2.0D=10.250.75
RD=0.14RD=0.18RD=0.10E=10.66666666670.33
Selection:
Example13Response
N1000D
% exposed40%10
% disease20%E10.90.451.31.7RR among
RR200.450.45selected=
Response=50%10
PopulationRespondersNon respond2.03.10.5
DDDWeighted average50%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103129231.42857142860.4E111157168.57142857140.1E on S|D=12.0
0865146000.10392312700.10472833300.1E on S|D=01.01.25
1000501.4285714286498.5714285714D on S|E=12
RR=2.0RR=3.1RR=0.5D on S|E=011.6666666667
OR=2.4OR=4.8OR=0.4D=10.250.75
RD=0.14RD=0.30RD=-0.08E=10.66666666670.33
ED2
E
D
S
D
E
D
D
E+D
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
Sel Bias
Selection bias examples
Fill inn gray cells
Selection:
Example1ResponseOnly E
N1000DNo bias
% exposed40%10
% disease20%E10.90.93.01.0RR among
RR200.30.3selected=
Response=54%10
PopulationRespondersNon respond2.02.02.0
DDDWeighted average54%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=03.03
1000540460D on S|E=11.0
RR=2.0RR=2.0RR=2.0D on S|E=01.01
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.14RD=0.14E=10.66666666670.33
Selection:
Example2ResponseOnly D
N1000DOR not biased
% exposed40%10
% disease20%E10.90.31.03.0RR among
RR200.90.3selected=
Response=42%10
PopulationRespondersNon respond2.01.62.3
DDDWeighted average42%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=01.01
1000420580D on S|E=13.0
RR=2.0RR=1.6RR=2.3D on S|E=03.03
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.21RD=0.03E=10.66666666670.33
Selection:
Example3ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10Ex 3 to 5 are variants of the same pattern
% disease20%E10.90.92.51.7RR among
RR200.90.3selected=
Response=59%10
PopulationRespondersNon respond2.00.912.3
DDDWeighted average59%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=03.02.5
1000591.4285714286408.5714285714D on S|E=11.0
RR=2.0RR=0.9RR=12.3D on S|E=03.01.6666666667
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.05RD=0.26E=10.66666666670.33
Selection:
Example4ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.90.92.61.4RR among
RR200.70.3selected=
Response=57%10
PopulationRespondersNon respond2.01.04.3
DDDWeighted average57%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.3
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5714285714
1000574.2857142857425.7142857143D on S|E=11.0
RR=2.0RR=1.0RR=4.3D on S|E=02.31.4444444444
OR=2.4OR=1.0OR=5.6D=10.250.75
RD=0.14RD=0.01RD=0.22E=10.66666666670.33
Selection:
Example5ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.70.92.51.3RR among
RR200.70.3selected=
Response=55%10
PopulationRespondersNon respond2.00.88.2
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E180257337.14285714290.2E1342962.85714285710.5E on S|D=11.0
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5
1000551.4285714286448.5714285714D on S|E=10.8
RR=2.0RR=0.8RR=8.2D on S|E=02.31.2962962963
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.04RD=0.48E=10.66666666670.33
Selection:
Example6ResponseBoth E and D through E and D
N1000DPositive association among responders
% exposed40%10
% disease20%E10.90.31.52.3RR among
RR200.30.3selected=
Response=37%10
PopulationRespondersNon respond2.03.80.4
DDDWeighted average37%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=01.01.5
1000368.5714285714631.4285714286D on S|E=13.0
RR=2.0RR=3.8RR=0.4D on S|E=01.02.3333333333
OR=2.4OR=7.2OR=0.3D=10.250.75
RD=0.14RD=0.40RD=-0.09E=10.66666666670.33
Selection:
Example7ResponseBoth E and D through E and D
N1000DBoth strata neg bias
% exposed40%10
% disease20%E10.90.82.51.3RR among
RR200.50.3selected=
Response=53%10
PopulationRespondersNon respond2.01.41.6
DDDWeighted average53%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103229331.42857142860.3E1115768.57142857140.2E on S|D=11.8
0865146000.1043154197.14285714290.2043360402.85714285710.1E on S|D=02.72.45
1000528.5714285714471.4285714286D on S|E=11.1
RR=2.0RR=1.4RR=1.6D on S|E=01.71.3055555556
OR=2.4OR=1.6OR=1.7D=10.250.75
RD=0.14RD=0.09RD=0.06E=10.66666666670.33
Selection:
Example8Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.90.452.02.0RR among
RR100.450.225selected=
Response=38%10
PopulationRespondersNon respond1.01.00.3
DDDWeighted average38%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E1803204000.2E1721442160.3E181761840.0E on S|D=12.0
01204806000.20541081620.30663724380.2E on S|D=02.02
1000378622D on S|E=12.0
RR=1.0RR=1.0RR=0.3D on S|E=02.02
OR=1.0OR=1.0OR=0.3D=10.250.75
RD=0.00RD=0.00RD=-0.11E=10.66666666670.33
Selection:
Example9Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.450.92.00.5RR among
RR200.2250.45selected=
Response=56%10
PopulationRespondersNon respond2.02.23.6
DDDWeighted average56%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E151257308.57142857140.2E1632991.42857142860.7E on S|D=12.0
0865146000.1019231250.71428571430.1066283349.28571428570.2E on S|D=02.02
1000559.2857142857440.7142857143D on S|E=10.5
RR=2.0RR=2.2RR=3.6D on S|E=00.50.5
OR=2.4OR=2.4OR=9.4D=10.250.75
RD=0.14RD=0.09RD=0.50E=10.66666666670.33
Selection:
Example10Response
N1000DStrong opposite effects
% exposed40%10
% disease20%E10.30.60.60.7RR among
RR200.90.8selected=
Response=69%10
PopulationRespondersNon respond2.01.15.4
DDDWeighted average69%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E134171205.71428571430.2E180114194.28571428570.4E on S|D=10.3
0865146000.1077411488.57142857140.209103111.42857142860.1E on S|D=00.80.6458333333
1000694.2857142857305.7142857143D on S|E=10.5
RR=2.0RR=1.1RR=5.4D on S|E=01.1250.7083333333
OR=2.4OR=1.1OR=8.4D=10.250.75
RD=0.14RD=0.01RD=0.33E=10.66666666670.33
Selection:
Example11ResponseThis and next: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.990.661.52.01.5RR among
RR200.4950.33selected=
Response=51%210
PopulationRespondersNon respond2.01.90.1
DDDWeighted average51%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1113189301.71428571430.4E119798.28571428570.0E on S|D=12.0
0865146000.1042170212.14285714290.2043345387.85714285710.1E on S|D=02.02
1000513.8571428571486.1428571429D on S|E=11.5
RR=2.0RR=1.9RR=0.1D on S|E=01.51.5
OR=2.4OR=2.4OR=0.1D=10.250.75
RD=0.14RD=0.18RD=-0.10E=10.66666666670.33
Selection:
Example12ResponseThis and previous: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.50.33333333331.52.01.5RR among
RR200.250.1666666667selected=
Response=26%210
PopulationRespondersNon respond2.01.91.8
DDDWeighted average26%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E15795152.3809523810.4E157190247.6190476190.2E on S|D=12.0
0865146000.102186107.14285714290.2064429492.85714285710.1E on S|D=02.02
1000259.5238095238740.4761904762D on S|E=11.5
RR=2.0RR=1.9RR=1.8D on S|E=01.51.5
OR=2.4OR=2.4OR=2.0D=10.250.75
RD=0.14RD=0.18RD=0.10E=10.66666666670.33
Selection:
Example13Response
N1000D
% exposed40%10
% disease20%E10.90.451.31.7RR among
RR200.450.45selected=
Response=50%10
PopulationRespondersNon respond2.03.10.5
DDDWeighted average50%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103129231.42857142860.4E111157168.57142857140.1E on S|D=12.0
0865146000.10392312700.10472833300.1E on S|D=01.01.25
1000501.4285714286498.5714285714D on S|E=12
RR=2.0RR=3.1RR=0.5D on S|E=011.6666666667
OR=2.4OR=4.8OR=0.4D=10.250.75
RD=0.14RD=0.30RD=-0.08E=10.66666666670.33
ED2
E
D
S
D
E
D
D
E+D
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
E
D
S
Sel Bias
Selection bias examples
Fill inn gray cells
Selection:
Example1ResponseOnly E
N1000DNo bias
% exposed40%10
% disease20%E10.90.93.01.0
RR200.30.3RR
Response=54%10
PopulationRespondersNon respond2.02.02.0
DDDWeighted average54%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=03.03
1000540460D on S|E=11.0
RR=2.0RR=2.0RR=2.0D on S|E=01.01
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.14RD=0.14E=10.66666666670.33
Selection:
Example2ResponseOnly D
N1000DOR not biased
% exposed40%10
% disease20%E10.90.31.03.0
RR200.90.3RR
Response=42%10
PopulationRespondersNon respond2.01.62.3
DDDWeighted average42%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=01.01
1000420580D on S|E=13.0
RR=2.0RR=1.6RR=2.3D on S|E=03.03
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.21RD=0.03E=10.66666666670.33
Selection:
Example3ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10Ex 3 to 5 are variants of the same pattern
% disease20%E10.90.92.51.7
RR200.90.3RR
Response=59%10
PopulationRespondersNon respond2.00.912.3
DDDWeighted average59%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=03.02.5
1000591.4285714286408.5714285714D on S|E=11.0
RR=2.0RR=0.9RR=12.3D on S|E=03.01.6666666667
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.05RD=0.26E=10.66666666670.33
Selection:
Example4ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.90.92.61.4
RR200.70.3RR
Response=57%10
PopulationRespondersNon respond2.01.04.3
DDDWeighted average57%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.3
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5714285714
1000574.2857142857425.7142857143D on S|E=11.0
RR=2.0RR=1.0RR=4.3D on S|E=02.31.4444444444
OR=2.4OR=1.0OR=5.6D=10.250.75
RD=0.14RD=0.01RD=0.22E=10.66666666670.33
Selection:
Example5ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.70.92.51.3
RR200.70.3RR
Response=55%10
PopulationRespondersNon respond2.00.88.2
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E180257337.14285714290.2E1342962.85714285710.5E on S|D=11.0
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5
1000551.4285714286448.5714285714D on S|E=10.8
RR=2.0RR=0.8RR=8.2D on S|E=02.31.2962962963
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.04RD=0.48E=10.66666666670.33
Selection:
Example6ResponseBoth E and D through E and D
N1000DPositive association among responders
% exposed40%10
% disease20%E10.90.31.52.3
RR200.30.3RR
Response=37%10
PopulationRespondersNon respond2.03.80.4
DDDWeighted average37%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=01.01.5
1000368.5714285714631.4285714286D on S|E=13.0
RR=2.0RR=3.8RR=0.4D on S|E=01.02.3333333333
OR=2.4OR=7.2OR=0.3D=10.250.75
RD=0.14RD=0.40RD=-0.09E=10.66666666670.33
Selection:
Example7ResponseBoth E and D through E and D
N1000DBoth strata neg bias
% exposed40%10
% disease20%E10.90.82.51.3
RR200.50.3RR
Response=53%10
PopulationRespondersNon respond2.01.41.6
DDDWeighted average53%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103229331.42857142860.3E1115768.57142857140.2E on S|D=11.8
0865146000.1043154197.14285714290.2043360402.85714285710.1E on S|D=02.72.45
1000528.5714285714471.4285714286D on S|E=11.1
RR=2.0RR=1.4RR=1.6D on S|E=01.71.3055555556
OR=2.4OR=1.6OR=1.7D=10.250.75
RD=0.14RD=0.09RD=0.06E=10.66666666670.33
Selection:
Example8Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.90.452.02.0
RR100.450.225RR
Response=38%10
PopulationRespondersNon respond1.01.00.3
DDDWeighted average38%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E1803204000.2E1721442160.3E181761840.0E on S|D=12.0
01204806000.20541081620.30663724380.2E on S|D=02.02
1000378622D on S|E=12.0
RR=1.0RR=1.0RR=0.3D on S|E=02.02
OR=1.0OR=1.0OR=0.3D=10.250.75
RD=0.00RD=0.00RD=-0.11E=10.66666666670.33
Selection:
Example9Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.450.92.00.5
RR200.2250.45RR
Response=56%10
PopulationRespondersNon respond2.02.23.6
DDDWeighted average56%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E151257308.57142857140.2E1632991.42857142860.7E on S|D=12.0
0865146000.1019231250.71428571430.1066283349.28571428570.2E on S|D=02.02
1000559.2857142857440.7142857143D on S|E=10.5
RR=2.0RR=2.2RR=3.6D on S|E=00.50.5
OR=2.4OR=2.4OR=9.4D=10.250.75
RD=0.14RD=0.09RD=0.50E=10.66666666670.33
Selection:
Example10Response
N1000DStrong opposite effects
% exposed40%10
% disease20%E10.30.60.60.7
RR200.90.8RR
Response=69%10
PopulationRespondersNon respond2.01.15.4
DDDWeighted average69%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E134171205.71428571430.2E180114194.28571428570.4E on S|D=10.3
0865146000.1077411488.57142857140.209103111.42857142860.1E on S|D=00.80.6458333333
1000694.2857142857305.7142857143D on S|E=10.5
RR=2.0RR=1.1RR=5.4D on S|E=01.1250.7083333333
OR=2.4OR=1.1OR=8.4D=10.250.75
RD=0.14RD=0.01RD=0.33E=10.66666666670.33
Selection:
Example11ResponseThis and next: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.990.661.52.01.5
RR200.4950.33RR
Response=51%210
PopulationRespondersNon respond2.01.90.1
DDDWeighted average51%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1113189301.71428571430.4E119798.28571428570.0E on S|D=12.0
0865146000.1042170212.14285714290.2043345387.85714285710.1E on S|D=02.02
1000513.8571428571486.1428571429D on S|E=11.5
RR=2.0RR=1.9RR=0.1D on S|E=01.51.5
OR=2.4OR=2.4OR=0.1D=10.250.75
RD=0.14RD=0.18RD=-0.10E=10.66666666670.33
Selection:
Example12ResponseThis and previous: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.50.33333333331.52.01.5
RR200.250.1666666667RR
Response=26%210
PopulationRespondersNon respond2.01.91.8
DDDWeighted average26%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E15795152.3809523810.4E157190247.6190476190.2E on S|D=12.0
0865146000.102186107.14285714290.2064429492.85714285710.1E on S|D=02.02
1000259.5238095238740.4761904762D on S|E=11.5
RR=2.0RR=1.9RR=1.8D on S|E=01.51.5
OR=2.4OR=2.4OR=2.0D=10.250.75
RD=0.14RD=0.18RD=0.10E=10.66666666670.33
Selection:
Example13Response
N1000D
% exposed40%10
% disease20%E10.90.451.31.7
RR200.450.45RR
Response=50%10
PopulationRespondersNon respond2.03.10.5
DDDWeighted average50%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103129231.42857142860.4E111157168.57142857140.1E on S|D=12.0
0865146000.10392312700.10472833300.1E on S|D=01.01.25
1000501.4285714286498.5714285714D on S|E=12
RR=2.0RR=3.1RR=0.5D on S|E=011.6666666667
OR=2.4OR=4.8OR=0.4D=10.250.75
RD=0.14RD=0.30RD=-0.08E=10.66666666670.33
ED2
E
D
R
D
E
D
D
E+D
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
-
Example 2Pattern:Only D influence responseResult:RR (and RD) biased, OR unbiasedODS, Case-Control
Sel Bias
Selection bias examples
Fill inn gray cells
Selection:
Example1ResponseOnly E
N1000DNo bias
% exposed40%10
% disease20%E10.90.93.01.0
RR200.30.3RR
Response=54%10
PopulationRespondersNon respond2.02.02.0
DDDWeighted average54%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=03.03
1000540460D on S|E=11.0
RR=2.0RR=2.0RR=2.0D on S|E=01.01
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.14RD=0.14E=10.66666666670.33
Selection:
Example2ResponseOnly D
N1000DOR not biased
% exposed40%10
% disease20%E10.90.31.03.0
RR200.90.3RR
Response=42%10
PopulationRespondersNon respond2.01.62.3
DDDWeighted average42%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=01.01
1000420580D on S|E=13.0
RR=2.0RR=1.6RR=2.3D on S|E=03.03
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.21RD=0.03E=10.66666666670.33
Selection:
Example3ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10Ex 3 to 5 are variants of the same pattern
% disease20%E10.90.51.21.5
RR200.50.5RR
Response=55%10
PopulationRespondersNon respond2.02.90.5
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103143245.71428571430.4E111143154.28571428570.1E on S|D=11.8
0865146000.10432573000.10432573000.1E on S|D=01.01.2
1000545.7142857143454.2857142857D on S|E=11.8
RR=2.0RR=2.9RR=0.5D on S|E=01.01.5333333333
OR=2.4OR=4.3OR=0.5D=10.250.75
RD=0.14RD=0.28RD=-0.07E=10.66666666670.33
Selection:
Example4ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.90.92.61.4
RR200.70.3RR
Response=57%10
PopulationRespondersNon respond2.01.04.3
DDDWeighted average57%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.3
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5714285714
1000574.2857142857425.7142857143D on S|E=11.0
RR=2.0RR=1.0RR=4.3D on S|E=02.31.4444444444
OR=2.4OR=1.0OR=5.6D=10.250.75
RD=0.14RD=0.01RD=0.22E=10.66666666670.33
Selection:
Example5ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.70.92.51.3
RR200.70.3RR
Response=55%10
PopulationRespondersNon respond2.00.88.2
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E180257337.14285714290.2E1342962.85714285710.5E on S|D=11.0
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5
1000551.4285714286448.5714285714D on S|E=10.8
RR=2.0RR=0.8RR=8.2D on S|E=02.31.2962962963
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.04RD=0.48E=10.66666666670.33
Selection:
Example6ResponseBoth E and D through E and D
N1000DPositive association among responders
% exposed40%10
% disease20%E10.90.31.52.3
RR200.30.3RR
Response=37%10
PopulationRespondersNon respond2.03.80.4
DDDWeighted average37%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=01.01.5
1000368.5714285714631.4285714286D on S|E=13.0
RR=2.0RR=3.8RR=0.4D on S|E=01.02.3333333333
OR=2.4OR=7.2OR=0.3D=10.250.75
RD=0.14RD=0.40RD=-0.09E=10.66666666670.33
Selection:
Example7ResponseBoth E and D through E and D
N1000DBoth strata neg bias
% exposed40%10
% disease20%E10.90.82.51.3
RR200.50.3RR
Response=53%10
PopulationRespondersNon respond2.01.41.6
DDDWeighted average53%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103229331.42857142860.3E1115768.57142857140.2E on S|D=11.8
0865146000.1043154197.14285714290.2043360402.85714285710.1E on S|D=02.72.45
1000528.5714285714471.4285714286D on S|E=11.1
RR=2.0RR=1.4RR=1.6D on S|E=01.71.3055555556
OR=2.4OR=1.6OR=1.7D=10.250.75
RD=0.14RD=0.09RD=0.06E=10.66666666670.33
Selection:
Example8Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.90.452.02.0
RR100.450.225RR
Response=38%10
PopulationRespondersNon respond1.01.00.3
DDDWeighted average38%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E1803204000.2E1721442160.3E181761840.0E on S|D=12.0
01204806000.20541081620.30663724380.2E on S|D=02.02
1000378622D on S|E=12.0
RR=1.0RR=1.0RR=0.3D on S|E=02.02
OR=1.0OR=1.0OR=0.3D=10.250.75
RD=0.00RD=0.00RD=-0.11E=10.66666666670.33
Selection:
Example9Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.450.92.00.5
RR200.2250.45RR
Response=56%10
PopulationRespondersNon respond2.02.23.6
DDDWeighted average56%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E151257308.57142857140.2E1632991.42857142860.7E on S|D=12.0
0865146000.1019231250.71428571430.1066283349.28571428570.2E on S|D=02.02
1000559.2857142857440.7142857143D on S|E=10.5
RR=2.0RR=2.2RR=3.6D on S|E=00.50.5
OR=2.4OR=2.4OR=9.4D=10.250.75
RD=0.14RD=0.09RD=0.50E=10.66666666670.33
Selection:
Example10Response
N1000DStrong opposite effects
% exposed40%10
% disease20%E10.30.60.60.7
RR200.90.8RR
Response=69%10
PopulationRespondersNon respond2.01.15.4
DDDWeighted average69%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E134171205.71428571430.2E180114194.28571428570.4E on S|D=10.3
0865146000.1077411488.57142857140.209103111.42857142860.1E on S|D=00.80.6458333333
1000694.2857142857305.7142857143D on S|E=10.5
RR=2.0RR=1.1RR=5.4D on S|E=01.1250.7083333333
OR=2.4OR=1.1OR=8.4D=10.250.75
RD=0.14RD=0.01RD=0.33E=10.66666666670.33
Selection:
Example11ResponseThis and next: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.990.661.52.01.5
RR200.4950.33RR
Response=51%210
PopulationRespondersNon respond2.01.90.1
DDDWeighted average51%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1113189301.71428571430.4E119798.28571428570.0E on S|D=12.0
0865146000.1042170212.14285714290.2043345387.85714285710.1E on S|D=02.02
1000513.8571428571486.1428571429D on S|E=11.5
RR=2.0RR=1.9RR=0.1D on S|E=01.51.5
OR=2.4OR=2.4OR=0.1D=10.250.75
RD=0.14RD=0.18RD=-0.10E=10.66666666670.33
Selection:
Example12ResponseThis and previous: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.50.33333333331.52.01.5
RR200.250.1666666667RR
Response=26%210
PopulationRespondersNon respond2.01.91.8
DDDWeighted average26%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E15795152.3809523810.4E157190247.6190476190.2E on S|D=12.0
0865146000.102186107.14285714290.2064429492.85714285710.1E on S|D=02.02
1000259.5238095238740.4761904762D on S|E=11.5
RR=2.0RR=1.9RR=1.8D on S|E=01.51.5
OR=2.4OR=2.4OR=2.0D=10.250.75
RD=0.14RD=0.18RD=0.10E=10.66666666670.33
Selection:
Example13Response
N1000D
% exposed40%10
% disease20%E10.90.451.31.7
RR200.450.45RR
Response=50%10
PopulationRespondersNon respond2.03.10.5
DDDWeighted average50%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103129231.42857142860.4E111157168.57142857140.1E on S|D=12.0
0865146000.10392312700.10472833300.1E on S|D=01.01.25
1000501.4285714286498.5714285714D on S|E=12
RR=2.0RR=3.1RR=0.5D on S|E=011.6666666667
OR=2.4OR=4.8OR=0.4D=10.250.75
RD=0.14RD=0.30RD=-0.08E=10.66666666670.33
ED2
E
D
R
D
E
D
D
E+D
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
Sel Bias
Selection bias examples
Fill inn gray cells
Selection:
Example1ResponseOnly E
N1000DNo bias
% exposed40%10
% disease20%E10.90.93.01.0
RR200.30.3RR
Response=54%10
PopulationRespondersNon respond2.02.02.0
DDDWeighted average54%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=03.03
1000540460D on S|E=11.0
RR=2.0RR=2.0RR=2.0D on S|E=01.01
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.14RD=0.14E=10.66666666670.33
Selection:
Example2ResponseOnly D
N1000DOR not biased
% exposed40%10
% disease20%E10.90.31.03.0
RR200.90.3RR
Response=42%10
PopulationRespondersNon respond2.01.62.3
DDDWeighted average42%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=01.01
1000420580D on S|E=13.0
RR=2.0RR=1.6RR=2.3D on S|E=03.03
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.21RD=0.03E=10.66666666670.33
Selection:
Example3ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10Ex 3 to 5 are variants of the same pattern
% disease20%E10.90.51.21.5
RR200.50.5RR
Response=55%10
PopulationRespondersNon respond2.02.90.5
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103143245.71428571430.4E111143154.28571428570.1E on S|D=11.8
0865146000.10432573000.10432573000.1E on S|D=01.01.2
1000545.7142857143454.2857142857D on S|E=11.8
RR=2.0RR=2.9RR=0.5D on S|E=01.01.5333333333
OR=2.4OR=4.3OR=0.5D=10.250.75
RD=0.14RD=0.28RD=-0.07E=10.66666666670.33
Selection:
Example4ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.90.92.61.4
RR200.70.3RR
Response=57%10
PopulationRespondersNon respond2.01.04.3
DDDWeighted average57%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.3
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5714285714
1000574.2857142857425.7142857143D on S|E=11.0
RR=2.0RR=1.0RR=4.3D on S|E=02.31.4444444444
OR=2.4OR=1.0OR=5.6D=10.250.75
RD=0.14RD=0.01RD=0.22E=10.66666666670.33
Selection:
Example5ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.70.92.51.3
RR200.70.3RR
Response=55%10
PopulationRespondersNon respond2.00.88.2
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E180257337.14285714290.2E1342962.85714285710.5E on S|D=11.0
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5
1000551.4285714286448.5714285714D on S|E=10.8
RR=2.0RR=0.8RR=8.2D on S|E=02.31.2962962963
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.04RD=0.48E=10.66666666670.33
Selection:
Example6ResponseBoth E and D through E and D
N1000DPositive association among responders
% exposed40%10
% disease20%E10.90.31.52.3
RR200.30.3RR
Response=37%10
PopulationRespondersNon respond2.03.80.4
DDDWeighted average37%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=01.01.5
1000368.5714285714631.4285714286D on S|E=13.0
RR=2.0RR=3.8RR=0.4D on S|E=01.02.3333333333
OR=2.4OR=7.2OR=0.3D=10.250.75
RD=0.14RD=0.40RD=-0.09E=10.66666666670.33
Selection:
Example7ResponseBoth E and D through E and D
N1000DBoth strata neg bias
% exposed40%10
% disease20%E10.90.82.51.3
RR200.50.3RR
Response=53%10
PopulationRespondersNon respond2.01.41.6
DDDWeighted average53%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103229331.42857142860.3E1115768.57142857140.2E on S|D=11.8
0865146000.1043154197.14285714290.2043360402.85714285710.1E on S|D=02.72.45
1000528.5714285714471.4285714286D on S|E=11.1
RR=2.0RR=1.4RR=1.6D on S|E=01.71.3055555556
OR=2.4OR=1.6OR=1.7D=10.250.75
RD=0.14RD=0.09RD=0.06E=10.66666666670.33
Selection:
Example8Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.90.452.02.0
RR100.450.225RR
Response=38%10
PopulationRespondersNon respond1.01.00.3
DDDWeighted average38%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E1803204000.2E1721442160.3E181761840.0E on S|D=12.0
01204806000.20541081620.30663724380.2E on S|D=02.02
1000378622D on S|E=12.0
RR=1.0RR=1.0RR=0.3D on S|E=02.02
OR=1.0OR=1.0OR=0.3D=10.250.75
RD=0.00RD=0.00RD=-0.11E=10.66666666670.33
Selection:
Example9Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.450.92.00.5
RR200.2250.45RR
Response=56%10
PopulationRespondersNon respond2.02.23.6
DDDWeighted average56%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E151257308.57142857140.2E1632991.42857142860.7E on S|D=12.0
0865146000.1019231250.71428571430.1066283349.28571428570.2E on S|D=02.02
1000559.2857142857440.7142857143D on S|E=10.5
RR=2.0RR=2.2RR=3.6D on S|E=00.50.5
OR=2.4OR=2.4OR=9.4D=10.250.75
RD=0.14RD=0.09RD=0.50E=10.66666666670.33
Selection:
Example10Response
N1000DStrong opposite effects
% exposed40%10
% disease20%E10.30.60.60.7
RR200.90.8RR
Response=69%10
PopulationRespondersNon respond2.01.15.4
DDDWeighted average69%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E134171205.71428571430.2E180114194.28571428570.4E on S|D=10.3
0865146000.1077411488.57142857140.209103111.42857142860.1E on S|D=00.80.6458333333
1000694.2857142857305.7142857143D on S|E=10.5
RR=2.0RR=1.1RR=5.4D on S|E=01.1250.7083333333
OR=2.4OR=1.1OR=8.4D=10.250.75
RD=0.14RD=0.01RD=0.33E=10.66666666670.33
Selection:
Example11ResponseThis and next: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.990.661.52.01.5
RR200.4950.33RR
Response=51%210
PopulationRespondersNon respond2.01.90.1
DDDWeighted average51%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1113189301.71428571430.4E119798.28571428570.0E on S|D=12.0
0865146000.1042170212.14285714290.2043345387.85714285710.1E on S|D=02.02
1000513.8571428571486.1428571429D on S|E=11.5
RR=2.0RR=1.9RR=0.1D on S|E=01.51.5
OR=2.4OR=2.4OR=0.1D=10.250.75
RD=0.14RD=0.18RD=-0.10E=10.66666666670.33
Selection:
Example12ResponseThis and previous: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.50.33333333331.52.01.5
RR200.250.1666666667RR
Response=26%210
PopulationRespondersNon respond2.01.91.8
DDDWeighted average26%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E15795152.3809523810.4E157190247.6190476190.2E on S|D=12.0
0865146000.102186107.14285714290.2064429492.85714285710.1E on S|D=02.02
1000259.5238095238740.4761904762D on S|E=11.5
RR=2.0RR=1.9RR=1.8D on S|E=01.51.5
OR=2.4OR=2.4OR=2.0D=10.250.75
RD=0.14RD=0.18RD=0.10E=10.66666666670.33
Selection:
Example13Response
N1000D
% exposed40%10
% disease20%E10.90.451.31.7
RR200.450.45RR
Response=50%10
PopulationRespondersNon respond2.03.10.5
DDDWeighted average50%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103129231.42857142860.4E111157168.57142857140.1E on S|D=12.0
0865146000.10392312700.10472833300.1E on S|D=01.01.25
1000501.4285714286498.5714285714D on S|E=12
RR=2.0RR=3.1RR=0.5D on S|E=011.6666666667
OR=2.4OR=4.8OR=0.4D=10.250.75
RD=0.14RD=0.30RD=-0.08E=10.66666666670.33
ED2
E
D
R
D
E
D
D
E+D
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
-
Example 3Pattern:Both E and D influence responseResult:Surprise: responders are unbiasedTheory: bias in at least one stratum
Sel Bias
Selection bias examples
Fill inn gray cells
Selection:
Example1ResponseOnly E
N1000DNo bias
% exposed40%10
% disease20%E10.90.93.01.0
RR200.30.3RR
Response=54%10
PopulationRespondersNon respond2.02.02.0
DDDWeighted average54%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=03.03
1000540460D on S|E=11.0
RR=2.0RR=2.0RR=2.0D on S|E=01.01
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.14RD=0.14E=10.66666666670.33
Selection:
Example2ResponseOnly D
N1000DOR not biased
% exposed40%10
% disease20%E10.90.31.03.0
RR200.90.3RR
Response=42%10
PopulationRespondersNon respond2.01.62.3
DDDWeighted average42%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=01.01
1000420580D on S|E=13.0
RR=2.0RR=1.6RR=2.3D on S|E=03.03
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.21RD=0.03E=10.66666666670.33
Selection:
Example3ResponseBoth E and D through E-D
N1000DPositive bias among responders
% exposed40%10
% disease20%E10.90.51.21.5
RR200.50.5RR
Response=55%10
PopulationRespondersNon respond2.02.90.5
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103143245.71428571430.4E111143154.28571428570.1E on S|D=11.8
0865146000.10432573000.10432573000.1E on S|D=01.01.2
1000545.7142857143454.2857142857D on S|E=11.8
RR=2.0RR=2.9RR=0.5D on S|E=01.01.5333333333
OR=2.4OR=4.3OR=0.5D=10.250.75
RD=0.14RD=0.28RD=-0.07E=10.66666666670.33
Selection:
Example4ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.90.92.61.4
RR200.70.3RR
Response=57%10
PopulationRespondersNon respond2.01.04.3
DDDWeighted average57%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.3
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5714285714
1000574.2857142857425.7142857143D on S|E=11.0
RR=2.0RR=1.0RR=4.3D on S|E=02.31.4444444444
OR=2.4OR=1.0OR=5.6D=10.250.75
RD=0.14RD=0.01RD=0.22E=10.66666666670.33
Selection:
Example5ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.70.92.51.3
RR200.70.3RR
Response=55%10
PopulationRespondersNon respond2.00.88.2
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E180257337.14285714290.2E1342962.85714285710.5E on S|D=11.0
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5
1000551.4285714286448.5714285714D on S|E=10.8
RR=2.0RR=0.8RR=8.2D on S|E=02.31.2962962963
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.04RD=0.48E=10.66666666670.33
Selection:
Example6ResponseBoth E and D through E and D
N1000DPositive association among responders
% exposed40%10
% disease20%E10.90.31.52.3
RR200.30.3RR
Response=37%10
PopulationRespondersNon respond2.03.80.4
DDDWeighted average37%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=01.01.5
1000368.5714285714631.4285714286D on S|E=13.0
RR=2.0RR=3.8RR=0.4D on S|E=01.02.3333333333
OR=2.4OR=7.2OR=0.3D=10.250.75
RD=0.14RD=0.40RD=-0.09E=10.66666666670.33
Selection:
Example7ResponseBoth E and D through E and D
N1000DBoth strata neg bias
% exposed40%10
% disease20%E10.90.82.51.3
RR200.50.3RR
Response=53%10
PopulationRespondersNon respond2.01.41.6
DDDWeighted average53%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103229331.42857142860.3E1115768.57142857140.2E on S|D=11.8
0865146000.1043154197.14285714290.2043360402.85714285710.1E on S|D=02.72.45
1000528.5714285714471.4285714286D on S|E=11.1
RR=2.0RR=1.4RR=1.6D on S|E=01.71.3055555556
OR=2.4OR=1.6OR=1.7D=10.250.75
RD=0.14RD=0.09RD=0.06E=10.66666666670.33
Selection:
Example8Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.90.452.02.0
RR100.450.225RR
Response=38%10
PopulationRespondersNon respond1.01.00.3
DDDWeighted average38%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E1803204000.2E1721442160.3E181761840.0E on S|D=12.0
01204806000.20541081620.30663724380.2E on S|D=02.02
1000378622D on S|E=12.0
RR=1.0RR=1.0RR=0.3D on S|E=02.02
OR=1.0OR=1.0OR=0.3D=10.250.75
RD=0.00RD=0.00RD=-0.11E=10.66666666670.33
Selection:
Example9Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.450.92.00.5
RR200.2250.45RR
Response=56%10
PopulationRespondersNon respond2.02.23.6
DDDWeighted average56%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E151257308.57142857140.2E1632991.42857142860.7E on S|D=12.0
0865146000.1019231250.71428571430.1066283349.28571428570.2E on S|D=02.02
1000559.2857142857440.7142857143D on S|E=10.5
RR=2.0RR=2.2RR=3.6D on S|E=00.50.5
OR=2.4OR=2.4OR=9.4D=10.250.75
RD=0.14RD=0.09RD=0.50E=10.66666666670.33
Selection:
Example10Response
N1000DStrong opposite effects
% exposed40%10
% disease20%E10.30.60.60.7
RR200.90.8RR
Response=69%10
PopulationRespondersNon respond2.01.15.4
DDDWeighted average69%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E134171205.71428571430.2E180114194.28571428570.4E on S|D=10.3
0865146000.1077411488.57142857140.209103111.42857142860.1E on S|D=00.80.6458333333
1000694.2857142857305.7142857143D on S|E=10.5
RR=2.0RR=1.1RR=5.4D on S|E=01.1250.7083333333
OR=2.4OR=1.1OR=8.4D=10.250.75
RD=0.14RD=0.01RD=0.33E=10.66666666670.33
Selection:
Example11ResponseThis and next: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.990.661.52.01.5
RR200.4950.33RR
Response=51%210
PopulationRespondersNon respond2.01.90.1
DDDWeighted average51%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1113189301.71428571430.4E119798.28571428570.0E on S|D=12.0
0865146000.1042170212.14285714290.2043345387.85714285710.1E on S|D=02.02
1000513.8571428571486.1428571429D on S|E=11.5
RR=2.0RR=1.9RR=0.1D on S|E=01.51.5
OR=2.4OR=2.4OR=0.1D=10.250.75
RD=0.14RD=0.18RD=-0.10E=10.66666666670.33
Selection:
Example12ResponseThis and previous: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.50.33333333331.52.01.5
RR200.250.1666666667RR
Response=26%210
PopulationRespondersNon respond2.01.91.8
DDDWeighted average26%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E15795152.3809523810.4E157190247.6190476190.2E on S|D=12.0
0865146000.102186107.14285714290.2064429492.85714285710.1E on S|D=02.02
1000259.5238095238740.4761904762D on S|E=11.5
RR=2.0RR=1.9RR=1.8D on S|E=01.51.5
OR=2.4OR=2.4OR=2.0D=10.250.75
RD=0.14RD=0.18RD=0.10E=10.66666666670.33
Selection:
Example13Response
N1000D
% exposed40%10
% disease20%E10.90.451.31.7
RR200.450.45RR
Response=50%10
PopulationRespondersNon respond2.03.10.5
DDDWeighted average50%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103129231.42857142860.4E111157168.57142857140.1E on S|D=12.0
0865146000.10392312700.10472833300.1E on S|D=01.01.25
1000501.4285714286498.5714285714D on S|E=12
RR=2.0RR=3.1RR=0.5D on S|E=011.6666666667
OR=2.4OR=4.8OR=0.4D=10.250.75
RD=0.14RD=0.30RD=-0.08E=10.66666666670.33
ED2
E
D
R
D
E
D
D
E+D
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
Sel Bias
Selection bias examples
Fill inn gray cells
Selection:
Example1ResponseOnly E
N1000DNo bias
% exposed40%10
% disease20%E10.90.93.01.0
RR200.30.3RR
Response=54%10
PopulationRespondersNon respond2.02.02.0
DDDWeighted average54%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=03.03
1000540460D on S|E=11.0
RR=2.0RR=2.0RR=2.0D on S|E=01.01
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.14RD=0.14E=10.66666666670.33
Selection:
Example2ResponseOnly D
N1000DOR not biased
% exposed40%10
% disease20%E10.90.31.03.0
RR200.90.3RR
Response=42%10
PopulationRespondersNon respond2.01.62.3
DDDWeighted average42%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=01.01
1000420580D on S|E=13.0
RR=2.0RR=1.6RR=2.3D on S|E=03.03
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.21RD=0.03E=10.66666666670.33
Selection:
Example3ResponseBoth E and D through E-D
N1000DPositive bias among responders
% exposed40%10
% disease20%E10.90.51.21.5
RR200.50.5RR
Response=55%10
PopulationRespondersNon respond2.02.90.5
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103143245.71428571430.4E111143154.28571428570.1E on S|D=11.8
0865146000.10432573000.10432573000.1E on S|D=01.01.2
1000545.7142857143454.2857142857D on S|E=11.8
RR=2.0RR=2.9RR=0.5D on S|E=01.01.5333333333
OR=2.4OR=4.3OR=0.5D=10.250.75
RD=0.14RD=0.28RD=-0.07E=10.66666666670.33
Selection:
Example4ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.90.92.61.4
RR200.70.3RR
Response=57%10
PopulationRespondersNon respond2.01.04.3
DDDWeighted average57%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.3
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5714285714
1000574.2857142857425.7142857143D on S|E=11.0
RR=2.0RR=1.0RR=4.3D on S|E=02.31.4444444444
OR=2.4OR=1.0OR=5.6D=10.250.75
RD=0.14RD=0.01RD=0.22E=10.66666666670.33
Selection:
Example5ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.70.92.51.3
RR200.70.3RR
Response=55%10
PopulationRespondersNon respond2.00.88.2
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E180257337.14285714290.2E1342962.85714285710.5E on S|D=11.0
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5
1000551.4285714286448.5714285714D on S|E=10.8
RR=2.0RR=0.8RR=8.2D on S|E=02.31.2962962963
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.04RD=0.48E=10.66666666670.33
Selection:
Example6ResponseBoth E and D through E and D
N1000DPositive association among responders
% exposed40%10
% disease20%E10.90.31.52.3
RR200.30.3RR
Response=37%10
PopulationRespondersNon respond2.03.80.4
DDDWeighted average37%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=01.01.5
1000368.5714285714631.4285714286D on S|E=13.0
RR=2.0RR=3.8RR=0.4D on S|E=01.02.3333333333
OR=2.4OR=7.2OR=0.3D=10.250.75
RD=0.14RD=0.40RD=-0.09E=10.66666666670.33
Selection:
Example7ResponseBoth E and D through E and D
N1000DBoth strata neg bias
% exposed40%10
% disease20%E10.90.82.51.3
RR200.50.3RR
Response=53%10
PopulationRespondersNon respond2.01.41.6
DDDWeighted average53%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103229331.42857142860.3E1115768.57142857140.2E on S|D=11.8
0865146000.1043154197.14285714290.2043360402.85714285710.1E on S|D=02.72.45
1000528.5714285714471.4285714286D on S|E=11.1
RR=2.0RR=1.4RR=1.6D on S|E=01.71.3055555556
OR=2.4OR=1.6OR=1.7D=10.250.75
RD=0.14RD=0.09RD=0.06E=10.66666666670.33
Selection:
Example8Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.90.452.02.0
RR100.450.225RR
Response=38%10
PopulationRespondersNon respond1.01.00.3
DDDWeighted average38%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E1803204000.2E1721442160.3E181761840.0E on S|D=12.0
01204806000.20541081620.30663724380.2E on S|D=02.02
1000378622D on S|E=12.0
RR=1.0RR=1.0RR=0.3D on S|E=02.02
OR=1.0OR=1.0OR=0.3D=10.250.75
RD=0.00RD=0.00RD=-0.11E=10.66666666670.33
Selection:
Example9Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.450.92.00.5
RR200.2250.45RR
Response=56%10
PopulationRespondersNon respond2.02.23.6
DDDWeighted average56%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E151257308.57142857140.2E1632991.42857142860.7E on S|D=12.0
0865146000.1019231250.71428571430.1066283349.28571428570.2E on S|D=02.02
1000559.2857142857440.7142857143D on S|E=10.5
RR=2.0RR=2.2RR=3.6D on S|E=00.50.5
OR=2.4OR=2.4OR=9.4D=10.250.75
RD=0.14RD=0.09RD=0.50E=10.66666666670.33
Selection:
Example10Response
N1000DStrong opposite effects
% exposed40%10
% disease20%E10.30.60.60.7
RR200.90.8RR
Response=69%10
PopulationRespondersNon respond2.01.15.4
DDDWeighted average69%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E134171205.71428571430.2E180114194.28571428570.4E on S|D=10.3
0865146000.1077411488.57142857140.209103111.42857142860.1E on S|D=00.80.6458333333
1000694.2857142857305.7142857143D on S|E=10.5
RR=2.0RR=1.1RR=5.4D on S|E=01.1250.7083333333
OR=2.4OR=1.1OR=8.4D=10.250.75
RD=0.14RD=0.01RD=0.33E=10.66666666670.33
Selection:
Example11ResponseThis and next: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.990.661.52.01.5
RR200.4950.33RR
Response=51%210
PopulationRespondersNon respond2.01.90.1
DDDWeighted average51%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1113189301.71428571430.4E119798.28571428570.0E on S|D=12.0
0865146000.1042170212.14285714290.2043345387.85714285710.1E on S|D=02.02
1000513.8571428571486.1428571429D on S|E=11.5
RR=2.0RR=1.9RR=0.1D on S|E=01.51.5
OR=2.4OR=2.4OR=0.1D=10.250.75
RD=0.14RD=0.18RD=-0.10E=10.66666666670.33
Selection:
Example12ResponseThis and previous: same DAG, different results
N1000D
% exposed40%10
% disease20%E10.50.33333333331.52.01.5
RR200.250.1666666667RR
Response=26%210
PopulationRespondersNon respond2.01.91.8
DDDWeighted average26%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E15795152.3809523810.4E157190247.6190476190.2E on S|D=12.0
0865146000.102186107.14285714290.2064429492.85714285710.1E on S|D=02.02
1000259.5238095238740.4761904762D on S|E=11.5
RR=2.0RR=1.9RR=1.8D on S|E=01.51.5
OR=2.4OR=2.4OR=2.0D=10.250.75
RD=0.14RD=0.18RD=0.10E=10.66666666670.33
Selection:
Example13Response
N1000D
% exposed40%10
% disease20%E10.90.451.31.7
RR200.450.45RR
Response=50%10
PopulationRespondersNon respond2.03.10.5
DDDWeighted average50%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103129231.42857142860.4E111157168.57142857140.1E on S|D=12.0
0865146000.10392312700.10472833300.1E on S|D=01.01.25
1000501.4285714286498.5714285714D on S|E=12
RR=2.0RR=3.1RR=0.5D on S|E=011.6666666667
OR=2.4OR=4.8OR=0.4D=10.250.75
RD=0.14RD=0.30RD=-0.08E=10.66666666670.33
ED2
E
D
R
D
E
D
D
E+D
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
E
D
R
-
Example 4Pattern:Both E and D influence responseResult:Surprise: both strata biased upwardsTrue RR is not a weighted average
Sel Bias
Selection bias examples
Fill inn gray cells
Selection:
Example1ResponseOnly E
N1000DNo bias
% exposed40%10
% disease20%E10.90.93.01.0
RR200.30.3RR
Response=54%10
PopulationRespondersNon respond2.02.02.0
DDDWeighted average54%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=03.03
1000540460D on S|E=11.0
RR=2.0RR=2.0RR=2.0D on S|E=01.01
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.14RD=0.14E=10.66666666670.33
Selection:
Example2ResponseOnly D
N1000DOR not biased
% exposed40%10
% disease20%E10.90.31.03.0
RR200.90.3RR
Response=42%10
PopulationRespondersNon respond2.01.62.3
DDDWeighted average42%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=11.0
0865146000.1077154231.42857142860.309360368.57142857140.0E on S|D=01.01
1000420580D on S|E=13.0
RR=2.0RR=1.6RR=2.3D on S|E=03.03
OR=2.4OR=2.4OR=2.4D=10.250.75
RD=0.14RD=0.21RD=0.03E=10.66666666670.33
Selection:
Example3ResponseBoth E and D through E-D
N1000DPositive bias among responders
% exposed40%10
% disease20%E10.90.51.21.5
RR200.50.5RR
Response=55%10
PopulationRespondersNon respond2.02.90.5
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103143245.71428571430.4E111143154.28571428570.1E on S|D=11.8
0865146000.10432573000.10432573000.1E on S|D=01.01.2
1000545.7142857143454.2857142857D on S|E=11.8
RR=2.0RR=2.9RR=0.5D on S|E=01.01.5333333333
OR=2.4OR=4.3OR=0.5D=10.250.75
RD=0.14RD=0.28RD=-0.07E=10.66666666670.33
Selection:
Example4ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.90.92.61.4
RR200.70.3RR
Response=57%10
PopulationRespondersNon respond2.01.04.3
DDDWeighted average57%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E11032573600.3E11129400.3E on S|D=11.3
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5714285714
1000574.2857142857425.7142857143D on S|E=11.0
RR=2.0RR=1.0RR=4.3D on S|E=02.31.4444444444
OR=2.4OR=1.0OR=5.6D=10.250.75
RD=0.14RD=0.01RD=0.22E=10.66666666670.33
Selection:
Example5ResponseBoth E and D through E or D
N1000DNegative association among responders
% exposed40%10
% disease20%E10.70.92.51.3
RR200.70.3RR
Response=55%10
PopulationRespondersNon respond2.00.88.2
DDDWeighted average55%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E180257337.14285714290.2E1342962.85714285710.5E on S|D=11.0
0865146000.1060154214.28571428570.3026360385.71428571430.1E on S|D=03.02.5
1000551.4285714286448.5714285714D on S|E=10.8
RR=2.0RR=0.8RR=8.2D on S|E=02.31.2962962963
OR=2.4OR=0.8OR=16.8D=10.250.75
RD=0.14RD=-0.04RD=0.48E=10.66666666670.33
Selection:
Example6ResponseBoth E and D through E and D
N1000DPositive association among responders
% exposed40%10
% disease20%E10.90.31.52.3
RR200.30.3RR
Response=37%10
PopulationRespondersNon respond2.03.80.4
DDDWeighted average37%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E110386188.57142857140.5E111200211.42857142860.1E on S|D=13.0
0865146000.10261541800.10603604200.1E on S|D=01.01.5
1000368.5714285714631.4285714286D on S|E=13.0
RR=2.0RR=3.8RR=0.4D on S|E=01.02.3333333333
OR=2.4OR=7.2OR=0.3D=10.250.75
RD=0.14RD=0.40RD=-0.09E=10.66666666670.33
Selection:
Example7ResponseBoth E and D through E and D
N1000DBoth strata neg bias
% exposed40%10
% disease20%E10.90.82.51.3
RR200.50.3RR
Response=53%10
PopulationRespondersNon respond2.01.41.6
DDDWeighted average53%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E1103229331.42857142860.3E1115768.57142857140.2E on S|D=11.8
0865146000.1043154197.14285714290.2043360402.85714285710.1E on S|D=02.72.45
1000528.5714285714471.4285714286D on S|E=11.1
RR=2.0RR=1.4RR=1.6D on S|E=01.71.3055555556
OR=2.4OR=1.6OR=1.7D=10.250.75
RD=0.14RD=0.09RD=0.06E=10.66666666670.33
Selection:
Example8Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.90.452.02.0
RR100.450.225RR
Response=38%10
PopulationRespondersNon respond1.01.00.3
DDDWeighted average38%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E1803204000.2E1721442160.3E181761840.0E on S|D=12.0
01204806000.20541081620.30663724380.2E on S|D=02.02
1000378622D on S|E=12.0
RR=1.0RR=1.0RR=0.3D on S|E=02.02
OR=1.0OR=1.0OR=0.3D=10.250.75
RD=0.00RD=0.00RD=-0.11E=10.66666666670.33
Selection:
Example9Response
N1000DOnly non-responders biased (needs no E-D effect)
% exposed40%10
% disease20%E10.450.92.00.5
RR200.2250.45RR
Response=56%10
PopulationRespondersNon respond2.02.23.6
DDDWeighted average56%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E151257308.57142857140.2E1632991.42857142860.7E on S|D=12.0
0865146000.1019231250.71428571430.1066283349.28571428570.2E on S|D=02.02
1000559.2857142857440.7142857143D on S|E=10.5
RR=2.0RR=2.2RR=3.6D on S|E=00.50.5
OR=2.4OR=2.4OR=9.4D=10.250.75
RD=0.14RD=0.09RD=0.50E=10.66666666670.33
Selection:
Example10Response
N1000DStrong opposite effects
% exposed40%10
% disease20%E10.30.60.60.7
RR200.90.8RR
Response=69%10
PopulationRespondersNon respond2.01.15.4
DDDWeighted average69%
10sumrisk10sumrisk10sumriskRRORRDRRORRD
E11142864000.3E134171205.71428571430.2E180114194.28571428570.4E on S|D=10.3
0865146000.1077411488.57142857140.209103111.42857142860.1E on S|D=00.80.6458333333
1000694.2857142