Selection Bias Concepts - PowerPoint PPT Presentation


Title: Selection Bias Concepts


1
Selection Bias Concepts
  • Hein Stigum
  • Presentation, data and programs at
  • http//folk.uio.no/heins/talks

2
Questions
  • Given measured appropriate variables
  • Can you adjust for confounding?
  • Yes
  • Can you adjust for selection bias?
  • Depends on the definition

3
Contents
  • Background
  • Define bias
  • Selection bias
  • as effect modification (old concept)
  • as collider stratification bias (new concept)
  • DAG structure
  • Examples
  • Size and direction of bias

4
Bias definition
  • Bias
  • Frequency expected risk ? true risk
  • Effect association ? causal effect

5
Selection bias concepts
  • Concept
  • DAG structure
  • Effect responders
  • ?
  • Effect non responders
  • Differential response bias
  • Differential loss to follow up
  • Healthy worker bias
  • Berksons bias (case control)
  • Effect
  • modification
  • Collider
  • stratification
  • bias

6
Selection bias as effect modification
7
Selection bias Risk
  • Selection of responders ?
  • The prevalence is different among
  • the responders compared to the full population
  • the responders compared to the non responders

R0
Non responders
Rp
Population
R1
Responders
Rp is the weighted mean of R0 and R1
8
Effect modification
  • Selection of responders ?
  • The effect of E on D is different among
  • the responders compared to the full population
  • the responders compared to the non responders

RR0
Non responders
RRp
Population
RR1
Responders
9
Problems
  • Is not a bias, RR0 and RR1 are the true effects
  • Is effect modification by selection variable S
  • Leads to the conclusion that
  • Biolocical effects are protected from bias
  • The bias can not be adjusted for
  • RRp is the average of RR0 and RR1

Not true for collider stratification bias
DAG structure
S
E
D
10
Selection bias as collider stratification bias
11
Example with paths
  • Study
  • Milk on bone density
  • Exclude Calcium supplements


  Path Type Status
1 ED Causal Open
2 ES?D Noncausal Open

2 ES?CD Noncausal Closed
Lessons learned Biological effect not
protected May adjust for selection bias
Structure Collider stratification
12
Examples
  • Differential response
  • Survey Alcohol and CHD
  • Differential loss to follow up
  • Randomized trial drug and disease
  • Healthy worker effect
  • Cross-section Melt hall dust and lung disease

Note no confounding
13
Selection bias structure
August 15
H.S.
13
14
Paths
  • 1. Causal

2. Confounding An open non-causal path without
colliders
3. Selection bias A non-causal path that is open
due to conditioning on a collider
BCVs?
15
Collider stratification bias
  • Selection bias Collider stratification bias
  • Selection bias, Path definition
  • A non causal path that is open due to
    conditioning on a collider

16
Selection bias examples
17
Folic acid and cardiac malformation
  • Selection Study only live born
  • Bias?

Yes, E?C?D is open
  • Selection Non grieving parents volonteer
  • Bias?

Yes, E?C?D is (partially) open
18
Education and unfaithfulness
  • Study the effect among couples in a relationship
    (not divorced)?


  Path Type Population Sample
1 ED Causal Open Open
2 ER?D Noncausal Closed Open
3 ER?SD Noncausal Closed Open
Selection bias
19
Size and Direction of bias
August 15
H.S.
19
20
Example 1, full table
(Adjusted) RRs
True and biased RRs
Proportion responding in 1,1 group
21
Example 2
Pattern Only D influence response
Result RR (and RD) biased, OR unbiased ODS,
Case-Control
22
Example 3
Pattern Both E and D influence response
Result Surprise responders are unbiased Theory
bias in at least one stratum
23
Example 4
Pattern Both E and D influence response
Result Surprise both strata biased upwards True
RR is not a weighted average
24
Example 5
Pattern Both E and D influence response
Result Same DAG, different results The DAG does
not fully determine the selection!
25
Summing up
  • Selection bias as effect modification
  • Is not a bias, should not be called selection
    bias
  • Has properties different from proper selection
    bias
  • Selection bias as collider stratification
  • Structure defined in DAG,
  • Distinct from confounding
  • Consistent with
  • Differential response bias
  • Differential loss to follow up
  • Healthy worker bias
  • Berksons bias (case control)

26
Litterature
  • Hernan and Robins, Causal Inference
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Selection Bias Concepts

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Selection Bias Concepts Hein Stigum Presentation, data and programs at: http://folk.uio.no/heins/talks * H.S. * Works only for true RR=1 ? Can also have both biased ... – PowerPoint PPT presentation

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Title: Selection Bias Concepts


1
Selection Bias Concepts
  • Hein Stigum
  • Presentation, data and programs at
  • http//folk.uio.no/heins/talks

2
Questions
  • Given measured appropriate variables
  • Can you adjust for confounding?
  • Yes
  • Can you adjust for selection bias?
  • Depends on the definition

3
Contents
  • Background
  • Define bias
  • Selection bias
  • as effect modification (old concept)
  • as collider stratification bias (new concept)
  • DAG structure
  • Examples
  • Size and direction of bias

4
Bias definition
  • Bias
  • Frequency expected risk ? true risk
  • Effect association ? causal effect

5
Selection bias concepts
  • Concept
  • DAG structure
  • Effect responders
  • ?
  • Effect non responders
  • Differential response bias
  • Differential loss to follow up
  • Healthy worker bias
  • Berksons bias (case control)
  • Effect
  • modification
  • Collider
  • stratification
  • bias

6
Selection bias as effect modification
7
Selection bias Risk
  • Selection of responders ?
  • The prevalence is different among
  • the responders compared to the full population
  • the responders compared to the non responders

R0
Non responders
Rp
Population
R1
Responders
Rp is the weighted mean of R0 and R1
8
Effect modification
  • Selection of responders ?
  • The effect of E on D is different among
  • the responders compared to the full population
  • the responders compared to the non responders

RR0
Non responders
RRp
Population
RR1
Responders
9
Problems
  • Is not a bias, RR0 and RR1 are the true effects
  • Is effect modification by selection variable S
  • Leads to the conclusion that
  • Biolocical effects are protected from bias
  • The bias can not be adjusted for
  • RRp is the average of RR0 and RR1

Not true for collider stratification bias
DAG structure
S
E
D
10
Selection bias as collider stratification bias
11
Example with paths
  • Study
  • Milk on bone density
  • Exclude Calcium supplements


  Path Type Status
1 ED Causal Open
2 ES?D Noncausal Open

2 ES?CD Noncausal Closed
Lessons learned Biological effect not
protected May adjust for selection bias
Structure Collider stratification
12
Examples
  • Differential response
  • Survey Alcohol and CHD
  • Differential loss to follow up
  • Randomized trial drug and disease
  • Healthy worker effect
  • Cross-section Melt hall dust and lung disease

Note no confounding
13
Selection bias structure
August 15
H.S.
13
14
Paths
  • 1. Causal

2. Confounding An open non-causal path without
colliders
3. Selection bias A non-causal path that is open
due to conditioning on a collider
BCVs?
15
Collider stratification bias
  • Selection bias Collider stratification bias
  • Selection bias, Path definition
  • A non causal path that is open due to
    conditioning on a collider

16
Selection bias examples
17
Folic acid and cardiac malformation
  • Selection Study only live born
  • Bias?

Yes, E?C?D is open
  • Selection Non grieving parents volonteer
  • Bias?

Yes, E?C?D is (partially) open
18
Education and unfaithfulness
  • Study the effect among couples in a relationship
    (not divorced)?


  Path Type Population Sample
1 ED Causal Open Open
2 ER?D Noncausal Closed Open
3 ER?SD Noncausal Closed Open
Selection bias
19
Size and Direction of bias
August 15
H.S.
19
20
Example 1, full table
(Adjusted) RRs
True and biased RRs
Proportion responding in 1,1 group
21
Example 2
Pattern Only D influence response
Result RR (and RD) biased, OR unbiased ODS,
Case-Control
22
Example 3
Pattern Both E and D influence response
Result Surprise responders are unbiased Theory
bias in at least one stratum
23
Example 4
Pattern Both E and D influence response
Result Surprise both strata biased upwards True
RR is not a weighted average
24
Example 5
Pattern Both E and D influence response
Result Same DAG, different results The DAG does
not fully determine the selection!
25
Summing up
  • Selection bias as effect modification
  • Is not a bias, should not be called selection
    bias
  • Has properties different from proper selection
    bias
  • Selection bias as collider stratification
  • Structure defined in DAG,
  • Distinct from confounding
  • Consistent with
  • Differential response bias
  • Differential loss to follow up
  • Healthy worker bias
  • Berksons bias (case control)

26
Litterature
  • Hernan and Robins, Causal Inference
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