Causal Diagrams for Epidemiological Research

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Causal Diagrams for Epidemiological Research
Eyal Shahar, MD, MPH Professor Division of
Epidemiology Biostatistics Mel and Enid
Zuckerman College of Public Health The University
of Arizona
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What is it and why does it matter?

• A tool (method) that
• clarifies our wordy or vague causal thoughts
  about the research topic
• helps us to decide which covariates should enter
  the statistical modeland which should not
• unifies our understanding of confounding bias,
  selection bias, and information bias

3
What is the key question in a non-randomized
study?

• When estimating the effect of E (exposure) on
  D (disease), what should we adjust for?
• or
• Confounder selection strategy

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Adjusting for ConfoundersCommon Practice

• The change-in-estimate method
• List potential confounders
• Adjust for (condition on) potential confounders
• Compare adjusted estimate to crude estimate
• (or fully adjusted to partially adjusted)
• Decide whether potential confounders were real
  confounders
• Decide how much confounding existed
• Premise The data informs us about confounding.

Are we asking too much from the data?
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Adjusting for ConfoundersCommon Practice

• What is a potential confounder?
• Typically, a cause of the disease that is
  associated with
• the exposure

Confounder
E
D

• What is the effect of a confounder?
• Contributes to the crude (observed, marginal)
  association
• between E and D

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Adjusting for ConfoundersCommon Practice

• Extension to multiple confounders

C1
C3
C2
E
E
D
E
D
D
C4
C6
C5
E
E
D
E
D
D
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Adjusting for ConfoundersCommon PracticeProblems

• A sequence of isolated, independent, causal
  diagrams
• but C1, C2, C3, C4, C5,.. might be connected
  causally
• Unidirectional arrow a causal direction
• but what is the meaning of the bidirectional
  arrow?
• Even with a single confounder, the
  change-in-estimate method could fail

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Adjusting for ConfoundersProblems

• An example where the change-in-estimate method
  fails

U1
U2
C
E
D

• The crude estimate may be closer to the truth
  than the C-adjusted estimate
• To be explained

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AlternativeA Causal Diagram

• A method for selecting covariates
• Extension of the confounder triangle
• Premises displayed in the diagram
• New terms
• Path
• Collider on a path
• Confounding path

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Selected references

• Pearl J. Causality models, reasoning, and
  inference. 2000. Cambridge University Press
• Greenland S et al. Causal diagrams for
  epidemiologic research. Epidemiology
  19991037-48
• Robins JM. Data, design, and background knowledge
  in etiologic inference. Epidemiology
  200111313-320
• Hernan MA et al. A structural approach to
  selection bias. Epidemiology 200415615-625
• Shahar E. Causal diagrams for encoding and
  evaluation of information bias. J Eval Clin Pract
  (forthcoming)

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A Causal Diagram Notation and Terms

• An arrowcausal direction between two variables

E
D

• An arrow could abbreviate both direct and
  indirect effects

U1
E
E
D
D
could summarize
U2
U3
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A Causal Diagram Notation and Terms

• A path between E and D any sequence of causal
  arrows that connects E to D

E
D
E
U1
U2
D
E
U1
U2
D
E
U1
U2
D
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A Causal Diagram Notation and Terms

• Circularity (self-causation) does not exist
  Directed Acyclic Graph

E
U1
D
U2

• A collider on the path between E and D

E
U1
U2
D

• E and U2 collide at U1

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A Causal Diagram Notation and Terms

• A confounding path for the effect of E on D Any
  path between E and D that meets the following
  criteria
• The arrow next to E points to E
• There are no colliders on the path

C
U1
V1
U2
V2
U3
E
D
In short a path showing a common cause of E and D
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• The paths below are NOT confounding paths for the
  effect of E on D

C
U1
V1
U2
C
V2
U3
U1
V1
E
D
U2
C
V2
U3
U1
V1
E
D
U2
V2
U3
E
D
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What can affect the association between E and
D?(Why do we observe an association between two
variables?)

• Causal path E causes D
• Causal path D causes E
• Confounding paths
• Adjustment for colliders on a path from E to D

E
D
D
E
C
E
D
Later
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Why does a confounding path affect the crude
(marginal) association between E and D?

• Intuitively
• Association being able to guess the value of
  one variable (D) from the value of another (E)
• E?D allows us to guess D from E (and E from D)
• A confounding path allows for sequential guesses
  along the path

C
U1
V1
U2
V2
U3
E
D
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How can we block a confounding path between E
and D?

• Condition on a variable on the path (on any
  variable)
• Methods for conditioning
• Restriction
• Stratification
• Regression

C
U1
V1
U2
V2
U3
E
D
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A point to remember

• We dont need to adjust for confounders (the top
  of the triangle.) Adjustment for any U or V
  below will do.
• U and V are surrogates for the confounder C

C
U1
V1
U2
V2
U3
E
D
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Example

• If the diagram below corresponds to reality, then
  we have several options for conditioning
• For example
• On C and U2
• Only on U2
• Only on U3

C
U1
V1
U2
V2
U3
E
D
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What can affect the association between E and D?

• Causal path E causes D
• Causal path D causes E
• Confounding paths
• Adjustment for colliders on a path from E to D

E
D
D
E
C
E
D
NOW!
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Conditioning on a ColliderA Trap

• A collider may be viewed as the opposite of a
  confounder
• Collider and confounder are symmetrical entities,
  like matter and anti-matter

C
U1
V1
U2
V2
U3
E
D
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Conditioning on a ColliderA Trap

• A path from E to D that contains a collider is
  NOT a confounding path. There is no transfer of
  guesses across a collider.
• A path from E to D that contains a collider does
  NOT generate an association between E and D
• Conditioning on the collider, however, will turn
  that path into a confounding path.

Why?
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Conditioning on a ColliderA Trap
C
V1
U1
U2
V2
U3
E
D
The horizontal line indicates an association (the
possibility of guesses) that was induced by
conditioning on a collider
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Properties of a ColliderIntuitive Explanation

• A dataset contains three variables for N cars
• Brake condition (good/bad)
• Street condition in the owners town (good/bad)
• Involved in an accident in the owners town?
  (yes/no)

Brake condition (good, bad)
Accident (yes, no)
Street condition (good, bad)

• Accident is a collider.
• Brake condition and street condition are not
  associated in the dataset. We cannot use the
  data to guess one from the other.

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Properties of a ColliderIntuitive Explanation

• Why cant we make a guess from the data?
• Lets try. Suppose we are told
• Car A has good brakes and car B has bad brakes.
• This information tells us nothing about the
  street condition in each owners town.

• Intuition a common effect (collider) does not
  induce an association between its causes
  (colliding variables)

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Properties of a ColliderIntuitive Explanation

• If, however, we condition (stratify) on the
  collider accident, we can make some guesses
  about the street condition from the brake
  condition.

Stratum 1 Accident yes
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Properties of a ColliderIntuitive Explanation

• Similarly, in the other stratum

Stratum 2 Accident no
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Properties of a Collider

• In summary
• Conditioning on a collider creates an association
  between the colliding variables and, therefore,
  may open a confounding path

Before conditioning on C
After conditioning on C
U1
U1
U2
U2
C
C
E
E
D
D
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Derivations

• The change-in-estimate method could fail if we
  condition on colliders, and thereby open
  confounding paths
• To (rationally) select covariates for adjustment,
  we must commit to a causal diagram (premises)
• (But we often say that we dont know and cant
  commit, and hope that the change-in-estimate
  method will work.)

• Causal inference, like all scientific inference,
  is conditional on premises (which may be
  false)not on ignorance

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Derivations

• Do not condition on colliders, if possible
• If you condition on a collider,
• Connect the colliding variables by a line
• Check if you opened a new confounding path
• Condition on another variable to block that new
  path

Conditioning on C alone
Conditioning on C and (U1 or U2)
U1
U1
U2
U2
C
C
E
E
D
D
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Practical advice

• Study one exposure at a time
• A model that may be good for exposure A might not
  be good for exposure B (even if B is in the
  model)
• Never adjust for an effect of the exposure
• Never adjust for an effect of the disease
• Never select covariates by stepwise regression
• Never look at p-values to decide on confounding
• (actually, never look at p-values)

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Extension to other problems of causal inquiry

• Causation always remains uncertain, even if we
  deal with a single confounder

Unbeknown to us the reality happens to be
We draw
U1
U2
C
C
E
E
D
D
And naively condition on C
And our adjustment may fail
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Extension to other problems of causal inquiry

• Estimating the direct effect by conditioning on
  an intermediary variable, I

I
D
E

• We should remember that variable I may be a
  collider

I
E
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Extension to other problems of causal inquiry

• Causal diagrams explain the mechanism of
  selection bias
• Example
• What happens if we estimate the effect of
  marital status on dementia in a sample of nursing
  home residents?
• Assume no effect
• both variables affect place of residence
  (home, or nursing home)

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Extension to other problems of causal inquiry
Marital status
Dementia
Place of residence (home, nursing home)

• By studying a sample of nursing home residents,
  we are conditioning on a collider (on a sampling
  collider) and might create an association
  between marital status and dementia in that
  stratum

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Extension to other problems of causal inquiry
Marital status
Dementia
Place of residence (home, nursing home)
Stratification
Nursing home
Home
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Extensions control selection bias(Source
Hernan et al, Epidemiology 2004)
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Extensions control selection bias(Source
Hernan et al, Epidemiology 2004)
Estrogen
MI
E
D
F
S (0,1)
S1 (our case-control sample)
S0 (remainder of the source cohort)
HRT
MI
E
D
Association of E and D was created
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Extensions information bias(LAST EXAMPLE)
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Summary Points

• The change-in-estimate method could fail if we
  condition on colliders, and thereby open
  confounding paths
• The theory of causal diagrams extends the idea of
  a confounder to the multi-confounder case
• Unification of confounding bias, selection bias,
  and information bias under a single theoretical
  framework

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• Back-door algorithm
• Sufficient set for adjustment
• Minimally sufficient set
• Differential losses to follow-up
• Time-dependent confounders
• Interpretation of hazard ratios
• Conditioning on a common effect always induced an
  association between its causes, but this
  association could be restricted to some levels of
  the common effect

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Age (young, old)
Sex
Smoking drive (low, high)
Physical activity (low, high)
Asthma (yes, no)
?
Smoking status
FEV1
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Age (young, old)
Sex
Smoking drive (low, high)
Physical activity (low, high)
Asthma (yes, no)
?
Smoking status
FEV1
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Age (young, old)
Sex
Smoking drive (low, high)
Physical activity (low, high)
Asthma (yes, no)
?
Smoking status
FEV1
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Pneumonia
Ulcer
Hospitalization Status hospitalized
not hospitalized
Abdominal Pain
?
Coughing
Stratification
hospitalized patients
other patients
Ulcer
Pneumonia
?
Abdominal Pain
Coughing
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Example Do men have higher systolic blood
pressure than women? (In other words estimate
the gender effect on systolic blood
pressure) The following table summarizes the
answer to this question from two regression models
  So, which is the true estimate and which is
biased?
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WHR
Gender
SBP
BMI
Z1
Z2
. .
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U
WHR
Gender
SBP
BMI
Z1
Z2
. .
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U
WHR
Gender
SBP
BMI
Z1
Z2
. .