Maria Glymour

Department of Epidemiology & Biostatistics

University of California, San Francisco

​

• 1

​

Introduction to Using Directed Acyclic Graphs in Dementia Research

Organization

1. Why bother learning to use DAGs?
2. Drawing and using DAGs
1. D-separation
1. Represent confounding
2. Represent selection/survival bias
3. Represent mediation
4. Represent effect modification

• 2

Why bother learning to use DAGs?

• DAGs are simple communication tools. They foster more precise language and reveal ambiguities in how we speak.
• What does this mean: “Reduction of leisure time activities is a risk factor for developing dementia”?
• DAGs represent special-case biases in pictures, so you can describe them even if you can’t remember the first names of the biases
• DAGs help guide analysis decisions. They are only guides because they merely represent the assumptions you choose to adopt.
• DAGs help you identify testable implications of your proposed causal structure or theoretical model.
• DAGs help you prioritize research questions based on the assumptions most pivotal (and questionable) in prior research, i.e., they are tools for triangulation.
• DAGs help you simulate data to understand your problems

• 3

Inferring Causation From Association

Statistical association between two variables X and Y may be due to:

1. Random fluctuation, chance
2. X caused Y
3. Y caused X
4. X and Y share a common cause
5. The statistical association was induced by conditioning on a common effect of X and Y (as in selection bias).

• 4

How we can use this

• Eliminating 4 of these explanations is usually the goal of an analysis.
• Knowing these 5 sources of statistical association helps identify the (set of) causal structure(s) that could have generated the observed statistical associations.
• DAGs are a tool to represent possible causal structures and evaluate whether a proposed causal structure could have generated the statistical associations observed, and therefore to rule out (or not) that structure

• 5

Organization

1. Counterfactual account of causation
2. The secret about correlation and causation
3. Drawing and using DAGs
1. D-separation
1. Represent confounding
2. Represent selection/survival bias
3. Represent mediation
4. Represent effect modification

​

• 6

Causal Directed Acyclic Graphs

• 7

X

Y

U

A

A

Y

U

X

Show your assumptions about the causal relationships among X, Y, and possible covariates in a causal diagram:

​

• If two variables shown in the graph have a common cause, you must show the cause in the graph.

​

• Do not allow causal “loops”.

Terminology

• Descendants
• The direct or indirect effects of a variable
• Paths
• A sequence of lines (edges) between two variables, regardless of direction of arrows
• Not retracing any line segments
• Colliders
• Common effect of two variables in a path: where the arrows ‘collide’.
• The two causes must both be “on the path”.
• Any variable on a path that is not a collider is a “non-collider”.
• Conditioning
• Examining the distribution of one variable within levels of another
• Regression adjustment, stratification, restriction

​

• 8

Colliders vs Non-Colliders

• 9

B

C

A

Colliders: common effects

Non-Colliders:

common causes (=confounders)

​

​

​

​

​

Or mediators

B

C

A

B

C

A

D-separation

• The assumptions shown in a causal diagram imply that a variable X will be independent of a variable Y, after conditioning on a set of variables {Z} if every path between X and Y is blocked by {Z}.

​

• The set of covariates {Z} blocks a path if and only if either:
1. The path contains a non-collider that is in {Z} , or
2. The path contains a collider which is not in {Z} , and no descendant of the collider is in {Z} .

​

• If there is an unblocked path linking X and Y, then X and Y will typically be statistically dependent

​

Places where the above doesn’t hold: (1) if there are perfectly offsetting balance between two paths or (2) the variables violate the consistency assumption, e.g., when we think a variable has a specific value (e.g.,”amyloid positive” or “high BMI”) there are actually different versions of that variable, and those different versions have different causes and effects (eg based on measuring amyloid fibrils vs plaques or central vs peripheral adiposity).

​

• 10

D-separation

• The assumptions shown in a causal diagram imply that a variable X will be independent of a variable Y, after conditioning on a set of variables {Z} if every path between X and Y is blocked by {Z}.

​

• The set of covariates {Z} blocks a path if and only if either:
1. The path contains a non-collider that is in {Z} , or
2. The path contains a collider which is not in {Z} , and no descendant of the collider is in {Z} .

​

• If there is an unblocked path linking X and Y, then X and Y will typically be statistically dependent

​

Places where the above doesn’t hold: (1) if there are perfectly offsetting balance between two paths or (2) the variables violate the consistency assumption, e.g., when we think a variable has a specific value (e.g.,”amyloid positive” or “high BMI”) there are actually different versions of that variable, and those different versions have different causes and effects (eg based on measuring amyloid fibrils vs plaques or central vs peripheral adiposity).

​

• 11

In small print because you shouldn’t worry about it now. But I hope you/we come back to this someday.

D-separation: intuition

• There may be many reasons that two variables are associated (some confounding, some mediated causation etc).
• Adjusting for a confounder of the two variables blocks that source of association between two variables
• Adjusting for a mediator between the two variables blocks that source of association between two variables
• Adjusting for a common effect of the two variables creates an association between the two variables

​

• 12

Example Causal Diagrams

• 13

3 Approaches to Demonstrating Causation

• Block all back door paths (condition on CPCs)

​

​

• Measure all front door paths (add up pathways)

​

​

• Use an instrumental variable

​

• 14

Identifying causal effects: the Back Door Criterion

• 15

DAGs Help With Research Design

• You are interested in estimating the effect of X on Y.
• Imagine the ways the world might work.
• If the world worked like this or like that, would your analysis plan successfully identify the effect of X on Y?
• What assumptions do you have to make to interpret your statistical association as a causal effect?
• Most often: what should I control for?
• Control for a set of variables sufficient to fulfill the back door criterion.
• Do not control for mediators or other variables that are potentially consequences of the independent variable (this would include variables that are consequences of the dependent variable)
• If you are interested in prediction, not causation, choosing controls is less difficult
• But if you are doing public health work, think hard about why a prediction question is of interest

• 16

Organization

1. Counterfactual account of causation
2. The secret about correlation and causation
3. Drawing and using DAGs
1. D-separation
1. Represent confounding
2. Instrumental variables/Randomized controlled trials
3. Represent selection/survival bias
4. Represent mediation
5. Represent effect modification

• 17

Confounding

• 18

Education

Dementia

Depression

• Education“confounds” the association between Depression and dementia.
• Conditioning on education would be sufficient to identify the effect of depression on dementia

Confounding

• 19

Education

Income

Depression

• Education“confounds” the association between Depression and Dementia.
• Conditioning on either education or income would be sufficient to identify the effect of depression on Dementia

Dementia

Unreliable Measures

• 20

Depression

Dementia

CESD₁

ε₁

Unreliable measures of a confounder

• 21

Education

Income

Depression

• Controlling for “high school completion” does not fully account for the confounding of the depression-dementia association by education

Dementia

High-school completion

Causal Structure for an RCT, a quasi-experiment, an instrumental variable

• 22

Education

Dementia

Random Assignment/Instrument

Exposure

• Random assignment has no arrows into it: there are no “causes” of randomization
• Random assignment influences exposure, and the only way random assignment influences the outcome of interest is via exposure.

Randomized Trial: Randomly Assign Therapy to Reduce Depression

• 23

Education

Depression

Dementia

Random Assignment

Anti-Dep Drug

• Random assignment has no arrows into it: there are no “causes” of randomization
• Random assignment influences Depression, but so does the confounder education.

Randomized Trial: Randomly Assign Therapy to Reduce Depression

• 24

Education

Depression

Dementia

Random Assignment

Anti-Dep Drug

• This is why the analysis must be based on comparing mortality across values of random assignment (ITT) not across values of depression.
• Random assignment to anti-depressants will be related to dementia only if depression influences dementia.

Things that go wrong with trials

• 25

Education

Depression

• If there is another pathway linking random assignment to the outcome, then you cannot interpret the ITT analysis as testing whether depression affects Dementia.

Dementia

Random Assignment

Anti-Dep Drug

Loss to Follow-Up in Trials

• 26

Participation in outcome assessment

Dementia Incidence

Randomization to intervention

Depression

• Imagine a study in which we randomize participants to an intervention to increase physical activity to reduce dementia incidence.

Physical

activity

Loss to Follow-Up in Trials

• 27

Participation in outcome assessment

Dementia Incidence

Randomization to intervention

Cognition Declined

• Sometimes the determinant of participation may be very closely tied to the outcome.

Physical

activity

Selection/Survival Bias as a Threat to Internal Validity in Observational Studies

• 28

Survival to age 65

Dementia

Education

Some gene

• Imagine studying education and dementia in a cohort of people age 65+
• Education, completed ~age 25, affects survival to age 65.

Selection Bias

• 29

Survival to age 65

Dementia

Education

Some gene

Here, we assume education has no effect on dementia.

Would it be statistically associated with dementia among people in your cohort of 65+ year olds?

Selection Bias Compromises Internal Validity

• 30

Heart Failure

Mortality

Obesity (pre-HF)

Some gene

• This is relevant in any study of patient samples (ie, almost any clinical epidemiology)
• Does obesity affect mortality of heart failure patients?

Obesity (post-HF)

Representing Direct Effects and Challenges in Estimating Direct Effects

• 31

M

Y

X

U

- Conventional approaches to estimating direct effects condition/adjust for the mediator (M), but if there is a confounder of the M-Y association, then X and Y would be associated conditional on M even if there was no indirect effect.

M

Y

X

U

Why would you condition on a collider?

Some “colliders” are not optional:

• Survival
• Diagnosis with a disease
• Selection into a study
• Providing complete data

​

• Two options:
• Identify a set of covariates that blocks the bias from conditioning on the collider (may need to use weighting rather than regression control)
• Use a bias analysis to quantify and correct

​

• 32

Some objections to DAGs

• DAGs do not display effect modification in the way we think about it
• If Z modifies the effect of X on Y, then Z must itself affect Y.
• Effect modification is scale dependent, so showing an effect modifier implies a scale and DAGs do not represent any scale
• Some progress on this: e.g., VanderWeele’s sufficient cause framework
• DAGs do not represent the magnitude of bias
• Major limitation
• Lots of work now on (a) signing the bias, and (b) estimating the magnitude
• Simulations and bias bounding formulas

• 33

Some objections to DAGs

• DAGs do not match the complex, dynamic feedback loops in the real world
• DAGs can represent feedback between two variables
• DAGs can represent complex interventions (e.g., deliver this set of 4 treatments vs only 2 of these)
• DAGs match (one of the) things you want to know: will intervening in a specific way elicit a change in health?
• To say “it’s all very complicated and impossible to specify which variables come first” is to abdicate any hope of guiding clinical or policy decisions.
• DAGs do not tell you everything, and complex systems simulations are often useful as a next step to predict spillovers and interactions with variables you do not have in your DAG. The simulation will presumably rely on causal parameter inputs. So start with the DAG.

• 34

Some objections to DAGs

• I’m not sure about which causal structure is right
• Do you know enough to rule some DAGs out?
• What are the commonalities across all plausible DAGs?
• Useful to state: under these assumptions, we can draw these inferences; need evidence on the assumptions from other sources
• I don’t know anything about the causal structure
• This is not an objection to DAGs, this is an objection to ever drawing causal inferences

• 35

Quizlet

• 36

1. Draw a DAG corresponding with a randomized controlled trial for the effect of Vitamin C (vs placebo) supplementation on Alzheimer’s disease (AD). Please draw the DAG to represent the null hypothesis that vitamin C has no effect on AD.
2. If your DAG does not include confounding of the association between Vitamin C use and AD, please add that now.
3. Modify the DAG to allow for the possibility of loss to follow-up
4. Modify the DAG to allow for the possibility that the study becomes unblinded, and knowledge of their randomization status influences participants’ cognitive test performance.
5. It turns out that in this trial, recruitment was conducted in a memory disorders clinic. Please modify the DAG to reflect this.
6. Further, treatment group was assigned based not on a random number, but rather on a systematic basis, so anyone who attended the memory clinic in the evening hours was assigned to the placebo, whereas anyone who attended the memory clinic during working hours was assigned to the Vitamin C group. Modify your DAG to reflect this situation.
7. If you conduct an intent to treat analysis in your original DAG (2), how many paths connect random assignment and AD?
8. If you conduct an intent-to-treat analysis in your DAG 6, how many paths connect random assignment and AD?
9. Bonus question: Can you predict the sign of the association between random assignment and AD under DAG 6?

end

• 37

Can you quantify the bias from collider stratification?

• Must make assumptions about the magnitude and direction of each causal association
• This is not specified in the DAG, the DAG only tells you conditional dependence/independence.
• Often the bias is small, but not always.
• Often the bias is negative.

• 38

Unreliable Measures

• 39

Depression

Mortality

CESD₁

ε₁

Unemployment

Unreliable Measures in Analyses of Change

• 40

X

C₁

Change in C₁

Y₁

ε₁

Y₂- Y₁

DAGs for missing data

• 41

Final quizlet: Estrogen Therapy and Bone Mineral Density in African-American and Caucasian Women

• Eskridge et al Am J Epi, 2010

Controlling for body size and composition, the authors examined the association between estrogen therapy and bone mineral density in older African-American and Caucasian women. In 1992–1998, 443 African-American and 989 Caucasian women aged 45–87 years were assessed for medication use, laboratory variables, behavioral characteristics, and bone mineral density. The mean age was 61.3 (95% confidence interval: 60.3, 62.3) years in African Americans and 71.0 (95% confidence interval: 70.4, 71.7) years in Caucasians (P < 0.001). All measures of body size and composition were significantly greater in the African-American women compared with Caucasian women (P < 0.001). As expected, African Americans had significantly higher bone mineral density at all 4 sites independent of age, weight, body composition, estrogen use, and lifestyle factors. Although Caucasians were significantly more likely to currently use estrogen (48.9% vs. 33.9%; P < 0.001), African Americans not using estrogen had significantly higher bone mineral density at all sites except the spine than Caucasians who were using estrogen. Regression models including age and lean mass explained the most variation in bone mineral density (R2 range = 0.13–0.37). Results suggest that higher levels of bone mineral density in African-American women were not due to estrogen use.

​

• 42

Getting Rich on Collider Bias

• The “Monty Hall Problem” / Let’s make a deal
• You can choose among 3 doors:
• Behind one is a fabulous prize
• Behind the other two is nothing (or perhaps, something crummy).
• You make a preliminary choice, and Monty Hall will open one of the other doors, always choosing one with nothing behind it.
• You may now revise your choice: do you keep the door you first chose or should you switch?
• Marilyn vos Savant had a famous fight about the Monty Hall problem… but the effect is so large that you can figure it out empirically in about 10 minutes.

​

• 43

Getting Rich on Collider Bias

• 44

Door with the Prize

Door You Choose First

Door Monty Hall Opens

Organization

1. Counterfactual account of causation
2. Drawing and using DAGs
3. DAGs for common biases
4. Contrasting IV-based methods and covariate adjustment/propensity scores

​

• 45

Demonstrating Causation

• Block all back door paths (condition on CPCs)

​

​

• Measure all front door paths (add up pathways)

​

​

• Use an instrumental variable

​

• 46

• Randomization can be thought of as a special case of an instrumental variable:

​

Random assignment🡪X🡪Y

​

• We wish to test whether exposure X affects disease Y
• We randomly assign people to receive treatment or exposure X
• We compare the outcome Y across levels of randomization (ITT), rather than across levels of exposure or take-up
• With imperfect compliance, we assume ITT is an underestimate of the causal effect of X on Y

​

​

• 47

• 47

Intuition for IV for health researchers: RCT

Intuition for IV

• The ITT is a valid test for the null hypothesis of no average causal effect of X on Y if:
• There is at least some take-up (randomization affects exposure)
• Randomization is fair (no common cause of randomization and the outcome)
• Randomization influences the outcome only via the treatment X (not via related treatment X’ or via compensatory pathways in the controls)

​

• These criteria for a valid RCT correspond exactly with the criteria for a valid IV/MR analysis

​

​

• 48

Instrument Assumptions

Randomization is an instrument for the influence of X on Y if:

• Randomization predicts X
• Randomization has no effect on Y unless the effect is mediated by X (implies that X does not affect Randomization)
• No other variables influence both Randomization and Y

• 49

• Predictor of Interest (X)

• Outcome of Interest (Y)

• Omitted Variable/
• Confounder

• Randomization

• Effect of Policy changes (fuzzy regression discontinuity)
• Distance to care provider
• Physician preference=what the physician prescribed to the previous patient with same indication
• Regional preferences: treatment differences between regions
• Timing of events: day of week of need for care
• Randomized encouragement studies
• Co-payment differences
• Secular trends or sudden changes in patterns (best with a comparison group or place)

• 50

Examples of Instrumental Variables

• Estimate the effect of additional education on dementia risk
• Estimate the effect of an extra day in the hospital on newborn readmission rates
• Estimate the effect of waiting longer for an organ transplant
• Estimate effect of receipt of care at a tertiary care hospital on AMI outcomes

• 51

Examples of Instrumental Variables

Caveats to IV

• Interpretation as LATE vs ETT vs PATE relies on additional assumptions
• Non-linear models behave in unexpected ways: area of active development
• Some common subtle errors: e.g., conditioning on endogenous variable (see Swanson et al Am J Epi 2015)
• “Weak” IV estimates biased towards OLS
• More sensitive to violation of structural assumptions than conventional methods

​

​

​

​

​

​

​

• 52

IV versus Covariate Adjustment Approaches

IV

• No direct effects from instrument to outcome
• No common causes of instrument and outcome
• Provides intent to treat estimate unless adjusted for “first stage”: typically this is what IV analyses do
• Can test the null even if there are unmeasured exposure-outcome confounders
• Estimating effect size requires more assumptions

COVARIATE ADJUSTMENT

• No common causes of exposure and outcome
• Must measure and correctly model all causes
• Doubly robust methods allow you two chances to get it right
• Propensity score models allow you to combine information on multiple confounders
• All require the assumption of blocking all back door paths

• 53

IV versus Covariate Adjustment Approaches

IV

• No direct effects from instrument to outcome
• No common causes of instrument and outcome
• Provides intent to treat estimate unless adjusted for “first stage”: typically this is what IV analyses do
• Can test the null even if there are unmeasured exposure-outcome confounders
• Estimating effect size requires more assumptions

COVARIATE ADJUSTMENT

• No common causes of exposure and outcome
• Must measure and correctly model all causes
• Doubly robust methods allow you two chances to get it right
• Propensity score models allow you to combine information on multiple confounders
• All require the assumption of blocking all back door paths

• 54

In different settings, one or the other set of assumptions may be more plausible. Often evidence is most convincing if combined across designs, because assumptions required are so different.

Limitations and controversies

• 55

Pitfalls due to consistency violations: it may be a big deal in dementia research

• We adopt a “consistency” assumption that potential outcome equals actual outcome among people with the specific exposure:
• Y_x=1= Y| X=1 (the potential outcome of Y setting X to 1 equals the actual value of Y among people for whom X=1)
• How could this possibly NOT be true? It seems like a tautology.
• Consider if X is “total brain amyloid burden”.
• But there are different types of amyloid in the brain

​

​

​

​

​

​

• 56

• Y_{aβ_monomer=high} ≠ Y_{aβ_fibril=high}
• And because:
• Y_{aβ_monomer=high} ≠ Y| Y_{aβ_fibril=high}
• We may see an apparent consistency violation:
• Y_aβ=high ≠ Y| Y_aβ=high
• Take home: worry if there are flavors of the thing we’re measuring and different flavors may have different effects on Y

​

​

​

Counterfactuals do not always satisfy intuitions about “causation”

• Can non-modifiable characteristics (sex, race) be causes?
• What’s the counterfactual for race and sex? Can you imagine the same individual but of a different race or sex?
• More challenging for race than sex, because race generally identified based on race of parents, so moment of intervention to change someone’s race is unclear.
• Some say “race is not a cause, racism is”. This is a red herring. Saying that race is a cause makes no claims about the mechanism one way or the other, may well be fully mediated by racism.
• Issue remains controversial. Most people’s research seems to treat these as causal but VanderWeele and Robinson offer some language to help you work around the intellectual incoherence if you are one of the people who studies race but doesn’t want ot discuss it as a cause.
• Hernan sometimes seems to take this a bit farther and argue that only “actions” not “states” can be causes.
• Generally useful to ask: what RCT would deliver the parameter I am interested in?

• 57

Counterfactuals do not always satisfy intuitions about “causation”

• What are the causes of over-determined outcomes?
• MaryAnne and Wanda are traveling through the desert with Earl. They both hate him. One night, MaryAnne poisons Earl’s water canteen and sneaks away. Wanda, not realizing MaryAnne has poisoned the water, pokes a hole in Earl’s canteen so all the water leaks out, and she sneaks away. In the morning, Earl wakes up alone, with no water. He dies of dehydration in the desert shortly thereafter. Who killed Earl?
• Rex the gang leader orders his subordinate Joe to shoot rival gang member, Ace. Rex and Joe shoot Ace at the same time. Either shot would have been sufficient to kill Ace. Is Joe responsible for Ace’s death?
• Important for judicial decisions attributing responsibility.
• Also important for thinking about public health implications of proposed interventions. Intervening on something mechanistically related to an outcome may not improve the outcome if it is over-determined.

• 58

Counterfactuals do not always satisfy intuitions about “causation”

• Survival bias: what if some values of X render Y undefined?
• If Earl smokes, he will die at age 70 of CVD; if Earl doe not smoke, he will develop dementia at age 71
• What is the effect of smoking on Earl’s dementia?

• 59

Often unclear how to draw the DAG: Difference in difference

• 60

Year * Group

Outcome

Eligible Group

Year of Policy Change

E(Y)=b₀+b₁*Group+b₂*Year+b₃*Group*Year

Year * Group

Outcome

Eligible Group

Year of Policy Change

M

U₁

U₂

Conditional on group and year of change, there are no confounders of the association between the interaction and the outcome.

Often unclear how to draw the DAG: Change scores vs change

• 61

X

C₁

Change in C₁

Y₁

ε₁

Y₂- Y₁

X

Change in Y

Y₁

U

Y₂

If you draw the DAG as on the left, adjusting for Y1 induces collider bias and a spurious association between X and change score.

If you draw the DAG as on the right, adjusting for Y1 is necessary to block the direct effect of Y1 on Y2.

I chose the DAG on the left because I consider change in C a biological phenomenon, indirectly measured with test scores. Changing the test scores would not change your brain, but changing your brain would change your test scores.

Causal discovery

• We always infer causal structures from statistical associations, but we typically start with a very narrow range of causal structures under consideration: X🡪Y or X Y
• With the d-separation rule, you can see that we can often rule in or out a much larger set of causal structures.
• Simple algorithm (SGS in TETRAD- many other/better available):
• Start with a complete undirected graph on all variables, with edges between all variables.
• For each pair of variables X and Y, and each set of other variables S, see if X is independent of Y given S; if so, remove the edge between X and Y.
• Find colliders by checking for conditional dependence (X🡪S🡨Y implies X and Y are marginally independent but conditional on S become dependent); orient the edges of colliders.
• Try to orient undirected edges by consistency with already-oriented edges; do this recursively until no more edges can be oriented.
• Controversial!

• 62

Conclusions

• Since the early 1980s, there has been a revolution in how we think about the link between statistical evidence and causal inferences
• This revolution has affected many disciplines and elicited many debates
• The tool set is in many ways different from typical statistical analysis, promoting clear articulation of questions and clear thinking about sources of bias
• These tools foster efficient communication, better reasoning about study design and analysis, and improved interpretation

​

​

• 63

Summary

In recent decades, there has been an outpouring of methods explicitly focusing on supporting causal inferences from observational (non-randomized) data. Much of this work is based on a counterfactual framework for causation and relies on Directed Acyclic Graphs (DAGs) as a core tool to represent causal hypotheses. In this talk, I will introduce the counterfactual account of causation, illustrate the distinction between counterfactual definitions of causal parameters and statistical comparisons used to estimate those parameters. I will introduce DAGs and the d-separation rule allowing us to link causal structures represented in DAGs to statistical associations. Many common biases encountered in epidemiologic studies are fruitfully represented in DAGs, and we will review a few examples. Finally, time permitting, we will introduce the use of instrumental variables, linking to a causal framework. Illustrative examples will be drawn from my research on dementia and stroke.

​

64

64

Conditioning on a Collider

If two variables are statistically independent, but have a common effect, then, within levels of this effect, they will be statistically dependent.

​

​

Really.

​

Usually.

​

65

65

A collider anecdote

Some tall people are fast, and some are slow.

Some short people are fast, and some are slow.

Knowing that somebody in the general population is short does not give you information about whether they are fast or slow.

​

NBA ball players must be either very tall, or very fast.

​

If you know an NBA ball player is short… what do you know about his speed?

66

66

A collider anecdote

Some tall people are fast, and some are slow.

Some short people are fast, and some are slow.

Knowing that somebody in the general population is short does not give you information about whether they are fast or slow.

​

NBA ball players must be either very tall, or very fast.

​

If you know an NBA ball player is short… what do you know about his speed?

67

NBA player

Speed

Height

67

A collider anecdote

I throw a party, and I only invite people who are either very rich or very funny.

​

You come to my party (you are very funny) and get stuck talking to the most boring person you have ever met.

​

Is he rich?

68

68

A collider anecdote

I throw a party, and I only invite people who are either very rich or very funny.

​

You come to my party (you are very funny) and get stuck talking to the most boring person you have ever met.

​

Is he rich?

69

Party invitation

Funniness

Wealth

69

A Collider Simulation: Please try this at home.

Make up some rules following the structure of the DAG, such that X and Y are independent causes of Z, then assess association between X and Y after conditioning on Z:

• X~N(0,1)
• Y~N(0,1)
• e~N(0,1)
• Z=X+Y+e
• n=100

​

70

70

X and Y are independent; X and Z are positively associated

71

Scatter X , Y

Scatter X , Z

Independent

Positively Associated

71

X is inversely associated with Y, conditional on Z

72

Scatter X , residual (Y|Z)

Inversely Associated

72

Quizlet

73

X₄

X₂

X₃

X₁

X₅

X₄

X₂

X₃

X₁

X₅

If you know that one of these three causal structures generated the data, and you have perfect measures of all 5 variables, can you tell which one is correct?

X₁

X₄

X₂

X₃

X₁

X₅

U

73

Quizlet

74

X₄

X₂

X₃

X₁

X₅

X₄

X₂

X₃

X₁

X₅

X₁, X₂, and X₃ predict X₅, but are independent of X₅ conditional on X₄.

X₄

X₂

X₃

X₁

X₅

U

X₁, X₂, and X₃ are independent of X₅, unless you condition on X_4, when they become associated with X₅

X₁ and X₃ are independent of X₅, unless you condition on X₂ or X_4, when they become associated with X₅

74

Organization

1. Drawing and using DAGs
2. DAGs for common biases
3. Contrasting IV-based methods and covariate adjustment/propensity scores
4. Limitations and controversies of counterfactuals and DAGs

​

​

75

75