Confounding and Directed Acyclic Graphs

Introduction

LEARNING OBJECTIVES
The student will be able to:

1. Define confounding.
2. Discuss the implications of confounding for epidemiological
research.
3. Describe the nature and uses of a directed acyclic graph.
4. Create a directed acyclic graph based on a real research
question, and use it to identify potential confounders.
5. Compare and contrast different methods to deal with
confounding.

Introduction

MOTIVATION

Confounding is the most
important topic in
epidemiology.

What do we mean when we say
one thing causes another?

Why are causes so important in
epidemiology?

What is the gold standard study
design for testing causal
hypotheses?

When is it not possible to use a
RCT?

Statistical Association
When variables vary similarly.
Correlated; Covary; Dependent

Draw Inferences
Statistical inferences
Causal inferences

“Correlation does not
imply causation.”

Confounding is...
“...the problem of confusing or mixing
of exposure effects with other
"extraneous" effects...”

Greenland S, Robins JM. Identifiability, exchangeability, and epidemiological confounding revisited.
Epidemiol Perspect Innov. 2009; 6: 4. doi: 10.1186/1742-5573-6-4

Early definitions were based on notions
of...
Comparability
or
Collapsibility

Comparability
Inherent difference in risk between
exposed and unexposed groups.

Greenland S, Robins JM. Identifiability, exchangeability, and epidemiological confounding. Int J
Epidemiol. 1986;15:413–419. doi: 10.1093/ije/15.3.413.

Collapsibility
Apparent differences between the crude
estimate of a statistical association and
strata-specific estimates.


Problems with collapsibility:
1.

Parameter estimates can change upon controlling for mediators,
by controlling for variables that introduce new biases, or because
of measurement error.

2.

There are situations where controlling for a “true” confounder
leads to no change in the estimate.

Greenland S, Robins JM. Identifiability, exchangeability, and epidemiological confounding revisited.
Epidemiol Perspect Innov. 2009; 6: 4. doi: 10.1186/1742-5573-6-4

Imagine that individuals can be classified
based on their inherent risk of the
outcome, prior to any exposure.
These classifications incorporate the
entirety of causal mechanisms
operating, known or unknown.

Rothman K. Causes. AJE. (1995) 141 (2):90-95.

Is exposure a cause of
disease?

Is there an assumption we can make
that allows us to infer that the
exposure causes the disease?

Counterfactuals, or Potential Outcomes

Yix = 1

Yix = 0

Exchangeability

The strong assumption that they are of
the same type.

Comparability assumption (or partial exchangeability):
The proportion who would fall ill in the absence of exposure is the same in both
groups.
(p1 + p3) = (q1 +q3)
Alternately, the baseline risk (prior to any possibility of exposure) is the same
in both groups.

Thus an observed difference in risk between exposure and unexposed is due to
the relative proportion of types 2 and 3 in the exposed.

If IPD > 0

Then P2 >P3

If IPD < 0

Then P3 > P2

If IPD = o

Then P3 = P2

We can, if we wish, further assume that
P3 (or P2) is equal to zero.

For example, we might assume
smoking is never good for anyone.
If P3 = 0 and IPD = 0

Then P2 = 0

Causal inferences, which we must make, rely on a strong
assumption – the comparability (or exchangeability) of
exposed and unexposed groups.
Comparability is synonymous with “no confounding”.
(p1 + p3) = (q1 + q3)


How seriously do
“epidemiologists” take
this?

“We adjusted for appropriate
confounders.”

...

Corollary 4:

“The greater the flexibility in designs, definitions,
outcomes, and analytical modes in a scientific field, the
less likely the research findings are to be true.”

“Implicit in these pressures* is a growing

dissatisfaction outside the field of epidemiology
with epidemiologic description and
correlation...”

Galea S. An Argument for a Consequentialist Epidemiology. AJE. 2013; doi: 10.1093/aje/kwt172

Good for science
Vs
Good for a scientist

Direct Acyclic Graphs

OVERVIEW
1. DAGs are a tool.

2. They help clarify causal thinking.
3. They guide the modelling process by helping to identify
potential confounding.
4. They have been used to identify many of the problems with
earlier approaches to confounding.

5. They are a great compliment to comparability based definitions
of confounding.

Traditional rules of thumb for identifying
confounders:
1.

It must be predictive of risk among the unexposed.

2.

It must be associated with the exposure in the population under
study.

3.

It must not fall on the causal path from exposure to outcome, or

be a consequence of the outcome.

Greenland S, Robins JM. Identifiability, exchangeability, and epidemiological confounding. Int
J Epidemiol. 1986;15:413–419. doi: 10.1093/ije/15.3.413.

These don’t always work. Is there
something better?

This is a graph.
It is directed.
It is acyclic.

In a DAG, any unblocked path between two
nodes implies a marginal (unadjusted)
association.

Algorithm for identifying confounders.
1. Erase all directed edges emanating from the exposure.

2. Identify all unblocked, backdoor paths between the exposure and
outcome.

Each of these paths implies confounding.
Confounding is removed by controlling for a
variable along that path.
Adjustment for one variable can address
confounding due to multiple paths.

Erase all directed edges emanating from
the exposure.

Identify unblocked, backdoor paths.

This means we can identify an optimal*
sufficient set for adjustment.

* The optimal sufficient set might be the smallest possible set, or the set that
is easiest to collect, or the least expensive, etc.

At what stage in the research process should
we employ a DAG?

Controlling for a collider has the effect of
inserting a new edge between its parents.

Fast and agile

Tough and strong

Rugby Ability

Glymour M. USING CAUSAL DIAGRAMS TO UNDERSTAND COMMON PROBLEMS IN SOCIAL EPIDEMIOLOGY. Methods in Social
Epidemiology

Fast and agile

Tough and strong

Rugby Ability

Algorithm for identifying confounders.
1. Erase all directed edges emanating from the exposure.
2. Identify all unblocked, backdoor paths from between the exposure

and outcome.
3. Define S, your sufficient set of variables needed to adjust for
confounding.
4. Draw an edge to connect all pairs of variables with a child in S, or a
child with a descendent in S.

5. Identify any new unblocked, backdoor paths, and update S.


MAKING A DAG
1. Identify an important health outcome, and a modifiable

exposure. Draw an arrow from the later to the former.
2. Think about what other variables might be related to these.
Brainstorm, use existing literature, etc.
3. Draw in any hypothesized causal paths.
4. Follow the steps previously outlined.


MAKING A DAG
5. Explore choices, and consider how these affect your optimal

sufficient set for adjustment (S).
6. Draw your DAG so it flows in the same direction you read (as
best as possible).
7. Use colour, notes, etc.
8. There are programs available, but pencil and lots of paper work

best at first.

Learning Task
• Based on the topic of your research thesis, create a DAG.
• It should include a preventable exposure, an important
outcome, and at least 3 other potentially important
covariates.
• Send me an image of your DAG before 17:00, next
Wednesday (ddahly@ucc.ie).

Confounders

SUMMARY
1. Epidemiologists should be preoccupied with causes.
2. Confounding is the single greatest threat to our causal inferences – which we
must make, or risk irrelevance.
3. Definitions and rules of thumb based on collapsibility are not sufficient to
identify many commonly encountered confounders.

4. Comparability based definitions are better, but don’t lend themselves to simple
rules of thumb.
5. Epidemiologists do not consistently use the same level of rigour when trying to

address confounding.
6. As a field, this limits our ability to effect positive change.


SUMMARY
1. DAGs are a useful tool.

2. They help clarify causal thinking.
3. They guide the modelling process by helping to identify
potential confounding.

Next week

PREVIEW
1. More DAG examples.

2. Critiques of DAGs, and my responses to these.
3. Methods for dealing with confounding, once you suspect it.

Confounding and Directed Acyclic Graphs

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