Confounding

LEARNING OBJECTIVESIntroduction

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.

MOTIVATIONIntroduction

Confounding is the most important topic in epidemiology.

Epidemiology is...

X Y

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?

Why?

When is it not possible to use a RCT?

X Y

Cause

X Y

Statistical Association

Statistical Association

When variables vary similarly.

Correlated; Covary; Dependent

Draw Inferences

Statistical inferences

Causal inferences

“Correlation does not imply

causation.”

BREAK

QUESTIONS?

DEFINITIONSConfounding

Synonym:

Spurious association

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.

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

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

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.

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)

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

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 scienceVs

Good for a scientist

BREAK

QUESTIONS?

OVERVIEWDirect Acyclic Graphs

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?

DirectedAcyclicGraphs

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

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?

But we aren’t done yet.

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 DAGDirect Acyclic Graphs

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 DAGDirect Acyclic Graphs

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).

SUMMARYConfounders

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.

SUMMARYDirect Acyclic Graphs

1. DAGs are a useful tool.

2. They help clarify causal thinking.

3. They guide the modelling process by helping to identify

potential confounding.

PREVIEWNext week

1. More DAG examples.

2. Critiques of DAGs, and my responses to these.

3. Methods for dealing with confounding, once you

suspect it.