Reducing bias through directed acyclic graphs.

Shrier I, Platt RW - BMC Med Res Methodol (2008)

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Figure 4: a-b. In Step 5 (4a), we strip all the arrowheads off all the lines. In Step 6 (4b), all lines touching the covariates neuromuscular fatigue (Z1) and tissue weakness (Z2) are deleted. Because the exposure of interest (warm up exercises) is dissociated from the Outcome (injury) after Step 6, the statistical model that includes the covariates neuromuscular fatigue and tissue weakness minimizes the potential bias for the estimate of effect of warm up exercises on the risk of injury.
Mentions: Step 4 is essential for the following reason. If two covariates both cause a third covariate, then adjustment for the third covariate (or an effect of the third covariate) creates a conditional association between the first two covariates (i.e. if one conditions on the child or descendant of the child, there is a conditional association between the parents), and could introduce bias [20]. For example, both rain and sprinklers can cause a football field to be wet. If one knows the grass is wet, then knowing the sprinklers were off improves your assessment of the probability that it rained; rain and sprinklers become associated when the common effect of "field wetness" is known. Consider a second example from the health sciences: both a thrombus and a haemorrhage can cause a stroke. If we condition on the patient having symptoms of a stroke and learn that there was no haemorrhage, the probability that a thrombotic event occurred is increased. By connecting the two parents of a common child in the figure after Steps 1–3 are completed, we are explicitly stating that we understand that these variables are associated because we have either conditioned on the value of the child or one of the child's descendants (otherwise the variable would have been removed in Step 2). As we shall later see, it is this conditional association that can cause the introduction of bias when traditional rules of confounding adjustment are applied without reference to a DAG. In DAG terminology, the child is called a "collider" because two directed arrows collide at the covariate (node).

Bottom Line: The traditional methods of adjusting for "potential confounders" may introduce conditional associations and bias rather than minimize it.Although previous published articles have discussed the role of the causal directed acyclic graph approach (DAGs) with respect to confounding, many clinical problems require complicated DAGs and therefore investigators may continue to use traditional practices because they do not have the tools necessary to properly use the DAG approach.Using the simple 6-step DAG approach to confounding and selection bias discussed is likely to reduce the degree of bias for the effect estimate in the chosen statistical model.

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Affiliation: Centre for Clinical Epidemiology and Community Studies, SMBD-Jewish General Hospital, McGill University, Montreal, Canada. ian.shrier@mcgill.ca

ABSTRACT

Background: The objective of most biomedical research is to determine an unbiased estimate of effect for an exposure on an outcome, i.e. to make causal inferences about the exposure. Recent developments in epidemiology have shown that traditional methods of identifying confounding and adjusting for confounding may be inadequate.

Discussion: The traditional methods of adjusting for "potential confounders" may introduce conditional associations and bias rather than minimize it. Although previous published articles have discussed the role of the causal directed acyclic graph approach (DAGs) with respect to confounding, many clinical problems require complicated DAGs and therefore investigators may continue to use traditional practices because they do not have the tools necessary to properly use the DAG approach. The purpose of this manuscript is to demonstrate a simple 6-step approach to the use of DAGs, and also to explain why the method works from a conceptual point of view.

Summary: Using the simple 6-step DAG approach to confounding and selection bias discussed is likely to reduce the degree of bias for the effect estimate in the chosen statistical model.

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