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. Author manuscript; available in PMC: 2017 Nov 1.

Published in final edited form as: Epidemiology. 2016 Nov;27(6):859–869. doi: 10.1097/EDE.0000000000000547

Causal Directed Acyclic Graphs describing a hypothetical study with exposures A(t), measured covariates C(t), and unmeasured variables U^* and U, and also outcome Y. Each scenario represents a different structure of bias due to exposure-covariate feedback. In scenario (a) stratifying on C(1) will block the effect of A(0) and Y and open the non-causal path . In scenarios (b) and (c) stratifying on C(1) opens the non-causal pathway . In all scenarios, adjusting for C(1) by stratification leads to bias. Adjusting by a g-method e.g. removing the arrow from C(1) to A(1) does not induce bias. Note that in (c) there is unmeasured confounding by U^* from the path A(0) ← U^* → C(1) → Y and g-methods will not remove it. Because Diagnostic 2 would pick up this unmeasured confounding as an imbalance e.g. A(0) ← U^* → C(1), it is most interpretable when investigators are diagnosing covariate history sufficient enough to support exchangeability assumptions (i.e. no unmeasured confounding).

Inline graphic — Causal Directed Acyclic Graphs describing a hypothetical study with exposures A(t), measured covariates C(t), and unmeasured variables U^* and U, and also outcome Y. Each scenario represents a different structure of bias due to exposure-covariate feedback. In scenario (a) stratifying on C(1) will block the effect of A(0) and Y and open the non-causal path . In scenarios (b) and (c) stratifying on C(1) opens the non-causal pathway . In all scenarios, adjusting for C(1) by stratification leads to bias. Adjusting by a g-method e.g. removing the arrow from C(1) to A(1) does not induce bias. Note that in (c) there is unmeasured confounding by U^* from the path A(0) ← U^* → C(1) → Y and g-methods will not remove it. Because Diagnostic 2 would pick up this unmeasured confounding as an imbalance e.g. A(0) ← U^* → C(1), it is most interpretable when investigators are diagnosing covariate history sufficient enough to support exchangeability assumptions (i.e. no unmeasured confounding).