Figure 1.

Illustrative example–directed acyclic graph for the hypothesis that obesity is causally related to pre-eclampsia

Deciding what we should and should not adjust for on the basis of this DAG:

Scenario 1

Assume that current knowledge does not imply a plausible effect of addictive personality on smoking or obesity, or that there is a direct relationship of SEP to PE risk, so these relationships (all shown with dashed arrows) are not included in the DAG in Scenario 1. We can make appropriate decisions about what needs to be adjusted for and what should not be adjusted for to obtain a valid estimate of the causal effect of obesity on PE if we assume that our DAG is correct [i.e. there are no other variables (nodes) or arrows that should be included] and that all variables are measured accurately (with little or no misclassification). We want to adjust for confounding–i.e. we want to block all back door paths. In this scenario there are four unblocked.

Unblocked backdoor paths

• PE-Age at pregnancy-SEP-Smoking-Obesity;
• PE-Age at pregnancy-SEP-Obesity;
• PE-Age at pregnancy-Smoking-Obesity;
• PE-Smoking-Obesity.

Because age at pregnancy is in the first three paths, we can block all three of those by adjusting for age at pregnancy only: assuming our DAG is correct and pregnancy age is accurately measured and so adjusting on it can fully block those paths. The last path does not include age; to block that we must control for smoking.

There is also one blocked path

• PE-Age at pregnancy -Smoking-SEP-Obesity; this is blocked because age and SEP collide on smoking.

However, we have said above that we have to adjust for smoking. When we do that, this path is unblocked and a spurious association between Pregnancy age and SEP is generated. In this scenario we are going to adjust for pregnancy age, which will block this path even when we adjust for smoking. To conclude, if we assume the DAG is correct and pregnancy age, obesity and PE are accurately measured (and there are no other sources of bias), then adjusting for pregnancy age and smoking will provide a valid causal estimate.

Scenario 2

New research/knowledge provides evidence that: (a) Addictive personality is relevant to our causal understanding of obesity on PE and must be added to the DAG as shown with dashed arrows (related to smoking and obesity) and (b) SEP is directly related to PE, also added to the DAG with a dashed arrow. This introduces one new unblocked path (in addition to the ones above):

• PE-SEP-Smoking-Addictive personality-Obesity.

We do not have a measure of Addictive personality or SEP, but we can block this path by adjusting for smoking (assuming our DAG is correct and no misclassification or other bias). We also still need to adjust for age and smoking to block the paths described above but now, when we adjust for smoking, we unblock the following blocked back door paths:

• PE-SEP-Addictive personality-Obesity;

Because we generate a spurious association between SEP and Addictive personality, if we do not have a measure of either of these in our dataset, the question is:

• Should we adjust for smoking to deal with confounding or should we not adjust for it because to do so would introduce collider bias?

The DAG cannot answer that–the answer lies in background knowledge and/or simulation studies that provide evidence for whether bias would be greatest with or without adjustment for smoking.

Should we adjust for gestational age in either scenario?

Very often in perinatal epidemiology gestational age is conditioned on–frequently this is done by excluding women who do not have a term delivery (i.e. where the baby is born before 37 weeks of completed gestation) either in the study design or analyses. In any analyses where exposure and outcome influence gestational age (as in this example, and commonly for many questions in this field), we should not do this. To do so potentially introduces a spurious association between Obesity and PE. In this specific case, that spurious association would be inverse and so this ‘collider’ bias could produce an effect estimate that is weaker than any true positive effect (biased towards the null). Note that whereas SEP would rarely be a plausible cause of ‘Age’ in this example, it is plausible to assume that SEP influences the age at which women start their family and hence become pregnant, with young women more likely to be from lower SEP and older from higher SEP.¹⁹