Directed Acyclic Graphs: Alternative tool for causal inference in epidemiology and biostatistics research and teaching

Figure 2 shows an example of a simple D/XG. Suppose we want to estimate the effect of vitamins on birth defects, which variables must be adjusted for? do we need to adjust for all four variables that showed in Figure 2?. Our objective is to determine Minimal Sufficient Adjustment Sets (MSAS) that not only easy to calculate but also saving the research resource of data collection. As discussed above, all backdoor paths from birth defects to vitamins must be blocked to obtain the true effect of vitamins on birth defects. There are three opening backdoor paths: (1) Birth defects <-Pre-natal care<-Socioeconomic status (SES)->Vitamins; (2) Birth defectsMaternal gcnctics->Difficulty conceiving-^Pre¬natal carc->Vitamins; and (3) Birth defects<-Pre-natal care->Vitamins; and one "natural blocked" backdoor path: (4) Birth defects <-Maternal genctics-> Difficulty conceiving-^ Pre-natal carc<-SES-> Vitamin (because Pre-natal care is a collider in this path). The most obvious confoundcr is pre-natal care, it is located in all three opening backdoor paths, therefore, when we adjust for it. all the three backdoor paths will be blocked. However, the adjustment of pre-natal care doesn’t mean that all the backdoor paths arc blocked. Since pre-natal care is also a collider for socioeconomic status and difficulty conceiving, adjusting for pre-natal care will open the "natural blocked” backdoor path number fourth. Therefore, adjusting for at least one more variable in the fourth backdoor path is needed. As a result, there are three possible MSAS: (I) pre-natal care and socioeconomic status; (2) pre-natal care and difficulty conceiving; (3) pre-natal care and maternal genetics. The choice then will be depended on our intent and available data. In more complex situations we can build a DAG using the six-step approach [II] or DAG software, which is free, developed by Textor J, et al [ 12] and available at httpt/Avww. dagitty.net. One of the main limitations of DAG that is only a qualitative approach thus cannot quantify the magnitude or direction of the bias. In order to calculate the magnitude of quantitative relationships. Structural equation modeling or Bayesian networks may be helpful.