| By introducing a number of new concepts, the directed acyclic graph causal framework is extended in a number of directions. First, by incorporating the notions of a monotonic effect, a weak monotonic effect and a signed edge, the directed acyclic graph causal framework can be extended so as to allow not only for the graphical representation of causal relations amongst variables but also for the sign of these causal relations. Results are developed relating monotonic effects to the sign of the causal effect of an intervention in the presence of intermediate variables. The incorporation of signed edges into the directed acyclic graph causal framework furthermore allows for the development of rules governing the relationship between monotonic effects and the sign of the covariance between two variables and also rules governing the sign of the bias which arises when control for confounding is inadequate.; Second, notions of minimal sufficient causation are incorporated within the directed acyclic graph causal framework. Doing so provides a clear theoretical link between two major conceptualizations of causality: one counterfactual-based and the other based on a more mechanistic understanding of causation. These minimal sufficient causes allow for the detection of conditional independencies within particular strata of the conditioning variable which were not evident on the original causal directed acyclic graph. The minimal sufficient cause representations are further used to derive conditions that imply the existence of monotonic effects and of biologic interactions and to derive rules governing minimal sufficient causation and the signs of the conditional covariances of the graph's variables.; Third, statistical tests are derived for the presence of biologic interactions by using the sufficient cause framework. Under the setting of monotonic effects, conditions for a biologic interaction are closely related to effect modification on the risk difference scale; through a series of examples, the concepts of effect modification and biologic interaction are contrasted.; Finally, the directed acyclic graph causal framework is used to provide a four-fold structural classification for effect modification on the risk difference scale: direct effect modification, indirect effect modification, effect modification by proxy and effect modification by common cause. |
