Alternative Graphical Causal Models and the Identification of Direct Effects

The subject-specific data from either an observational or experimental study consist of a string of numbers. These numbers represent a series of empirical measurements. Calculations are performed on these strings and causal inferences are drawn. For example, an investigator might conclude that the analysis provides strong evidence for ‘‘both an indirect effect of cigarette smoking on coronary artery disease through its effect on blood pressure and a direct effect not mediated by blood pressure.’’ The nature of the relationship between the sentence expressing these causal conclusions and the statistical computer calculations performed on the strings of numbers has been obscure. Since the computer algorithms are well-defined mathematical objects, it is crucial to provide formal causal models for the English sentences expressing the investigator’s causal inferences. In this chapter we restrict ourselves to causal models that can be represented by a directed acyclic graph. There are two common approaches to the construction of causal models. The first approach posits unobserved fixed ‘potential’ or ‘counterfactual’ outcomes for each unit under different possible joint treatments or exposures. The second approach posits relationships between the population distribution of outcomes under experimental interventions (with full compliance) to the set of (conditional) distributions that would be observed under passive observation (i.e., from observational data). We will refer to the former as ‘counterfactual’ causal models and the latter as ‘agnostic’ causal models (Spirtes, Glymour, & Scheines, 1993) as the second approach is agnostic as to whether unit-specific counterfactual outcomes exist, be they fixed or stochastic. The primary difference between the two approaches is ontological: The counterfactual approach assumes that counterfactual variables exist, while the agnostic approach does not require this. In fact, the counterfactual theory logically subsumes the agnostic theory in the sense that the counterfactual approach is logically an extension of the latter approach. In particular, for a given graph the causal contrasts (i.e. parameters) that are well-defined under the agnostic approach are also well-defined under the counterfactual approach.