Practical Implications of Modes of Statistical Inference for Causal Effects and the Critical Role of the Assignment Mechanism

Causal inference in an important topic and one that is now attracting serious attention of statisticians. Although there exist recent discussions concerning the general definition of causal effects and a substantial literature on specific techniques for the analysis of data in randomized and nonrandomized studies, there has been relatively little discussion of modes of statistical inference for causal effects. This presentation briefly describes and contrasts four basic modes of statistical inference for causal effects, emphasizes the common underlying causal framework with a posited assignment mechanism, and describes practical implications in the context of an example involving the effects of switching from a name-band to a generic drug. A fundamental conclusion is that in such nonrandomized studies, sensitivity of inference to the assignment mechanism is the dominant issue, and it cannot be avoided by changing modes of inference, for instance, by changing from randomization-based to Bayesian methods.