Augmented designs to assess principal strata direct effects

Many studies involving causal questions are often concerned with understanding the causal pathways by which a treatment affects an outcome. Thus, the concept of 'direct' versus 'indirect' effects comes into play. We tackle the problem of disentangling direct and indirect effects by investigating new augmented experimental designs, where the treatment is randomized, and the mediating variable is not forced, but only randomly encouraged. There are two key features of our framework: we adopt a principal stratification approach, and we mainly focus on principal strata effects, avoiding involving a priori counterfactual outcomes. Using non-parametric identification strategies, we provide a set of assumptions, which allow us to identify partially the causal estimands of interest: the principal strata direct effects. Some examples are shown to illustrate our design and causal estimands of interest. Large sample bounds for the principal strata average direct effects are provided, and a simple hypothetical example is used to show how our augmented design can be implemented and how the bounds can be calculated. Finally our augmented design is compared and contrasted with a standard randomized design.