Polydesigns in Causal Inference

In an increasingly common class of studies, the goal is to evaluate causal effects of treatments that are only partially controlled by the investigator. In such studies there are two conflicting features: (1) a model on the full design and data can identify the causal effects of interest, but the model’s use in extreme regions of the data (e.g., where the outcome of interest is rare) can be sensitive to model misspecification; and (2) the induced model on a reduced design, i.e., of a subset of data (e.g., conditional likelihood on matched pairs) can be more robust to a full model’s misspecification, but it does not generally identify the causal effects. We propose to assess inference sensitivity to designs by exploring combinations of both the full and reduced designs. We show that using such a “polydesign” generates a rich class of methods that can identify the causal effect and that can also be more robust to misspecification than the full model and design. We also discuss implementation of polydesign inference.