Evidence Factors in Fuzzy Regression Discontinuity Designs with Sequential Treatment Assignments

Many observational studies often involve multiple levels of treatment assignment. In particular, fuzzy regression discontinuity (RD) designs have sequential treatment assignment processes: first based on eligibility criteria, and second, on (non-)compliance rules. In such fuzzy RD designs, researchers typically use either an intent-to-treat approach or an instrumental variable-type approach, and each is subject to both overlapping and unique biases. This paper proposes a new evidence factors framework for fuzzy RD designs with sequential treatment assignments, which may be influenced by different levels of decision-makers. Each of the proposed evidence factors aims to test the same causal null hypothesis while potentially being subject to different types of biases. Our proposed framework utilizes the local RD randomization and randomization-based inference. We evaluate the effectiveness of our proposed framework through simulation studies and two real datasets on pre-kindergarten programs and testing accommodations.