Randomization Inference for Matched Pairs with Binary Outcomes

@misc{wilson2026randomization,
  title = {{Randomization Inference for Matched Pairs with Binary Outcomes}},
  author = {Bob Wilson},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03227},
  eprint = {2609.03227},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03227},
}

TY  - UNPB
TI  - Randomization Inference for Matched Pairs with Binary Outcomes
AU  - Bob Wilson
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03227
UR  - https://arxiv.org/abs/2609.03227
AB  - We give an exact randomization-based confidence set for the average treatment effect (ATE) in matched-pair studies with a binary outcome, requiring neither monotonicity nor any distributional assumption beyond the within-pair coin flip. At its core is an analytic solution to the worst-case allocation of attributable effects: two binomial-symmetry lemmas identify the pattern hardest to reject as a single boundary corner, so testing null hypotheses needs no integer program and no numerical search. Inverting the test via binary search yields a prediction set for the attributable effect in O(log S) Binomial tail calculations; the Bonferroni proposition of Rigdon and Hudgens (2015) produces the ATE confidence set at the same computational cost. The same corner extends without further machinery to a sensitivity analysis for matched observational studies under Rosenbaum's Γ-model. A simple formula for the design sensitivity illuminates when an observational study can hope to provide evidence for an effect.
ER  -