PairMatch

Randomization inference for matched pairs with binary outcomes.

Given pairs in which one treated unit is matched to one control and each unit's outcome is 0 or 1, this library produces exact confidence sets for the treatment effect and reports how much unmeasured confounding the finding withstands. It assumes nothing beyond the within-pair coin flip — in particular it does not assume the treatment effect is monotonic, and it fits no outcome model.

The method inverts a worst-case McNemar test for the attributable effects A_1 and A_0 and combines them via the Rigdon–Hudgens Bonferroni proposition. The worst-case allocation of effects has a closed form, so the confidence sets cost O(log S) binomial tail evaluations — no integer program and no numerical search.

Install

uv pip install .

The distribution is named PairMatch; the import package is pair_match.

Python 3.11+. Depends on numpy, scipy, pandas, tabulate, and matplotlib.

Quick start

from pair_match import PairedOutcomeTable

# treated_y[i] and control_y[i] are the 0/1 outcomes of the i-th pair.
table = PairedOutcomeTable.from_outcomes(treated_y, control_y)

print(table)             # the 2x2 table, margins, and success rates
print(table.analyze())   # effect, confidence set, p-value, sensitivity value

|    ATT |   Conf Int**    |   iSuccesses |  Conf Int**  |   p-Value* |   Γ• |
|--------+-----------------+--------------+--------------+------------+------|
| +7.72% | -1.75%, +17.19% |          +22 |   -5, +49    |      0.193 |    1 |

The last column is Rosenbaum's sensitivity value: the largest hidden-bias odds ratio at which the finding still holds. A Γ• near 1 means even slight unmeasured confounding would overturn the result.

What is in scope

This package covers the estimation half of a matched study. How the pairs were formed — propensity-score matching, exact matching on a few keys, or a pairing already present in the data — is up to you; supply the pairs and it takes over from there.

Documentation

pair_match/USAGE.md is the full guide — also available at runtime:

import pair_match
print(pair_match.usage())

Every public class and method carries a NumPy-style docstring, which is the authoritative reference for parameters, defaults, and edge cases.

Tests

uv sync
uv run python -m pytest

References

• Wilson, Bob. 2026. "Randomization Inference for Matched Pairs with Binary Outcomes." arXiv:2609.03227. https://arxiv.org/abs/2609.03227
• Rosenbaum, Paul R. 2002. "Attributing Effects to Treatment in Matched Observational Studies." Journal of the American Statistical Association 97 (457): 183–192.
• Rigdon, Joseph, and Michael G. Hudgens. 2015. "Randomization Inference for Treatment Effects on a Binary Outcome." Statistics in Medicine 34 (6): 924–935.
• Rosenbaum, Paul R. 2020. Design of Observational Studies. 2nd ed. Springer Series in Statistics.