# The uniform general signed rank test and its design sensitivity

## TL;DR

This paper introduces the uniform general signed rank test, a new distribution-free method for observational studies that adaptively maximizes design sensitivity, outperforming traditional tests especially in large samples.

## Contribution

The paper proposes a novel, non-asymptotic, distribution-free signed rank test that adaptively combines multiple tests to achieve optimal design sensitivity in sensitivity analysis.

## Key findings

- The uniform test attains the maximum design sensitivity among a family of signed rank tests.
- Simulation results demonstrate the test's superior performance in moderate to large samples.
- The test maintains robustness under Rosenbaum's sensitivity model.

## Abstract

A sensitivity analysis in an observational study tests whether the qualitative conclusions of an analysis would change if we were to allow for the possibility of limited bias due to confounding. The design sensitivity of a hypothesis test quantifies the asymptotic performance of the test in a sensitivity analysis against a particular alternative. We propose a new, non-asymptotic, distribution-free test, the uniform general signed rank test, for observational studies with paired data, and examine its performance under Rosenbaum's sensitivity analysis model. Our test can be viewed as adaptively choosing from among a large underlying family of signed rank tests, and we show that the uniform test achieves design sensitivity equal to the maximum design sensitivity over the underlying family of signed rank tests. Our test thus achieves superior, and sometimes infinite, design sensitivity, indicating it will perform well in sensitivity analyses on large samples. We support this conclusion with simulations and a data example, showing that the advantages of our test extend to moderate sample sizes as well.