  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.
