A note on monotonicity assumptions for exact unconditional tests in binary matched-pairs designs

Area of Science:

• Biostatistics
• Statistical Inference
• Clinical Trial Design

Background:

• Exact unconditional tests are crucial for analyzing 2x2 matched-pairs binary data, especially with small sample sizes.
• Lloyd's E+M p-value offers improved performance over existing M and C p-values.
• Analytical calculation of the E+M p-value traditionally requires the Barnard convexity condition, which is theoretically difficult to establish.

Purpose of the Study:

• To demonstrate that a weaker condition, conditional monotonicity, is sufficient for calculating M, C, and E+M p-values.
• To extend the applicability of these exact unconditional tests to noninferiority testing scenarios.

Main Methods:

• Reformulation of the conditions required for exact unconditional tests.
• Investigation of the conditional monotonicity property for 2x2 matched-pairs binary data.
• Application of the conditional monotonicity condition to noninferiority tests.

Main Results:

• Conditional monotonicity is shown to be sufficient for calculating the exact sizes of M, C, and E+M p-values.
• The theoretical challenge of the Barnard convexity condition is circumvented.
• The conditional monotonicity condition is proven applicable to noninferiority tests.

Conclusions:

• Conditional monotonicity provides a more accessible and broadly applicable condition for exact unconditional tests in biostatistics.
• This finding simplifies the computation and expands the use of E+M, M, and C p-values, particularly in noninferiority trial settings.