A comparison of exact tests for trend with binary endpoints using Bartholomew's statistic

Area of Science:

• Biostatistics
• Statistical Methods
• Epidemiology

Background:

• Trend tests are crucial for binary variables across scientific fields.
• Standard Cochran-Armitage tests require arbitrary score assignments.
• Existing methods like Bartholomew's test have issues with type I error control in finite samples.

Purpose of the Study:

• To investigate the use of exact probability distributions for trend tests.
• To compare conditional and unconditional approaches for analyzing trends in binary data.
• To improve type I error control and statistical power in trend analysis.

Main Methods:

• Developed four tests utilizing exact probability distributions.
• Considered one conditional approach based on fixed marginal totals.
• Examined three unconditional approaches with fixed group sample sizes.

Main Results:

• All four proposed tests maintain actual type I error rates below nominal levels, exhibiting slight conservatism.
• Unconditional tests demonstrate significantly less conservatism compared to the conditional test.
• Unconditional approaches yield a notable power advantage over the conditional method.

Conclusions:

• Exact probability distributions provide a robust framework for trend testing with binary variables.
• Unconditional trend tests offer superior performance in terms of power and error control for finite samples.
• The findings recommend unconditional approaches for more reliable trend analysis in research.