Some tests for detecting trends based on the modified Baumgartner-Weiβ-Schindler statistics.

Area of Science:

• Biostatistics
• Statistical Methods

Background:

• Trend testing is crucial for analyzing binomial data across multiple groups.
• Existing methods may lack power or accurate Type I error control in certain scenarios.

Purpose of the Study:

• To propose and evaluate a modified nonparametric Baumgartner-Weiβ-Schindler test for trend detection among K binomial populations.
• To compare different p-value calculation approaches for their Type I error rates and statistical power.

Main Methods:

• A modified nonparametric Baumgartner-Weiβ-Schindler test statistic was developed.
• Exact conditional and unconditional p-value calculation methods were explored, including maximization, confidence interval, and E+M approaches.
• Performance was assessed through simulations examining Type I error and power.

Main Results:

• The conditional and E+M approaches performed well in terms of Type I error and power.
• The E+M approach maintained an actual Type I error rate closer to the nominal level.
• The E+M approach exhibited higher power than other methods, particularly in unbalanced data.

Conclusions:

• The modified nonparametric test with the E+M p-value calculation approach is recommended for trend testing in K binomial populations.
• The E+M approach offers a robust method for controlling Type I error and enhancing power, especially in complex data structures.