Test for linear trend in 2 x K ordered tables with open-ended categories

Area of Science:

• Biostatistics
• Statistical Methods
• Epidemiology

Background:

• Evaluating trends in ordered categorical data is common in scientific research.
• Standard methods may not apply when the last category's score is unknown (open-ended category).
• The Cochran-Armitage-Mantel (CAM) trend test often encounters such open-ended categories.

Purpose of the Study:

• To propose a novel statistical method for trend evaluation in 2 x K ordered tables.
• To specifically address tables with an open-ended category where the last score is not predefined.
• To provide a robust method applicable to scenarios like CAM trend analysis.

Main Methods:

• Development of a statistical method for trend assessment in ordered tables.
• Focus on tables with an open-ended category.
• Derivation of the test statistic's distribution and use of simulations to verify asymptotic properties.

Main Results:

• The study presents the distribution of the proposed test statistic.
• Simulations confirm the asymptotic behavior of the method.
• The method is demonstrated effectively using a real-world dataset.

Conclusions:

• The proposed method offers a reliable way to evaluate trends in ordered tables with open-ended categories.
• This technique enhances the applicability of trend analysis in fields utilizing CAM tests.
• The findings are validated through theoretical distribution analysis and empirical simulations.