Hypothesis tests for and against a simple order among proportions estimated by pooled testing

Area of Science:

• Biostatistics
• Statistical genetics
• Epidemiology

Background:

• Pooled testing is increasingly used to estimate the prevalence of rare traits across various scientific fields.
• Existing methods for analyzing pooled testing data often have limitations when dealing with multiple binomial proportions.
• Order-restricted hypothesis testing provides a framework for analyzing such data, building on prior work by Tebbs and Swallow.

Purpose of the Study:

• To develop and evaluate novel statistical tests for analyzing k > 2 binomial proportions estimated via pooled testing.
• To address scenarios involving testing for equality of proportions against an isotonic alternative and detecting violations of isotonicity.
• To extend the methodologies for order-restricted inference in the context of pooled testing.

Main Methods:

• The study proposes new hypothesis tests for order-restricted inference with pooled testing data.
• It involves analyzing scenarios with multiple binomial proportions (k > 2).
• Small-sample performance of the proposed tests is characterized.

Main Results:

• New tests are proposed for testing equality versus isotonic alternatives and for testing violations of isotonicity.
• The small-sample performance of these novel procedures is analyzed.
• The methods are demonstrated using real-world data from an HIV study and an agricultural experiment.

Conclusions:

• The developed methods offer advancements in statistical analysis for pooled testing applications.
• These new tests provide valuable tools for researchers in public health, genetics, and agriculture.
• The study highlights the utility of order-restricted hypothesis testing in complex pooled testing scenarios.