Hypothesis testing in a mixture case-control model.

Area of Science:

• Statistics
• Biostatistics
• Genetics

Background:

• Mixture proportion testing is crucial in diverse scientific fields, including epidemiology, genetics, and clinical trials.
• Accurate estimation of mixture proportions is essential for valid statistical inference in these applications.

Purpose of the Study:

• To develop and evaluate a novel generalized score test statistic for accurately assessing mixture proportions in two-sample data.
• To address the challenge of unknown mixture proportions (λ) in scenarios involving group one and a mixture of group one and group two.

Main Methods:

• The study proposes a generalized score test statistic under the assumption of a linear log ratio of probability density functions.
• The asymptotic distribution of the test statistic is shown to be a weighted chi-squared random variable under the null hypothesis (λ=0).
• Permutation methods are employed to enhance the reliability of finite sample approximations.

Main Results:

• The proposed generalized score test statistic is demonstrated to be asymptotically a weighted chi-squared distribution.
• The weight in the chi-squared distribution is determined by the sampling fractions of the groups.
• Simulation studies and real-world data applications validate the effectiveness of the proposed method.

Conclusions:

• The developed generalized score test provides a statistically sound approach for testing mixture proportions.
• The method is versatile and applicable to a wide range of scientific disciplines requiring mixture analysis.
• The use of permutation methods ensures robust performance in finite sample scenarios.