Statistical properties of the quantile normalization method for density curve alignment

Area of Science:

• Bioinformatics
• Statistical analysis
• Computational biology

Background:

• Quantile normalization is a widely used technique for aligning density curves in microarray data analysis.
• The method by Bolstad et al. (2003) is particularly popular.
• Understanding its large sample properties is crucial for reliable data interpretation.

Purpose of the Study:

• To investigate the large sample properties of the quantile normalization method.
• To establish the consistency of quantile normalization as a structural expectation procedure.
• To address limitations of the method in specific data scenarios, such as mixtures.

Main Methods:

• Analysis of large sample properties of quantile normalization.
• Proof of consistency using concepts from Wasserstein space and barycenters of measures.
• Development of a novel methodology to overcome identified limitations.

Main Results:

• The study proves the consistency of the quantile normalization method for density curve alignment.
• It demonstrates that quantile normalization can fail in cases involving data mixtures.
• A new methodology is proposed to effectively handle these mixture cases.

Conclusions:

• Quantile normalization is a consistent method for density curve alignment under certain conditions.
• The proposed new methodology offers a solution for scenarios where quantile normalization is inadequate.
• This research contributes to more robust microarray data analysis.