Inference with Transposable Data: Modeling the Effects of Row and Column Correlations

Area of Science:

• Statistics
• Bioinformatics
• Genomics

Background:

• Large-scale data matrices often exhibit complex correlations between row and column variables.
• Such dependencies, like those in microarray data due to batch effects, violate assumptions of standard statistical inference.
• This impacts the reliability of detecting significant features, such as genes.

Purpose of the Study:

• To investigate the impact of row and column correlations on large-scale matrix inference.
• To develop a method for addressing these correlations in matrix-variate data.
• To improve the accuracy and power of statistical tests and multiple testing procedures.

Main Methods:

• Modeling matrix data using the matrix-variate normal distribution.
• Simultaneously estimating row and column covariance matrices.
• Applying a de-correlation (sphering) procedure to the data before inference.

Main Results:

• The proposed de-correlation method effectively addresses unanticipated correlations.
• Test statistics more closely adhere to null distributions after de-correlation.
• Multiple testing procedures demonstrate improved control over error rates.

Conclusions:

• The developed method significantly enhances statistical power in large-scale inference.
• It reduces bias and variance in estimating the false discovery rate.
• This approach offers a robust solution for analyzing correlated matrix data, particularly in genomics.