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

TL;DR

This paper addresses the challenge of large-scale inference in transposable matrix data by modeling row and column correlations, proposing a method to improve statistical power and false discovery rate estimation.

Contribution

It introduces a transposable regularized covariance model to estimate covariances and de-correlate data, enhancing inference accuracy in correlated matrix data.

Findings

Improved statistical power in detecting significant variables.

More accurate false discovery rate estimation.

Effective handling of row and column correlations.

Abstract

We consider the problem of large-scale inference on the row or column variables of data in the form of a matrix. Often this data is transposable, meaning that both the row variables and column variables are of potential interest. An example of this scenario is detecting significant genes in microarrays when the samples or arrays may be dependent due to underlying relationships. We study the effect of both row and column correlations on commonly used test-statistics, null distributions, and multiple testing procedures, by explicitly modeling the covariances with the matrix-variate normal distribution. Using this model, we give both theoretical and simulation results revealing the problems associated with using standard statistical methodology on transposable data. We solve these problems by estimating the row and column covariances simultaneously, with transposable regularized covariance models, and de-correlating or sphering the data as a pre-processing step. Under reasonable assumptions, our method gives test statistics that follow the scaled theoretical null distribution and are approximately independent. Simulations based on various models with structured and observed covariances from real microarray data reveal that our method offers substantial improvements in two areas: 1) increased statistical power and 2) correct estimation of false discovery rates.