Model-free prediction test with application to genomics data

Abstract

Testing the significance of predictors in a regression model is one of the most important topics in statistics. This problem is especially difficult without any parametric assumptions on the data. This paper aims to test the null hypothesis that given confounding variables Z , X does not significantly contribute to the prediction of Y under the model-free setting, where X and Z are possibly high dimensional. We propose a general framework that first fits nonparametric machine learning regression algorithms on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Y</mml:mi> <mml:mo>|</mml:mo> <mml:mi>Z</mml:mi> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Y</mml:mi> <mml:mo>|</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>Z</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> , then compares the prediction power of the two models. The proposed method allows us to leverage the strength of the most powerful regression algorithms developed in the modern machine learning community. The P value for the test can be easily obtained by permutation. In simulations, we find that the proposed method is more powerful compared to existing methods. The proposed method allows us to draw biologically meaningful conclusions from two gene expression data analyses without strong distributional assumptions: 1) testing the prediction power of sequencing RNA for the proteins in cellular indexing of transcriptomes and epitopes by sequencing data and 2) identification of spatially variable genes in spatially resolved transcriptomics data.

Topics & Concepts