期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2022
卷号：119
期号：34
DOI：10.1073/pnas.2205518119
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Significance
Statistical theory has mostly focused on testing the dependence between covariates and response under parametric or semiparametric models. In reality, the model assumptions might be too restrictive to be satisfied, and it is of substantial interest to test the significance of the prediction in a completely model-free setting. Our proposed method is nonparametric and can be applied to a wide range of real applications. It can borrow the strength of the most powerful machine learning regression algorithms and is computationally efficient. We apply the inference approach to the recent cellular indexing of transcriptomes and epitopes by sequencing data and spatially resolved transcriptomics data. The proposed method is more powerful and can produce biologically meaningful results.
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
Y
|
Z
and
Y
|
(
X
,
Z
)
, 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.
