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TEST OF SIGNIFICANCE FOR HIGH-DIMENSIONAL LONGITUDINAL DATA.

ABSTRACT: This paper concerns statistical inference for longitudinal data with ultrahigh dimensional covariates. We first study the problem of constructing confidence intervals and hypothesis tests for a low dimensional parameter of interest. The major challenge is how to construct a powerful test statistic in the presence of high-dimensional nuisance parameters and sophisticated within-subject correlation of longitudinal data. To deal with the challenge, we propose a new quadratic decorrelated inference function approach, which simultaneously removes the impact of nuisance parameters and incorporates the correlation to enhance the efficiency of the estimation procedure. When the parameter of interest is of fixed dimension, we prove that the proposed estimator is asymptotically normal and attains the semiparametric information bound, based on which we can construct an optimal Wald test statistic. We further extend this result and establish the limiting distribution of the estimator under the setting with the dimension of the parameter of interest growing with the sample size at a polynomial rate. Finally, we study how to control the false discovery rate (FDR) when a vector of high-dimensional regression parameters is of interest. We prove that applying the Storey (2002)'s procedure to the proposed test statistics for each regression parameter controls FDR asymptotically in longitudinal data. We conduct simulation studies to assess the finite sample performance of the proposed procedures. Our simulation results imply that the newly proposed procedure can control both Type I error for testing a low dimensional parameter of interest and the FDR in the multiple testing problem. We also apply the proposed procedure to a real data example.

SUBMITTER: Fang EX

PROVIDER: S-EPMC8277154 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:MotivationThere are a number of well-established methods such as principal component analysis (PCA) for automatically capturing systematic variation due to latent variables in large-scale genomic data. PCA and related methods may directly provide a quantitative characterization of a complex biological variable that is otherwise difficult to precisely define or model. An unsolved problem in this context is how to systematically identify the genomic variables that are drivers of systematic variation captured by PCA. Principal components (PCs) (and other estimates of systematic variation) are directly constructed from the genomic variables themselves, making measures of statistical significance artificially inflated when using conventional methods due to over-fitting.ResultsWe introduce a new approach called the jackstraw that allows one to accurately identify genomic variables that are statistically significantly associated with any subset or linear combination of PCs. The proposed method can greatly simplify complex significance testing problems encountered in genomics and can be used to identify the genomic variables significantly associated with latent variables. Using simulation, we demonstrate that our method attains accurate measures of statistical significance over a range of relevant scenarios. We consider yeast cell-cycle gene expression data, and show that the proposed method can be used to straightforwardly identify genes that are cell-cycle regulated with an accurate measure of statistical significance. We also analyze gene expression data from post-trauma patients, allowing the gene expression data to provide a molecularly driven phenotype. Using our method, we find a greater enrichment for inflammatory-related gene sets compared to the original analysis that uses a clinically defined, although likely imprecise, phenotype. The proposed method provides a useful bridge between large-scale quantifications of systematic variation and gene-level significance analyses.Availability and implementationAn R software package, called jackstraw, is available in CRAN.Contactjstorey@princeton.edu.

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TEST OF SIGNIFICANCE FOR HIGH-DIMENSIONAL LONGITUDINAL DATA.

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