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Regularization Methods for High-Dimensional Instrumental Variables Regression With an Application to Genetical Genomics.

ABSTRACT: In genetical genomics studies, it is important to jointly analyze gene expression data and genetic variants in exploring their associations with complex traits, where the dimensionality of gene expressions and genetic variants can both be much larger than the sample size. Motivated by such modern applications, we consider the problem of variable selection and estimation in high-dimensional sparse instrumental variables models. To overcome the difficulty of high dimensionality and unknown optimal instruments, we propose a two-stage regularization framework for identifying and estimating important covariate effects while selecting and estimating optimal instruments. The methodology extends the classical two-stage least squares estimator to high dimensions by exploiting sparsity using sparsity-inducing penalty functions in both stages. The resulting procedure is efficiently implemented by coordinate descent optimization. For the representative L1 regularization and a class of concave regularization methods, we establish estimation, prediction, and model selection properties of the two-stage regularized estimators in the high-dimensional setting where the dimensionality of co-variates and instruments are both allowed to grow exponentially with the sample size. The practical performance of the proposed method is evaluated by simulation studies and its usefulness is illustrated by an analysis of mouse obesity data. Supplementary materials for this article are available online.

SUBMITTER: Lin W

PROVIDER: S-EPMC4573639 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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Regularization Methods for High-Dimensional Instrumental Variables Regression With an Application to Genetical Genomics.

Lin Wei W Feng Rui R Li Hongzhe H

Journal of the American Statistical Association 20150101 509

In genetical genomics studies, it is important to jointly analyze gene expression data and genetic variants in exploring their associations with complex traits, where the dimensionality of gene expressions and genetic variants can both be much larger than the sample size. Motivated by such modern applications, we consider the problem of variable selection and estimation in high-dimensional sparse instrumental variables models. To overcome the difficulty of high dimensionality and unknown optimal ...[more]

PMID: 26392642

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Project description:Genome-wide analysis of gene expression or protein binding patterns using different array or sequencing based technologies is now routinely performed to compare different populations, such as treatment and reference groups. It is often necessary to normalize the data obtained to remove technical variation introduced in the course of conducting experimental work, but standard normalization techniques are not capable of eliminating technical bias in cases where the distribution of the truly altered variables is skewed, i.e. when a large fraction of the variables are either positively or negatively affected by the treatment. However, several experiments are likely to generate such skewed distributions, including ChIP-chip experiments for the study of chromatin, gene expression experiments for the study of apoptosis, and SNP-studies of copy number variation in normal and tumour tissues. A preliminary study using spike-in array data established that the capacity of an experiment to identify altered variables and generate unbiased estimates of the fold change decreases as the fraction of altered variables and the skewness increases. We propose the following work-flow for analyzing high-dimensional experiments with regions of altered variables: (1) Pre-process raw data using one of the standard normalization techniques. (2) Investigate if the distribution of the altered variables is skewed. (3) If the distribution is not believed to be skewed, no additional normalization is needed. Otherwise, re-normalize the data using a novel HMM-assisted normalization procedure. (4) Perform downstream analysis. Here, ChIP-chip data and simulated data were used to evaluate the performance of the work-flow. It was found that skewed distributions can be detected by using the novel DSE-test (Detection of Skewed Experiments). Furthermore, applying the HMM-assisted normalization to experiments where the distribution of the truly altered variables is skewed results in considerably higher sensitivity and lower bias than can be attained using standard and invariant normalization methods.

Project description:BackgroundLeaf morphology varies extensively among plant species and is under strong genetic control. Mutagenic screens in model systems have identified genes and established molecular mechanisms regulating leaf initiation, development, and shape. However, it is not known whether this diversity across plant species is related to naturally occurring variation at these genes. Quantitative trait locus (QTL) analysis has revealed a polygenic control for leaf shape variation in different species suggesting that loci discovered by mutagenesis may only explain part of the naturally occurring variation in leaf shape. Here we undertook a genetical genomics study in a poplar intersectional pseudo-backcross pedigree to identify genetic factors controlling leaf shape. The approach combined QTL discovery in a genetic linkage map anchored to the Populus trichocarpa reference genome sequence and transcriptome analysis.ResultsA major QTL for leaf lamina width and length:width ratio was identified in multiple experiments that confirmed its stability. A transcriptome analysis of expanding leaf tissue contrasted gene expression between individuals with alternative QTL alleles, and identified an ADP-ribosylation factor (ARF) GTPase (PtARF1) as a candidate gene for regulating leaf morphology in this pedigree. ARF GTPases are critical elements in the vesicular trafficking machinery. Disruption of the vesicular trafficking function of ARF by the pharmacological agent Brefeldin A (BFA) altered leaf lateral growth in the narrow-leaf P. trichocarpa suggesting a molecular mechanism of leaf shape determination. Inhibition of the vesicular trafficking processes by BFA interferes with cycling of PIN proteins and causes their accumulation in intercellular compartments abolishing polar localization and disrupting normal auxin flux with potential effects on leaf expansion.ConclusionsIn other model systems, ARF proteins have been shown to control the localization of auxin efflux carriers, which function to establish auxin gradients and apical-basal cell polarity in developing plant organs. Our results support a model where PtARF1 transcript abundance changes the dynamics of endocytosis-mediated PIN localization in leaf cells, thus affecting lateral auxin flux and subsequently lamina leaf expansion. This suggests that evolution of differential cellular polarity plays a significant role in leaf morphological variation observed in subgenera of genus Populus.

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Regularization Methods for High-Dimensional Instrumental Variables Regression With an Application to Genetical Genomics.

Publications

Regularization Methods for High-Dimensional Instrumental Variables Regression With an Application to Genetical Genomics.

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