Valid post-selection inference in model-free linear regression

Kuchibhotla, Arun Kumar; Brown, Lawrence D.; Buja, Andreas; Cai, Junhui; George, Edward I.; Zhao, Linda

doi:10.1214/19-aos1917

Cited by 34 publications

(32 citation statements)

References 18 publications

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“…Simultaneous selection, estimation and inference have been studied recently (Berk et al 2013;van de Geer et al 2014). Kuchibhotla et al (2020) also provide an upper bound for post-selection inference P-values when taking into account the selection bias. These enhancements of our proposed method will be investigated in future studies.…”

Section: Discussionmentioning

confidence: 99%

A structured brain‐wide and genome‐wide association study using ADNI PET images

et al. 2021

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A multistage variable selection method is introduced for detecting association signals in structured brain-wide and genome-wide association studies (brain-GWAS). Compared to conventional methods that link one voxel to one single nucleotide polymorphism (SNP), our approach is more efficient and powerful in selecting the important signals by integrating anatomic and gene grouping structures in the brain and the genome, respectively. It avoids resorting to a large number of multiple comparisons while effectively controlling the false discoveries. Validity of the proposed approach is demonstrated by both theoretical investigation and numerical simulations. We apply our proposed method to a brain-GWAS using Alzheimer's Disease Neuroimaging Initiative positron emission tomography (ADNI PET) imaging and genomic data. We confirm previously reported association signals and also uncover several novel SNPs and genes that are either associated with brain glucose metabolism or have their association significantly modified by Alzheimer's disease status.

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Section: Discussionmentioning

confidence: 99%

A structured brain‐wide and genome‐wide association study using ADNI PET images

et al. 2021

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“…In Section 1, we mentioned the work by Kuchibhotla et al [15] which generally provides stronger guarantees at the price of increased conservatism. In order to assess this conservatism, we executed a small simulation study applying their method to this Toeplitz design.…”

Section: Posimentioning

confidence: 99%

“…In order to assess this conservatism, we executed a small simulation study applying their method to this Toeplitz design. For this, we use the software available in the GitHub repository cited in [15].…”

Section: Posimentioning

confidence: 99%

“…We conduct a similar simulation study as in Section 4.1 for the logistic model (15). We reuse the matrix X coming from a Toeplitz covariance design from Section 4.1 with dimensions n = 100 and p = 200.…”

Section: Multicarving For Logistic Regressionmentioning

confidence: 99%

“…Recent developments by Kuchibhotla et al [15] lead to computationally efficient procedures with similar guarantees. They derive a method to construct confidence regions such that they contain the true parameter in any submodel simultaneously with probability at least 1 − α.…”

Section: Introductionmentioning

confidence: 99%

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Multicarving for high-dimensional post-selection inference

Schultheiss

Renaux

Bühlmann

2021

Electron. J. Statist.

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We consider post-selection inference for high-dimensional (generalized) linear models. Data carving from Fithian, Sun and Taylor [10] is a promising technique to perform this task. However, it suffers from the instability of the model selector and hence, may lead to poor replicability, especially in high-dimensional settings. We propose the multicarve method inspired by multisplitting to improve upon stability and replicability. Furthermore, we extend existing concepts to group inference and illustrate the applicability of the methodology also for generalized linear models.

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A structured brain‐wide and genome‐wide association study using ADNI PET images

Liu

Nan

Zhu

2021

Alzheimer's & Dementia

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Background Detecting association signals between the brain and the genome using ultrahigh‐dimensional PET neuroimaging scans and GWAS SNP data Method A multi‐stage variable selection method is introduced for detecting association signals in structured brain‐wide and genome‐wide association studies (brain‐GWAS). Validity of the proposed approach is demonstrated by both theoretical investigation and numerical simulations. We apply our proposed method to a brain‐GWAS using ADNI PET imaging and genomic data. Result We confirm previously reported association signals (e.g. IL8RB and COLEC12 genes) and also uncover several novel SNPs and genes (e.g. GALNT4 and RIN2 genes) that either are associated with brain glucose metabolism or have their association significantly modified by Alzheimer's disease status. Conclusion Compared to conventional single‐voxel‐to‐single‐SNP methods, our approach is more efficient and powerful in selecting the important signals by integrating anatomic and gene grouping structures in the brain and the genome, respectively. It avoids resorting to large number of multiple comparisons while effectively controlling the false discoveries.

show abstract

Valid post-selection inference in model-free linear regression

Cited by 34 publications

References 18 publications

A structured brain‐wide and genome‐wide association study using ADNI PET images

A structured brain‐wide and genome‐wide association study using ADNI PET images

Multicarving for high-dimensional post-selection inference

A structured brain‐wide and genome‐wide association study using ADNI PET images

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