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Abstract

In this work, we develop a novel Bayesian regression framework that can be used to complete variable selection in high dimensional settings. Unlike existing techniques, the proposed approach can leverage side information to inform about the sparsity structure of the regression coefficients. This is accomplished by replacing the usual inclusion probability in the spike and slab prior with a binary regression model which assimilates this extra source of information. To facilitate model fitting, a computationally efficient and easy to implement Markov chain Monte Carlo posterior sampling algorithm is developed via carefully chosen priors and data augmentation steps. The finite sample performance of our methodology is assessed through numerical simulations, and we further illustrate our approach by using it to identify genetic markers associated with the nicotine metabolite ratio; a key biological marker associated with nicotine dependence and smoking cessation treatment.

Keywords

Biomarker conditional means prior nicotine metabolite ratio side information spike and slab prior

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References

Tibshirani

. Regression shrinkage and selection via the lasso. J R Stat Soc: Ser B (Methodological) 1996; 58: 267–288.

Zou

. The adaptive lasso and its oracle properties. J Am Stat Assoc 2006; 101: 1418–1429.

Fan

. Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc 2001; 96: 1348–1360.

Fan

Feng

. Network exploration via the adaptive LASSO and SCAD penalties. Ann Appl Stat 2009; 3: 521.

Zou

Hastie

. Regularization and variable selection via the elastic net. J R Stat Soc: Ser B (statistical methodology) 2005; 67: 301–320.

Meinshausen

Bühlmann

. Stability selection. J R Stat Soc: Ser B (Statistical Methodology) 2010; 72: 417–473.

Candes

Fan

Janson

, et al. Panning for gold. J R Stat Soc Ser B (Statistical Methodology) 2018; 80: 551–577.

Lin

. The Bayesian elastic net. Bayesian Anal 2010; 5: 151–170.

Park

Casella

. The Bayesian Lasso. J Am Stat Assoc 2008; 103: 681–686.

10.

Polson

Carvalho

Scott

. The horseshoe estimator for sparse signals. Biometrika 2010; 97: 465–480.

11.

Dunson

Armagan

Lee

. Generalized double Pareto shrinkage. Stat Sin 2013; 23: 119–143.

12.

Mitchell

Beauchamp

. Bayesian variable selection in linear regression. J Am Stat Assoc 1988; 83: 1023–1032.

13.

George

McCulloch

. Variable selection via Gibbs sampling. J Am Stat Assoc 1993; 88: 881–889.

14.

Ishwaran

Rao

. Spike and slab variable selection: frequentist and Bayesian strategies. Ann Stat 2005; 33: 730–773.

15.

Malsiner-Walli

Wagner

. Comparing spike and slab priors for Bayesian variable selection. Aust J Stat 2011; 40: 241–164.

16.

Wagner

Duller

. Bayesian model selection for logistic regression models with random intercept. Comput Stat Data Anal 2012; 56: 1256–1274.

17.

Titsias

Lázaro-Gredilla

. Spike and slab variational inference for multi-task and multiple kernel learning. Adv Neural Inf Process Syst 2011; 24: 2339–2347.

18.

Scheipl

Fahrmeir

Kneib

. Spike-and-slab priors for function selection in structured additive regression models. J Am Stat Assoc 2012; 107: 1518–1532.

19.

Hernández-Lobato

Suárez

. Expectation propagation in linear regression models with spike-and-slab priors. Mach Learn 2015; 99: 437–487.

20.

Ročková

. Bayesian estimation of sparse signals with a continuous spike-and-slab prior. Ann Stat 2018; 46: 401–437.

21.

Ročková

George

. The spike-and-slab lasso. J Am Stat Assoc 2018; 113: 431–444.

22.

Wang

Sarkar

Carbonetto

, et al. A simple new approach to variable selection in regression, with application to genetic fine mapping. J R Stat Soc Ser B: Stat Methodol 2020; 82: 1273–1300.

23.

Ročková

George

. EMVS: the EM approach to Bayesian variable selection. J Am Stat Assoc 2014; 109: 828–846.

24.

Banerjee

Mukherjee

Sun

. Adaptive sparse estimation with side information. J Am Stat Assoc 2020; 115: 2053–2067.

25.

Banerjee

Mukherjee

Dutta

, et al. A large-scale constrained joint modeling approach for predicting user activity, engagement, and churn with application to freemium mobile games. J Am Stat Assoc 2020; 115: 538–554.

26.

Bedrick

Christensen

Johnson

. A new perspective on priors for generalized linear models. J Am Stat Assoc 1996; 91: 1450–1460.

27.

Korte

Farlow

. The advantages and limitations of trait analysis with GWAS: a review. Plant Methods 2013; 9: 1–9.

28.

Cantor

Lange

Sinsheimer

. Prioritizing GWAS results: a review of statistical methods and recommendations for their application. Am J Human Genet 2010; 86: 6–22.

29.

Ishwaran

Rao

. Detecting differentially expressed genes in microarrays using Bayesian model selection. J Am Stat Assoc 2003; 98: 438–455.

30.

Frühwirth-Schnatter

Wagner

. Bayesian variable selection for random intercept modeling of Gaussian and non-Gaussian data. Bayesian Stat 2011; 9: 165–200.

31.

Polson

Scott

Windle

. Bayesian inference for logistic models using Pólya–gamma latent variables. J Am Stat Assoc 2013; 108: 1339–1349.

32.

Hoff

. A first course in Bayesian statistical methods. 580. New York: Springer, 2009.

33.

Kolonel

Henderson

Hankin

, et al. A multiethnic cohort in Hawaii and Los Angeles: baseline characteristics. Am J Epidemiol 2000; 151: 346–357.

34.

Murphy

Park

Thompson

, et al. Nicotine N-glucuronidation relative to N-oxidation and C-oxidation and UGT2B10 genotype in five ethnic/racial groups. Carcinogenesis 2014; 35: 2526–2533.

35.

Baurley

Edlund

Pardamean

, et al. Genome-wide association of the laboratory-based nicotine metabolite ratio in three ancestries. Nicotine Tob Res 2016; 18: 1837–1844.

36.

Barbieri

Berger

. Optimal predictive model selection. Ann Stat 2004; 32: 870–897.

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SIGHR: Side information guided high-dimensional regression

Abstract

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