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. 2018 Apr;10(1):117-138.
doi: 10.1007/s12561-017-9189-9. Epub 2017 Mar 24.

A Powerful Test for SNP Effects on Multivariate Binary Outcomes using Kernel Machine Regression

Clemontina A Davenport  1 , Arnab Maity  2 , Patrick F Sullivan  3 , Jung-Ying Tzeng  4
Affiliations

A Powerful Test for SNP Effects on Multivariate Binary Outcomes using Kernel Machine Regression

Clemontina A Davenport et al. Stat Biosci. 2018 Apr.

Abstract

Evaluating multiple binary outcomes is common in genetic studies of complex diseases. These outcomes are often correlated because they are collected from the same individual and they may share common marker effects. In this paper, we propose a procedure to test for effect of a SNP-set on multiple, possibly correlated, binary responses. We develop a score-based test using a nonparametric modeling framework that jointly models the global effect of the marker set. We account for the nonlinear effects and potentially complicated interaction between markers using reproducing kernels. Our testing procedure only requires estimation under the null hypothesis and we use multivariate generalized estimating equations (GEEs) to estimate the model components to account for the correlation among the outcomes. We evaluate finite sample performance of our test via simulation study and demonstrated our methods using the CATIE antibody study data and the CoLaus Study data.

Keywords: IBS kernel; correlated binary responses; generalized estimating equations; kernel machine; nonparametric regression.

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Conflict of interest statement

The authors have no conflicts of interest to declare.

Figures

Fig. 1
Fig. 1
Power calculations for multivariate KMR (circle lines), univariate logistic KMR with Bonferroni correction (triangle lines), and PC GEE (plus lines) for sample size n = 200, number of SNPs p = 9 (solid lines) and p = 30 (dashed lines), and different correlations θ. The top panel (a)–(d) refers to Case 1 where the response is only correlated through the subject effects. The bottom panel (e)–(h) refers to Case 2 where the responses have correlation from shared marker effects. The effect of the SNPs is scaled by a.
Fig. 2
Fig. 2
Power calculations for multivariate KMR (circle lines), univariate logistic KMR with Bonferroni correction (triangle lines), and PC GEE (plus lines) for sample size n = 400, number of SNPs p = 9 (solid lines) and p = 30 (dashed lines), and different correlations θ. The top panel (a)–(d) refers to Case 1 where the response is only correlated through the subject effects. The bottom panel (e)–(h) refers to Case 2 where the responses have correlation from shared marker effects. The effect of the SNPs is scaled by a.
Fig. 3
Fig. 3
Estimated correlation matrices among SNPs for BTN2A1 (a) and POM121L2 (b) from the CATIE study, and HCRTR1 (c) from the CoLaus study.
See this image and copyright information in PMC

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