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. 2018 Feb;42(1):64-79.
doi: 10.1002/gepi.22096. Epub 2018 Jan 3.

Inference on phenotype-specific effects of genes using multivariate kernel machine regression

Arnab Maity  1 , Jing Zhao  2 , Patrick F Sullivan  3 , Jung-Ying Tzeng  1   2   4   5
Affiliations

Inference on phenotype-specific effects of genes using multivariate kernel machine regression

Arnab Maity et al. Genet Epidemiol. 2018 Feb.

Abstract

We consider the problem of assessing the joint effect of a set of genetic markers on multiple, possibly correlated phenotypes of interest. We develop a kernel machine based multivariate regression framework, where the joint effect of the marker set on each of the phenotypes is modeled using prespecified kernel functions with unknown variance components. Unlike most existing methods that mainly focus on the global association between the marker set and the phenotype set, we develop estimation and testing procedures to study phenotype-specific associations. Specifically, we develop an estimation method based on the penalized likelihood approach to estimate phenotype-specific effects and their corresponding standard errors while accounting for possible correlation among the phenotypes. We develop testing procedures for the association of the marker set with any subset of phenotypes using a score-based variance components testing method. We assess the performance of our proposed methodology via a simulation study and demonstrate the utility of the proposed method using the Clinical Antipsychotic Trials of Intervention Effectiveness (CATIE) data.

Keywords: kernel machine; mixed models; multivariate regression; restricted maximum likelihood; variance components.

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Conflict of interest statement

The authors have no conflict of interest.

Figures

Figure 1
Figure 1
Results for estimation of hk(·) for k = 1 (left column), k = 2 (middle column) and k = 3 (right column) using different covariance settings for n = 100 and M = 9.
Figure 2
Figure 2
Results for estimation of hk(·) for k = 1 (left column), k = 2 (middle column) and k = 3 (right column) using different covariance settings for n = 200 and M = 9.
Figure 3
Figure 3
Results for estimation of hk(·) for k = 1 (left column), k = 2 (middle column) and k = 3 (right column) using different covariance settings for n = 200 and M = 30.
Figure 4
Figure 4
Simulation results for testing one h function (Scenario (A)). Displayed are the power of our test (shaded bars) along with SKAT test with Bonferroni correction (Non-shaded bars) for different settings with α = 0.05 (dashed horizontal line).
Figure 5
Figure 5
Simulation results for testing two h functions (Scenario (B)). Displayed are the power of our test (shaded bars) along with SKAT test with Bonferroni correction (Non-shaded bars) for different settings with α = 0.05 (dashed horizontal line).
Figure 6
Figure 6
Simulation results for testing two h functions when only one is significant (Scenario (C)). Displayed are the power of our test (shaded bars) along with SKAT test with Bonferroni correction (Non-shaded bars) for different settings with α = 0.05 (dashed horizontal line).
Figure 7
Figure 7
Simulation results for testing two h functions they have different directions of effect for different phenotypes (Scenario (D)). Displayed are the power of our test (shaded bars) along with SKAT test with Bonferroni correction (Non-shaded bars) for different settings with α = 0.05 (dashed horizontal line).
Figure 8
Figure 8
Estimation results of CATIE Antibody analysis. Displayed are the 95% simultaneous confidence intervals for point estimates of h1, h2 and h3 for different genotype combinations as present in the data set (sorted by their point estimate values). Estimates from the multivariate model and separate univariate models are displayed in the left and right columns, respectively.
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