The Generalized Higher Criticism for Testing SNP-Set Effects in Genetic Association Studies

<p>It is of substantial interest to study the effects of genes, genetic pathways, and networks on the risk of complex diseases. These genetic constructs each contain multiple SNPs, which are often correlated and function jointly, and might be large in number. However, only a sparse subset of SNPs in a genetic construct is generally associated with the disease of interest. In this article, we propose the generalized higher criticism (GHC) to test for the association between an SNP set and a disease outcome. The higher criticism is a test traditionally used in high-dimensional signal detection settings when marginal test statistics are independent and the number of parameters is very large. However, these assumptions do not always hold in genetic association studies, due to linkage disequilibrium among SNPs and the finite number of SNPs in an SNP set in each genetic construct. The proposed GHC overcomes the limitations of the higher criticism by allowing for arbitrary correlation structures among the SNPs in an SNP-set, while performing accurate analytic <i>p</i>-value calculations for any finite number of SNPs in the SNP-set. We obtain the detection boundary of the GHC test. We compared empirically using simulations the power of the GHC method with existing SNP-set tests over a range of genetic regions with varied correlation structures and signal sparsity. We apply the proposed methods to analyze the CGEM breast cancer genome-wide association study. Supplementary materials for this article are available online.</p

Demographic and exposure characteristics of mother-newborn pairs.

a<p>For 2003, 1 US dollar was equal to 4.07 Poland Zlotych (PLN).</p>b<p>Reported taking at least one smoked, grilled or barbequed food >twice/wk.</p>c<p>Drank at least one glass of wine, beer, or liquor per day during pregnancy.</p

The observed and predicted individual gestational Σ8 c-PAH exposure using semi-parametric mixed effects model^a.

<p>a. Black, open circle represents the observed concentration of Σ8 c-PAHs. Black line represents the pooled cohort mean during the entire monitoring period. Three persons were randomly selected to demonstrate estimated personal Σ8 c-PAHs exposure during her entire pregnancy period (in color). Based on the semi-parametric mixed effects model, Pearson's correlation coefficients between observed vs. predicted prenatal exposure were 0.91, 0.98 and 0.96 for the third, sixth and the eighth month.</p

Correlation between fetal growth ratio with other anthropometric indicators^a.

a<p>Severity was defined as non-case (≥85%), mild (80–84.99%), moderate (75–79.99%), and severe (<75%) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0035464#pone.0035464-Kramer2" target="_blank">[46]</a>.</p>b<p>Sample size is reduced from 344 to 342 because two newborns had gestational age of 43 and 29 weeks, which fell outside the plausible range <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0035464#pone.0035464-Malinowski1" target="_blank">[34]</a>.</p>**<p>Test of linear trend with increasing severity of FGR, p<0.001.</p

Mixed Effects Model Estimated ln-unit Σ8 C-PAH Exposure and Their Effects on Ponderal Index.

<p>The ln Σ8 c-PAHs effects on the outcome was estimated as a mean effect per trimester-wise exposure and 95% confidence interval.</p

Mixed Effects Model Estimated ln-unit Σ8 C-PAH Exposure and Their Effects on Fetal Growth Ratio.

<p>The ln Σ8 c-PAHs effects on FGR was estimated as a mean effect per trimester-wise exposure and 95% confidence interval.</p

Semi-Parametric Mixed Model Estimated ln-Unit Σ8 C-PAH Exposure and Their Point-Wise Effects on Cephalization Index.

<p>Exposure was estimated using semi-parametric mixed effects model. Figure shows continuous, point-wise effect throughout the trimester based on functional linear model. The bold line shows regression coefficient per natural-log (ln) unit exposure to airborne PAHs. The dotted lines show point-wise 95% confidence interval.</p

Mixed Effects Model Estimated ln-unit Σ8 C-PAH Exposure and Their Effects on Cephalization Index.

<p>The ln Σ8 c-PAHs effects on the outcome was estimated as a mean effect per trimester-wise exposure and 95% confidence interval.</p

Power, the causal SNP and the genotyped SNPs in scenario B2 based on the <i>ASAH1</i> gene.

<p>The top plot shows the power (<i>y</i>-axis) of each method over the locations (<i>x</i>-axis) of the causal SNPs. The triangles in the plot are the locations of the genotyped SNPs. The bar-plot in the middle shows the MAFs of all SNPs. The bottom plot shows the LD structure of the 154 SNPs downloaded from the HapMap project.</p

Empirical type I error rates at the significant level of 0.05 for LKM and PCA.

<p>The type-I error rates significantly different from the nominal type-I error level are highlighted by using italics font.</p