Different types of correlation coefficients when the variables <i>X</i> and <i>Y</i> are continuous, binary, or ordinal.

<p>Different types of correlation coefficients when the variables <i>X</i> and <i>Y</i> are continuous, binary, or ordinal.</p

The Q-Q plot of observed <i>p</i>-values versus expected <i>p</i>-values based on the multivariate test.

<p>The Q-Q plot of observed <i>p</i>-values versus expected <i>p</i>-values based on the multivariate test.</p

Simulation results for the empirical power with varied correlations <i>ρ</i> and genetic effect sizes (<i>e</i>₁, …, <i>e</i>₆).

<p>The <i>Latent</i> column is the power with the proposed method applied to 6 latent phenotypes. The <i>Mixed</i> column is the power with the proposed method applied to 6 observed phenotypes. The <i>Dichotomous</i> column is the power when the observed phenotypes are dichotomized. The <i>Continuous</i> column is the power when the phenotypes in mixed measurements are treated as continuous variables. The number of iterations is 10⁶ when all genetic effect sizes are zero and 10⁴ for other situations.</p

The correlations among the 6 FTND items.

<p>The correlations among the 6 FTND items.</p

The distributions of phenotypes: FTND 1, FTND 2, …, FTND 6, FTND total, and FTND total (Binary).

<p>FTND total (Binary) is derived from FTDN total according to whether FTND total score is less than 6 or not.</p

The relationship between the covariance <i>cov</i>[−2<i>log</i>(<i>p</i>_<i>u</i>), −2<i>log</i>(<i>p</i>_<i>v</i>)] and the correlation <i>ρ</i>.

<p>The title in each panel indicates the types of data simulated. The solid curve in each panel corresponds to our covariance estimates using <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169893#pone.0169893.e005" target="_blank">Eq (3)</a>. The dotted curves are the true covariances calculated from the simulated data.</p

The Q-Q plots of observed <i>p</i>-values versus expected <i>p</i>-values based on the marginal tests.

<p>The Q-Q plots of observed <i>p</i>-values versus expected <i>p</i>-values based on the marginal tests.</p

Comparison of empirical Power and Type-1 error rates of gene-based association tests for a quantitative trait simulated under models with interactions.

<p>TAS denotes the number of trait associated SNPs. Machine learning test is based on ensemble learning variation 1 with the following components: multiple linear regression, support vector machine with linear kernel and random forests with m_try = 1 and n_tree = 1000.</p><p>Comparison of empirical Power and Type-1 error rates of gene-based association tests for a quantitative trait simulated under models with interactions.</p

Comparison of empirical power and Type-1 error rates of gene-based association tests for simulated datasets assuming linkage equilibrium.

<p>DSL denotes the number of disease susceptibility markers. Machine learning test is based on ensemble learning variation 1 with the following components: logistic regression, support vector machine with linear kernel and random forests with m_try = 1 and n_tree = 1000.</p><p>Comparison of empirical power and Type-1 error rates of gene-based association tests for simulated datasets assuming linkage equilibrium.</p

Powerful Tests for Multi-Marker Association Analysis Using Ensemble Learning

<div><p>Multi-marker approaches have received a lot of attention recently in genome wide association studies and can enhance power to detect new associations under certain conditions. Gene-, gene-set- and pathway-based association tests are increasingly being viewed as useful supplements to the more widely used single marker association analysis which have successfully uncovered numerous disease variants. A major drawback of single-marker based methods is that they do not look at the joint effects of multiple genetic variants which individually may have weak or moderate signals. Here, we describe novel tests for multi-marker association analyses that are based on phenotype predictions obtained from machine learning algorithms. Instead of assuming a linear or logistic regression model, we propose the use of ensembles of diverse machine learning algorithms for prediction. We show that phenotype predictions obtained from ensemble learning algorithms provide a new framework for multi-marker association analysis. They can be used for constructing tests for the joint association of multiple variants, adjusting for covariates and testing for the presence of interactions. To demonstrate the power and utility of this new approach, we first apply our method to simulated SNP datasets. We show that the proposed method has the correct Type-1 error rates and can be considerably more powerful than alternative approaches in some situations. Then, we apply our method to previously studied asthma-related genes in 2 independent asthma cohorts to conduct association tests.</p></div