Some characteristics of the study subjects belonging to the CLI dataset.

<p>Some characteristics of the study subjects belonging to the CLI dataset.</p

Gene-gene (SNP-SNP) joint relevance and interactions for asthma susceptibility.

*<p>Interaction terms were forced into logistic regression using the enter method. The main effects entered are indicated with underscore.</p>**<p>Posterior probability of joint relevance.</p>***<p>P-value and exp(B) values corresponding to the interaction terms in logistic regression using continuous variables.</p

The posterior probability of strong relevance of predictors for each target and for a multi-target case based on the CLI data set.

<p>Target variables: IgE level - <i>IgE</i>, Eosinophil level – <i>Eos</i>, Rhinitis – <i>Rhi</i>, Asthma – <i>Ast</i>.</p><p>“<i>Exist</i>” denotes the probability of strong relevance with respect to a given target.</p><p>“<i>Only</i>” denotes posteriors for strong relevance to exactly one of the targets.</p><p>“<i>OtherThan</i>”denotes posteriors for strong relevance to any other target than the one specified by the subcolumn.</p><p>“<i>AP</i>” column contains an approximation of multi-target strong relevance based on the individual strong relevance posteriors of the targets.</p><p>“<i>MT</i>” denotes the posterior of multi-target strong relevance.</p

Illustration of different dependency types between variables in a Bayesian Network structure.

<p><i>Pairwise relevance relations</i>: Direct causal relevance (e.g., Y1 and SNP1 have common edge), Transitive causal relevance (e.g., there are two directed paths between Y3 and SNP5), Confounded relevance (e.g., Y2 and SNP3 have a common ancestor SNP1), Association (e.g., Y1 and SNP1, because SNP1 is directly related to Y1; Y3 and SNP5, because SNP5 is transitively related to Y3; Y2 and SNP3, because they are in a confounded relation), Pure interactionist relevance (e.g., Y1 and SNP7 have common child), Strong relevance (e.g., Y1 and SNP1, because SNP1 is directly related to Y1; Y1 and SNP7, because they are in pure interaction). <i>Relevance of variable sets</i>: Strong relevance (e.g., the variable set consisting of Y2's parents, its children, and the other parents of its children is {Y1, SNP9, Y3, SNP7}). <i>Relevance for multiple target variables</i>: Strong relevance to one or more targets (e.g., the variable set consisting of {Y1,Y2,Y3}'s parents, its children, and the other parents of its children is {SNP1, SNP4, SNP7, SNP9}). <i>Red nodes</i>: potential target variables, <i>Green nodes</i>: SNP variables.</p

The posterior probability of strong relevance for the most relevant SNPs in case of RA and CLI data.

*<p><i>RA – Asthma</i>: RA dataset, Asthma as target.</p><p><i>RA – Multitarget</i>: RA dataset, Asthma and Rhinitis as targets.</p>**<p><i>CLI – Asthma</i>: CLI dataset, Asthma as target.</p><p><i>CLI – Multitarget</i>: CLI dataset, IgE level-Eosinophil level-Rhinitis-Asthma as targets.</p

The most probable univariate (MBM), bivariate (2-MBS), trivariate (3-MBS) subsets of variables (Asthma dataset).

<p>Relevant SNPs having high or moderately high posteriors, i.e. high probability of being a member of the Markov blanket (MBM) of the target variable <i>Asthma</i> (<b>A</b>). Relevant SNP sets of size 2 (<b>B</b>); and of size 3 (<b>C</b>) indicating partial strong relevance. 2-MBS and 3-MBS denote the k = 2 and k = 3 sized subsets of Markov blanket sets. A high <i>k</i>-MBS posterior of a set of SNPs indicates their joint relevance and possible interactions between the SNPs.</p

Hypothesized connection between FRMD6 and Birc5 in the conserved Hippo pathway.

<p>Hypothetic hippo pathway components in mammals are shown in various colors, with pointed and blunt arrowheads indicating activating and inhibitory interactions, respectively. The pathway regulates transcriptions of several genes, among others that of <i>Birc5</i>. Based on <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033573#pone.0033573-Zhao1" target="_blank">[36]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033573#pone.0033573-Heallen1" target="_blank">[37]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033573#pone.0033573-Dong1" target="_blank">[38]</a>. According to this pathway lower level of <i>FRMD6</i> might be associated with higher level of <i>Birc5</i>, as was found in the lung of the animal model of asthma.</p

The posterior probability of strong relevance of predictors for each target and for a multi-target case based on the CLI data set.

<p>Posterior probabilities for strong relevance to Asthma, Rhinitis, Eosinophil and IgE level are indicated by different columns. Posteriors of joint strong relevance, i.e. multi-target relevance and its approximation based on the individual posteriors for strong relevance with respect to Asthma, Rhinitis, Eosinophil and IgE level are denoted by orange and blue curves, respectively. The approximation assumes independence between the targets, whereas the multi-target posterior accounts for the possible dependencies between the targets.</p

The a posteriori probability that a SNP is directly relevant (D-Relevant), associated, strongly relevant (S-Relevant), transitive or in pure interaction with asthma using the RA data set.

<p>The a posteriori probability that a SNP is directly relevant (D-Relevant), associated, strongly relevant (S-Relevant), transitive or in pure interaction with asthma using the RA data set.</p

A possible dependency model in asthma.

<p>An example for a possible transitive association between IgE and Asthma. Although there is a possible direct relationship, IgE level may relate to asthma indirectly via eosinophil or a presence of allergy.</p