Benchmark of all methods.

<p>cor denotes Pearson's product moment correlation coefficient, dcor distance covariance, hoeffd Hoeffding's D, MIC denotes MIC, novelTest.chisq is our test based on Pearson's test and novelTest.ext is our test based on extreme paths. Each plot shows the power (on the y-axis) against the MI (x-axis). We examine 8 different types of dependence: linear, quadratic, cubic, sine with period , , circle, step function and the dependence called "patchwork copula'' (<b>A–H</b>)</p

Diagrams explaining Equations 1 and 2 for , and (panel A) and (panel B) with the reference point at coordinates .

<p><b>A</b>: We define 3 regions I, II and III (black, red and blue points respectively). Region I has the least number of constraints and the number of admissible configurations is the number of possibilities to draw points from positions without replacement nor ordering: . The number of admissible configurations for region II is given by the number of rows available and the number of columns which remain to be filled according to . Region III has the remaining points freely distributed, yielding admissible configurations. <b>B</b>: In the case we add an additional region of points exactly at distance (green points). There can be such points. Region I has size and admissible configurations with the number of points strictly inside the square of distance . Region IIa and IIb are symmetric and handled analogous to region II in panel A with and . Region III has admissible configurations analogous to panel A.</p

Performance on WHO data.

<p>novelTest.ext denotes our test based on extreme paths, dcor distance covariance and hoeffd Hoeffding's D. All methods were applied to all comparison between pairwise variables which had Pearson's product moment correlation coefficient near zero to exclude linear relationships. Only pairwise complete observations were used as most methods cannot handle missing vallues. All comparisons include ate least 81 datapoints. In total we compare all 3 methods on 2971 variable pairs.</p

Interaction effects calculated by multiple linear regression.

<p>This schematic visualization of second order linear regression models interaction effects. The diagram of the linear regression model includes two main covariates (strain <i>H</i> and stimulation with <i>Γ</i>) and their interaction covariate <i>H∶Γ</i>. The main covariates can assume two values (<i>H</i>: C57BL/6 or BALB/c; <i>Γ</i>: IFN-γ stimulation or no stimulation). The arrows indicate the estimated effects β. The pink and turquoise arrows reflect the aggravating or alleviating interaction effects as deviations from the additive model. A second order linear model can dissect the effects arising from two perturbations and their interaction by looking at the magnitude and significance of its regression covariates. Most importantly, the interaction covariate can indicate either an alleviating (weaker than expected from the single intervention effects) or aggravating (stronger than expected) interaction. The linear model includes two main covariates <i>H</i> and <i>Γ</i> and their interaction covariate <i>Η∶Γ</i>.</p

Additional file 2 of Joint analysis of PK and immunogenicity outcomes using factorization model − a powerful approach for PK similarity study

Additional file 2

Additional file 1 of Joint analysis of PK and immunogenicity outcomes using factorization model − a powerful approach for PK similarity study

Additional file 1

Experimental setup.

<p>Experimental setup.</p

Eruption plot.

<p>A: Effect size is displayed along the x-axis at log₂ scale and the y-axis shows the negative log₁₀ p-value. The vertical blue lines indicate 1.5 fold up and down-regulation and the horizontal blue line indicates a significance of 0.05 after Bonferroni adjustment. They bound the regions of biological interest (ROI), which are characterized by a sufficiently high effect, and a sufficiently low p-value. I.e., biologically interesting effects are found in the top left and the top right segment of the plot. Each gene is represented by an arrow comparing the effect size and significance estimate of a covariate (the interaction covariate <i>H∶Γ</i> in this case) between Model 1 (arrow tail) to Model 2 (arrow head). The details of Models 1 and 2 are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091840#pone-0091840-t002" target="_blank">Table 2</a>. Black and grey arrows represent genes completely contained within ROI and excluded completely from ROI, respectively. Red and blue arrows represent genes that are located within ROI solely in Model 1 and Model 2, respectively. B: Density plot of the p-values of Model 1 (red) and Model 2 (green). The dashed lines indicate the median of each density.</p

Schematic visualization for the interpretation of the eruption plot.

<p>The results of two models can be compared in the eruption plot. The arrows of an eruption plot can have different sizes and directions. This scheme helps to interpret the arrow. Effect size is displayed along the x-axis and the significance on the y-axis. The red area shows the region of interest (ROI).</p

Cluster and pathway analysis.

<p>A: the effect estimates of Model 3 were subjected to a hierarchical cluster analysis. Genes are displayed in the rows, which showed a significant global effect (F-test p-value <0.05 after FDR correction and at least one of the covariates having +/−1.5 fold change). The three columns are the covariates <i>Η</i>, <i>Γ</i>, and <i>Η∶Γ</i>. The column <i>strain</i> shows differences between C57BL/6 and BALB/c, up-regulation shown in red and down-regulation shown in green. The column <i>Γ</i> shows in red up-regulation in BALB/c and in green down-regulation upon IFN-γ stimulation. The third column helps to distinguish alleviating and aggravating effects. Aggravating effects are represented in pink and alleviating effects in turquoise. P-values are plotted separately in a heatmap. The order of the genes is given by the effect estimate clustering. P-values are given in −log₁₀ scale and start from 0 displayed in colors ranging from blue to white. B: The results of a pathway enrichment analysis of cluster 6 as a bar plot. The direction of regulation of the genes of cluster 6 is indicated by the color bar. Gene Ontology ‘Biological Process’ terms and KEGG pathway categories (p<0.01) are sorted from bottom (most significant) to top. To reduce redundancy, similar terms are represented by the most significant and specific term. For complete list of functional annotations see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091840#pone.0091840.s010" target="_blank">Table S2</a>. The right side shows the results of a TFBS analysis of this gene cluster. The two most significantly represented TFBS are given by the name of the transcription factor, the motif, and the p-value.</p