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This is especially important when variables are known to have non-linear and changing relationships between them. We applied Fisher's transformation to the correlations, so that they follow approximate normal distributions. Smooth terms were calculated with the smoothing ��s�� option of Smad family the ��gam�� function in the mgcv R package (Wood, 2011). The thin plate regression spline ��tp�� was used, which is a low rank isotropic smoother of any number of covariates. Smoothing parameter estimation of the independent variable (absolute TSS distance) was calculated with the Generalized Cross Validation (GCV) method. Penalized regression models gain computational efficiency by choosing a relatively small basis, known as k. By default, we set this value to 20. Although variations in the basis have a small impact on the model, we ensured that k-values were not so small to cause over-smoothing by using the ��gam.check�� function. P-values were computed by randomly re-shuffling 20,000 times in order to calculate the null distribution of the differencing variance estimator. Low P-values may indicate that the basis dimension is too low. We confirmed that all models had approximately normal residuals and that the values of the estimates divided by the residual variance (a.k.a k-index) were close to 1. Plots were created with the ggtools function implemented in the ggplot2 R package (Wickham, 2009). Literature search We used PubMed (McEntyre and Lipman, 2001) to search for most of the bibliography cited in this paper. Results Gene expression correlation with average methylation intensity We evaluated the relationship between DNA methylation and expression Laccase across more than 6200 genes in all the tumor and normal tissue samples (Supplementary Table 1). We observed significant learn more differences of absolute Pearson's correlation in all the five study groups (10% FDR; Table ?Table22 and Figure ?Figure3).3). Spearman's correlation reduced the level of significant datasets to 4 of 5 (10% FDR), since in this case the breast cancer dataset was not significant (Q-value = 0.214; Table ?Table2).2). Notably, most of these absolute values were higher in normal tissues than in cancer, except for the Lung Adenocarcinoma dataset. Similarly, the signed correlation values revealed significant Pearson's and Spearman's differences between tumor and normal samples in all study cohorts (FDR