IUSMMT: Survival mediation analysis of gene expression with multiple DNA methylation exposures and its application to cancers of TCGA
Fig 2
An overview of IUSMMT for examining the mediation effect in survival model.
Here, a = (α1, …, αK) is the vector of effect sizes of a set of DNA methylation CpG sites (i.e., the exposures) on the gene expression level (i.e., the mediator), with K the number of CpG sites within that gene; and β is the expression-survival effect; S indicates the total number of genes; n denotes the sample size. (A) IUSMMT first separately evaluates the significance of a and β, and calculates Pα and Pβ; where Pα is obtained by a variance component-based score test within the linear mixed-effects model by assuming each of a following a mean-zero normal distribution with an unknown variance τ2, while Pβ is yielded through the Wald test within the Cox linear mixed-effects model. Then, IUSMMT takes the two P-values as input. (B) The hypothesis testing of mediation effect is to examine whether the product of α and β is zero or not (i.e., H0: αβ = 0) and can be divided into three composite null sub-hypotheses. (C) In the three-component mixture null distribution, κ10 stands for the probability that the exposures are related to the mediator in the exposure-mediator model but the mediator is not associated with the survival outcome in the mediator-outcome model; κ01 stands for the probability that the exposures are not related to the mediator in the exposure-mediator model but the mediator is associated with the survival outcome in the mediator-outcome model; κ00 stands for the probability that the exposures are not related to the mediator in the exposure-mediator model and the mediator is not associated with the survival outcome in the mediator-outcome model. The definition of other notations used in B and C can be found in the Materials and Methods section.