Fig 1.
Statistical framework of the survival mediation analysis with multiple exposures, one mediator and one censored outcome.
The mediation analysis involves in multiple DNA methylations (M) as exposures, one gene expression (G) as the mediator and one survival time as the outcome (T). There are two types of effects from M to T: the direct effect of M on T (i.e., γDE) and the indirect effect of M on T via the intermediate variable G. The indirect effect represents the amount of mediation coming from two sources: the effect from M to G (i.e., α) and the effect from G to T (i.e., β).
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.
Table 1.
Estimated and true proportion parameters (mean and standard deviation) in the three-component mixture null distribution under the five simulation scenarios with different sample sizes and numbers of mediation tests.
Fig 3.
The QQ plot (A) and the average power curve (B-C) for IUSMMT and IUT. The QQ plot (A) is under the scenario of sparse nulls. The average power curve is calculated when the mediation strength parameter τ2 increases under the sparse alternative (B) and the dense alternative (C). Here, n = 400, β = 0.3, and τ2 = 0.01, 0.02, 0.04, 0.05 or 0.10 at the x-axis. The magnitude of τ2 quantifies the strength of association between DNA methylation CpG sites and gene expression. In B and C, the number of genes (i.e., mediators) was set to 104.
Fig 4.
Upset plot and heatmap plot of the P-values (A-F). In the heatmaps of γTE (A) and γDE (C), the color of each box indicates the magnitude of the P-value. The number in the comment part represents the P-value processed by the negative logarithmic transformation. The darker the color, the smaller the P-value. In the Upset plots of γTE, β, γDE, IUT, and IUSMMT, each bar shows the number of shared genes. In these Upset plots, the blue part represents cancer type-specific genes, and the red, green, orange, and purple parts represent genes shared in two, three, four and five types of cancers. (F) The heatmap of the P-values of the 14 overlapped genes across all the cancers. The color of each box indicates the magnitude of the P-value. The number in the comment part represents the P-value processed by the negative log transformation, the darker the color, the smaller the P-value.
Table 2.
Number of associated regions of DNA methylation CpG sites and genes identified in the survival mediation analysis.
Table 3.
Estimated proportion parameters in the three-component mixture null distribution for 10 TCGA cancers.
Table 4.
Direction of the effect of methylations on expression and the effect of expression on the survival risk of cancers for identified genes with mediating influence.