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196 Journey into genetics and genomicsFIGURE 18.1Causal mediation diagram: S is a SNP; G is a mediator, e.g., gene expression;Y is an outcome; and X a vector of covariates.tial interest to develop statistical methods for risk prediction using massiveNGS data.18.4.3 Integration of different ’omics data and mediationanalysisAn important emerging problem in genetic and genomic research is how tointegrate different types of genetic and genomic data, such as SNPs, geneexpressions, DNA methylation data, to improve understanding of disease susceptibility.The statistical problem of jointly modeling different types of geneticand genomic data and their relationships with a disease can be describedusing a causal diagram (Pearl, 2001) and be framed using a causal mediationmodel (VanderWeele and Vansteelandt, 2010) based on counterfactuals. Forexample, one can jointly model SNPs, gene expressions and a disease outcomeusing the causal diagram in Figure 18.1, with gene expression serving as apotential mediator.To formulate the problem, assume for subject i ∈{1,...,n}, an outcomeof interest Y i is dichotomous (e.g., case/control), whose mean is associatedwith q covariates (X i ), p SNPs (S i ), mRNA expression of a gene (G i ) andpossibly interactions between the SNPs and the gene expression aslogit{Pr(Y i =1|S i ,G i , X i )} = X ⊤ i β X + S ⊤ i β S + G i β G + S ⊤ i G i β GS , (18.2)where β X ,β S ,β G ,β GS are the regression coefficients for the covariates, theSNPs, the gene expression, and the interactions of the SNPs and the gene