Table 2 Description of multi-omics models for estimating variance components.
From: Integrative multi-omics analysis to gain new insights into COVID-19
Analysis scope | Model | Description |
|---|---|---|
Model 1. Single-omics analysis: estimate variance components using omics layers separately | \(\mathbf{Y}=\mathbf{E}+\varvec{\upepsilon}\) | \(\mathbf{Y}\) is the vector of COVID-19 outcome, \(\mathbf{G}\) is the vector of genome effect, and \(\varvec{\upepsilon}\) is the vector of residuals, \(\mathbf{T}\) is the vector of transcriptome effect, \(\mathbf{M}\) is the vector metabolome effect, \(\mathbf{E}\) is the vector of exposome effect. G\(\mathbf{x}\mathbf{E}\) is the vector of gene by environment interaction, T\(\mathbf{x}\mathbf{E}\) is the vector of transcriptome by environment interaction, M\(\mathbf{x}\mathbf{E}\) is the vector of metabolome by environment interaction. r\(\mathbf{G},\mathbf{E}\) is the vector of covariance between genome and exposome, r\(\mathbf{T},\mathbf{E}\) is the vector of covariance between genome and exposome, and r\(\mathbf{M},\mathbf{E}\) is the vector of covariance between metabolome and exposome. G\(\mathbf{x}\mathbf{T}\) is the vector of genome by transcriptome interaction, r\(\mathbf{G},\mathbf{T}\) is the vector of covariance between genome and transcriptome. T\(\mathbf{x}\mathbf{M}\) is the vector of transcriptome by metabolome interaction, r\(\mathbf{T},\mathbf{M}\) is the vector of covariance between transcriptome and metabolome. |
\(\mathbf{Y}=\mathbf{T}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{M}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{G}+\varvec{\upepsilon}\) | ||
Model 2: Pairwise omics analysis: joint analysis of genome, transcriptome, and metabolome | \(\mathbf{Y}=\mathbf{G}+\mathbf{T}+\varvec{\upepsilon}\) | |
\(\mathbf{Y}=\mathbf{G}+\mathbf{M}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{G}+\mathbf{E}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{T}+\mathbf{M}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{T}+\mathbf{E}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{M}+\mathbf{E}+\varvec{\upepsilon}\) | ||
Model 3. Joint model fitting each omics data type with exposome | \(\mathbf{Y}=\mathbf{G}+\mathbf{E}+\mathbf{G}\mathbf{x}\mathbf{E}+\varvec{\upepsilon}\) | |
\(\mathbf{Y}=\mathbf{T}+\mathbf{E}+\mathbf{T}\mathbf{x}\mathbf{E}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{M}+\mathbf{E}+\mathbf{M}\mathbf{x}\mathbf{E}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{G}+\mathbf{E}+\mathbf{r}\mathbf{G},\mathbf{E}+\mathbf{G}\mathbf{x}\mathbf{E}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{T}+\mathbf{E}+\mathbf{r}\mathbf{T},\mathbf{E}+\mathbf{T}\mathbf{x}\mathbf{E}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{M}+\mathbf{E}+\mathbf{r}\mathbf{M},\mathbf{E}+\mathbf{M}\mathbf{x}\mathbf{E}+\varvec{\upepsilon}\) | ||
Model 4. Joint models fitting genome and transcriptome and their interplay | \(\mathbf{Y}=\mathbf{G}+\mathbf{T}+\varvec{\upepsilon}\) | |
\(\mathbf{Y}=\mathbf{G}+\mathbf{T}+\mathbf{E}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{G}+\mathbf{T}+\mathbf{G}\mathbf{x}\mathbf{T}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{G}+\mathbf{T}+\mathbf{r}\mathbf{G},\mathbf{T}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{G}+\mathbf{T}+\mathbf{G}\mathbf{x}\mathbf{T}+\mathbf{E}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{G}+\mathbf{T}+\mathbf{G}\mathbf{x}\mathbf{T}+\mathbf{r}\mathbf{G},\mathbf{T}+\mathbf{E}+\varvec{\upepsilon}\) | ||
Model 5. Joint models fitting transcriptome and metabolome and their interplay | \(\mathbf{Y}=\mathbf{T}+\mathbf{M}+\varvec{\upepsilon}\) | |
\(\mathbf{Y}=\mathbf{T}+\mathbf{M}+\mathbf{E}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{T}+\mathbf{M}+\mathbf{T}\mathbf{x}\mathbf{M}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{T}+\mathbf{M}+\mathbf{r}\mathbf{T},\mathbf{M}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{T}+\mathbf{M}+\mathbf{T}\mathbf{x}\mathbf{M}+\varvec{\upepsilon}\) | ||
\(\mathbf{Y}=\mathbf{T}+\mathbf{M}+\mathbf{T}\mathbf{x}\mathbf{M}+\mathbf{r}\mathbf{T},\mathbf{M}+\mathbf{E}+\varvec{\upepsilon}\) |
