Simulated gene expression data for demonstrating the features of Bayenet.
data("dat")dat consists of four components: X, Y, clin, coef.
The data model for generating Y
Use subscript \(i\) to denote the \(i\)th subject. Let \((Y_{i}, X_{i}, clin_{i})\) (\(i=1,\ldots,n\)) be independent and identically distributed random vectors. \(Y_{i}\) is a continuous response variable representing the cancer outcome and disease phenotype. \(X_{i}\) is the \(p\)--dimensional vector of genetic factors. The clinical factors is denoted as the \(q\)-dimensional vector \(clin_{i}\). The \(\epsilon\) follows some heavy-tailed distribution. Considering the following model: $$Y_{i} = \alpha_{0} + \sum_{k=1}^{q}\gamma_{k}C_{ik}+\sum_{j=1}^{p}\beta_{j}X_{ij}+\epsilon_{i},$$ where \(\alpha_{0}\) is the intercept, \(\gamma_{k}\)'s and \(\beta_{j}\)'s are the regression coefficients corresponding to effects of clinical factors and genetic variants, respectively. Denote \(\gamma=(\gamma_{1}, \ldots, \gamma_{q})^{T}\), \(\beta=(\beta_{1}, \ldots, \beta_{p})^{T}\). Then model can be written as $$Y_{i} = C_{i}\gamma + X_{i}\beta + \epsilon_{i}.$$
Bayenet