A random coefficients model for regional co-expression associated with DNA copy number.

Regional co-expression refers to the phenomenon of contiguous genes exhibiting similar expression patterns. Among others, DNA copy number aberrations may be causally involved in regional co-expression. We propose a random coefficients model to explain regional co-expression from DNA copy number information, while modeling residual co-expression due to other causes by a correlated error structure. We show how the model parameters may be estimated (computationally efficient and consistently) from high-dimensional data, and suggest several robustifications of the estimation procedure. From the model we are able to assess whether there is a shared effect on expression levels due to the DNA copy number aberrations, but also whether this effect is homogeneous across genes. In two examples we use the proposed methodology to investigate the association between DNA copy number aberrations and regional co-expression.