eQTL analysis with bimodal gene expression

Question

[agatawesol]

I am trying to find eQTLs for a gene with a bimodal expression pattern: for a group of individuals the gene is not expressed and for the remaining individuals it is normally distributed. Does anyone know of an appropriate data transformation, or what type of model to use for the linear regression? I assume the group of patients with zero values would cause troubles in a normal linear regression test, because then my data as a whole is not normally distributed?