Cancer treatments can be highly toxic and frequently only a subset of the patient population will benefit from a given treatment. Tumour genetic makeup plays an important role in cancer drug sensitivity. We suspect that gene expression markers could be used as a decision aid for treatment selection or dosage tuning. Using in vitro cancer cell line dose-response and gene expression data from the Genomics of Drug Sensitivity in Cancer (GDSC) project, we build a dose-varying regression model. Unlike existing approaches, this allows us to estimate dosage-dependent associations with gene expression. We include the transcriptomic profiles as dose-invariant covariates into the regression model and assume that their effect varies smoothly over the dosage levels. A two-stage variable selection algorithm (variable screening followed by penalized regression) is used to identify genetic factors that are associated with drug response over the varying dosages. We evaluate the effectiveness of our method using simulation studies focusing on the choice of tuning parameters and cross-validation for predictive accuracy assessment. We further apply the model to data from five BRAF targeted compounds applied to different cancer cell lines under different dosage levels. We highlight the dosage-dependent dynamics of the associations between the selected genes and drug response, and we perform pathway enrichment analysis to show that the selected genes play an important role in pathways related to tumorigenesis and DNA damage response.