The pursuit of precision oncology heavily relies on large-scale genomic and pharmacological data garnered from preclinical cancer model systems such as cell lines. While cell lines are instrumental in understanding the interplay between genomic programs and drug response, it well-established that they are not fully representative of patient tumors. Development of integrative methods that can systematically assess the commonalities between patient tumors and cell-lines can help bridge this gap. To this end, we introduce the Integrative Principal Component Regression (iPCR) model which uncovers both joint and model-specific structured variations in the genomic data of cell lines and patient tumors through matrix decompositions. The extracted joint variation is then used to predict patient drug responses based on the pharmacological data from preclinical models. Moreover, the interpretability of our model allows for the identification of key driver genes and pathways associated with the treatment-specific response in patients across multiple cancers. We demonstrate that the outputs of the iPCR model can assist in inferring both model-specific and shared co-expression networks between cell lines and patients. We show that iPCR performs favorably compared to competing approaches in predicting patient drug responses, in both simulation studies and real-world applications, in addition to identifying key genomic drivers of cancer drug responses.