Human iPSC-derived somatic cells provide a powerful, renewable and reproducible tool for modeling cellular responses to external perturbation in vitro, especially for non-blood cell-types such as cardiomyocytes which are extremely challenging to collect and even then are typically only available post-mortem. We investigate using a panel of such cell lines to understand the genetic basis of interindividual differences in response to a specific chemotherapy drug, doxorubicin. Anthracycline-induced cardiotoxicity (ACT) is a key limiting factor in setting optimal chemotherapy regimes, with almost half of patients expected to develop congestive heart failure given high doses. However, the genetic basis of sensitivity to anthracyclines remains unclear. We created a panel of human iPSC-derived cardiomyocytes from 45 individuals and performed RNA-seq after 24h exposure to varying doxorubicin dosages. The transcriptomic response is substantial: the majority of genes are differentially expressed and over 6000 genes show evidence of differential splicing, the later driven by reduced splicing fidelity in the presence of doxorubicin. We show that inter-individual variation in transcriptional response is predictive of in vitro cell damage, which in turn is associated with in vivo ACT risk. We developed an efficient linear mixed model, suez, which detects 447 response-expression quantitative trait loci (QTLs). Combining suez with our RNA splicing quantification algorithm LeafCutter we find 42 response-splicing QTLs. These molecular response QTLs are enriched for lower p-values in ACT genome-wide association and enable prediction of cellular damage, supporting the in vivo relevance of our map of genetic regulation of cellular response to anthracyclines.