Understanding mechanisms of resistance to PARP inhibitors (PARPi) represents a clinically relevant goal that is addressed in this study using a novel methodology. A framework has been developed formulating a mathematical model accounting for intrinsic resistance to the PARPi olaparib, identified by fitting the model to tumour growth metrics from breast cancer patient-derived xenograft (PDX) data. Pre-treatment transcriptomic profiles were used together with the calculated resistance in order to extract baseline biomarkers of resistance to olaparib, as well as potential combination targets. Predicted biomarkers were then assessed for validity and novelty through differential survival analysis, modelling of combination data and pathway enrichment analysis. The model provided both a classification of responses, as well as a continuous description of resistance, allowing for more robust biomarker associations and capturing the variability observed. 36 resistance gene markers were identified, including multiple Homologous Recombination Repair (HRR) pathway genes that are a key part of olaparib’s mechanism-of-action. High levels of WEE1 expression were also linked to resistance, highlighting an opportunity for combining a PARPi with the WEE1 inhibitor. This framework facilitates a fully automated way of capturing response to treatment, including intrinsic resistance, and accounts for the biological and pharmacological response variability captured within PDX studies and hence provides a precision medicine approach.