Mixed effects modeling of radiotherapy in combination with immune checkpoint blockade or inhibitors of the DNA damage response pathway

Dosage optimization to maximize efficacy and minimize toxicity is a potential issue when administering radiotherapy (RT) in combination with immune checkpoint blockade (ICB) or inhibitors of the DNA Damage Response Pathway (DDRi) in the clinic. Preclinical models and mathematical modeling can help identify ideal dosage schedules to observe beneficial effects of a tri-therapy. The aim of this study is to describe a mathematical model to capture the impact of RT in combination with inhibitors of the DNA Damage Response Pathway or blockade of the immune checkpoint protein - programmed death ligand 1 (PD-L1). This model describes how RT mediated activation of antigen presenting cells can induce an increase in cytolytic T cells capable of targeting tumor cells, and how combination drugs can potentiate the immune response by inhibiting the rate of T cell exhaustion. The model was fitted using preclinical data, where MC38 tumors were treated in vivo with RT alone or in combination with anti-PD-L1 as well as with either olaparib or the ataxia telangiectasia mutated (ATM) inhibitor-AZD0156. The model successfully described the observed data and goodness-of-fit, using visual predictive checks also confirmed a successful internal model validation for each treatment modality. The results demonstrated that the anti-PD-L1 effect in combination with RT was maximal in vivo and any additional benefit of DDRi at the given dosage and schedule used was undetectable. Model fit results indicated AZD0156 to be a more potent DDRi than olaparib. Simulations of alternative doses indicated that reducing efficacy of anti-PD-L1 by 68% would potentially provide evidence for a benefit of ATM inhibition in combination with ICB and increase the relative efficacy of tri-therapy.