A large proportion of patients with cancer are unresponsive to treatment with immune checkpoint blockade and other immunotherapies. Here, we report a mathematical model of the time course of tumour responses to immune checkpoint inhibitors. The model takes into account intrinsic tumour growth rates, the rates of immune activation and of tumour–immune cell interactions, and the efficacy of immune-mediated tumour killing. For 124 patients, four cancer types and two immunotherapy agents, the model reliably described the immune responses and final tumour burden across all different cancers and drug combinations examined. In validation cohorts from four clinical trials of checkpoint inhibitors (with a total of 177 patients), the model accurately stratified the patients according to reduced or increased long-term tumour burden. We also provide model-derived quantitative measures of treatment sensitivity for specific drug–cancer combinations. The model can be used to predict responses to therapy and to quantify specific drug–cancer sensitivities in individual patients.

大部分癌症患者对免疫检查点阻断和其他免疫疗法的治疗无反应。在这里，我们报告了肿瘤对免疫检查点抑制剂反应时间过程的数学模型。该模型考虑了内在的肿瘤生长速率、免疫激活速率和肿瘤-免疫细胞相互作用的速率，以及免疫介导的肿瘤杀伤效果。对于 124 名患者、四种癌症类型和两种免疫治疗药物，该模型可靠地描述了所有不同癌症和所检查药物组合的免疫反应和最终肿瘤负荷。在来自四项检查点抑制剂临床试验（共有 177 名患者）的验证队列中，该模型根据减少或增加的长期肿瘤负荷准确地对患者进行分层。我们还提供模型衍生的特定药物-癌症组合治疗敏感性的定量测量。该模型可用于预测对治疗的反应并量化个体患者的特定药物-癌症敏感性。