A mathematical model for the quantification of a patient’s sensitivity to checkpoint inhibitors and long-term tumour burden

Abstract

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.

Early prediction of clinical response to checkpoint inhibitor therapy in human solid tumors through mathematical modeling

“…These values are depicted in Figure 3 . These results suggest that, while Λ and µ give significantly separated classification ranges for partial/complete response versus stable/progressive disease, the specific value of the binary classification threshold is likely a function of the unique disease-drug combination used, as observed in our prior studies ( Butner et al, 2021 ). This point was explored further through a ‘leave-one-cancer-type-out’ validation study within the calibration cohort, wherein one cancer type was removed from the calibration cohort and used as validation against the parameter ranges in the reduced calibration set obtained from Borghaei et al, 2015 ; Antonia et al, 2015 ; Le et al, 2015 ; Motzer et al, 2015 ; Powles et al, 2014 ; and Topalian et al, 2012 .…”

Current Landscape and Future Directions of Biomarkers for Immunotherapy in Hepatocellular Carcinoma

“…Mathematical modeling is one approach to bridge the scientific knowledge gaps that exist for these interactions. Butner et al 59 , 60 have recently shown in a series of papers that ICI response can be modeled on “super parameters” that describe the “Anti-tumor immune state”, the “tumor cell kill rate” of ICI, and the tumor proliferation rate. The investigators demonstrated that some of these super parameters could be estimated by taking measurements of the tumor volume from standard computed tomography (CT) scans over time, and that these could be used to predict outcomes and long-term benefits of ICI in many solid tumors.…”

The Role of the Immune Response in Brain Metastases: Novel Imaging Biomarkers for Immunotherapy

“…It is was initially suggested that the interaction of radiation and ICI can cause a temporary increase in size and edema where SRS was given prior to ICI in some patients, but other studies with the same histology and agents have not reproduced this, showing instead a gradually declining volume of edema and tumor with response ( 56 , 57 ). A recent paper used a mathematical model of immunotherapy efficacy based on conventional anatomic imaging to examine the response to ICI (ipilimumab and nivolumab) amongst patients with BM from different clinical trials ( 58 ). The BM growth rate at first restaging was as accurate as the retrospective determination of immune response at predicting response, and no additional imaging beyond the clinical structural scans were used.…”