Mathematical prediction of clinical outcomes in advanced cancer patients treated with checkpoint inhibitor immunotherapy

Abstract

We present a mechanistic mathematical model of immune checkpoint inhibitor therapy to address the oncological need for early, broadly applicable readouts (biomarkers) of patient response to immunotherapy. The model is built upon the complex biological and physical interactions between the immune system and cancer, and is informed using only standard-of-care CT. We have retrospectively applied the model to 245 patients from multiple clinical trials treated with anti–CTLA-4 or anti–PD-1/PD-L1 antibodies. We found that model parameters distinctly identified patients with common (n = 18) and rare (n = 10) malignancy types who benefited and did not benefit from these monotherapies with accuracy as high as 88% at first restaging (median 53 days). Further, the parameters successfully differentiated pseudo-progression from true progression, providing previously unidentified insights into the unique biophysical characteristics of pseudo-progression. Our mathematical model offers a clinically relevant tool for personalized oncology and for engineering immunotherapy regimens.

Modeling Radioimmune Response—Current Status and Perspectives

“…Butner et al. ( 33 ) presented a model approach that intends to describe the clinical outcome of immune therapy. Remarkably, they applied their model to clinical data and demonstrated its capability for discriminating between therapy responders and non-responders based on early assessments of tumor growth.…”

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

“…It is a simplified and user-friendly version originated from a complex set of partial differential equations, which takes into account spatial relationships within the tumor microenvironment. The full mathematical derivation has been demonstrated elsewhere (35), but its underlying cancer biology is also schematically depicted in Figure 1. It is ultimately represented by:…”

“…After stratifying each patient into a RECIST v1.1 category, Λ and µ were compared between responding and non-responding patients by using a Wilcoxon rank sum test and compared to the literature either as a continuous variable (Λ) or by using thresholds (µ). For comparison with biomarkers reported in the literature, Λ was converted to an estimated intratumoral CD8+ T-cell count (for details, the interested reader is referred to (35)) by assuming each CD8+ T-cell would kill one tumor cell on average (the assumed mean "fitness" of the immune cell population (50)), and that there were 5,558 cells/mm 2 in the tumor microenvironment, as has been quantitatively measured in melanoma (51). For comparison with PD-L1 staining, µ was converted from its raw numerical value to a percentage; no other scaling of the variable was performed as the number of cancer cells bound by anti-PD-1/PD-L1 therapy action is the dominant term in the integral specified in Equation S4 in ref.…”

“…The mathematical model presented in this report is based on an extensive series of prior methodological reports (20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34), but with rigorous emphasis on parameters related to the cancer immune response to the treatment with checkpoint inhibitors in the setting of patients with solid tumors. In particular, we have developed a model that contains key mechanistic biological and physical processes involved in checkpoint inhibitor therapy, which has been objectively validated against imaging data of patient tumor burden and measured response, defined by both change in total tumor burden and patient survival (35). To date, this modeling work has only examined tumor response on a bulk scale, without confirming the mechanistic links between key model parameters and the underlying biology they describe.…”

Imaging-Based Subtypes of Pancreatic Ductal Adenocarcinoma Exhibit Differential Growth and Metabolic Patterns in the Pre-Diagnostic Period: Implications for Early Detection

“…These scans can offer a unique opportunity to study the evolutionary nature of PDAC tumors. To this end, the application of physiologically-relevant mathematical models that can utilize serial scans, clinical and biological data to model tumor growth (15)(16)(17)(18), and predict disease prognosis may help in evaluating screening strategies and achieving the goal of personalized approaches based on disease biology.…”