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

Abstract

Background: Checkpoint inhibitor therapy of cancer has led to markedly improved survival of a subset of patients in multiple solid malignant tumor types, yet the factors driving these clinical responses or lack thereof are not known. We have developed a mechanistic mathematical model for better understanding these factors and their relations in order to predict treatment outcome and optimize personal treatment strategies.

Methods: Here, we present a translational mathematical model dependent on three key parameters for describing efficacy of checkpoint inhibitors in human cancer: tumor growth rate (α), tumor-immune infiltration (Λ), and immunotherapy-mediated amplification of anti-tumor response (µ). The model was calibrated by fitting it to a compiled clinical tumor response dataset (n = 189 patients) obtained from published anti-PD-1 and anti-PD-L1 clinical trials, and then validated on an additional validation cohort (n = 64 patients) obtained from our in-house clinical trials.

Results: The derived parameters Λ and µ were both significantly different between responding versus nonresponding patients. Of note, our model appropriately classified response in 81.4% of patients by using only tumor volume measurements and within 2 months of treatment initiation in a retrospective analysis. The model reliably predicted clinical response to the PD-1/PD-L1 class of checkpoint inhibitors across multiple solid malignant tumor types. Comparison of model parameters to immunohistochemical measurement of PD-L1 and CD8+ T cells confirmed robust relationships between model parameters and their underlying biology.

Conclusions: These results have demonstrated reliable methods to inform model parameters directly from biopsy samples, which are conveniently obtainable as early as the start of treatment. Together, these suggest that the model parameters may serve as early and robust biomarkers of the efficacy of checkpoint inhibitor therapy on an individualized per-patient basis.

Funding: We gratefully acknowledge support from the Andrew Sabin Family Fellowship, Center for Radiation Oncology Research, Sheikh Ahmed Center for Pancreatic Cancer Research, GE Healthcare, Philips Healthcare, and institutional funds from the University of Texas M.D. Anderson Cancer Center. We have also received Cancer Center Support Grants from the National Cancer Institute (P30CA016672 to the University of Texas M.D. Anderson Cancer Center and P30CA072720 the Rutgers Cancer Institute of New Jersey). This research has also been supported in part by grants from the National Science Foundation Grant DMS-1930583 (ZW, VC), the National Institutes of Health (NIH) 1R01CA253865 (ZW, VC), 1U01CA196403 (ZW, VC), 1U01CA213759 (ZW, VC), 1R01CA226537 (ZW, RP, WA, VC), 1R01CA222007 (ZW, VC), U54CA210181 (ZW, VC), and the University of Texas System STARS Award (VC). BC acknowledges support through the SER Cymru II Programme, funded by the European Commission through the Horizon 2020 Marie Skłodowska-Curie Actions (MSCA) COFUND scheme and the Welsh European Funding Office (WEFO) under the European Regional Development Fund (ERDF). EK has also received support from the Project Purple, NIH (U54CA210181, U01CA200468, and U01CA196403), and the Pancreatic Cancer Action Network (16-65-SING). MF was supported through NIH/NCI center grant U54CA210181, R01CA222959, DoD Breast Cancer Research Breakthrough Level IV Award W81XWH-17-1-0389, and the Ernest Cockrell Jr. Presidential Distinguished Chair at Houston Methodist Research Institute. RP and WA received serial research awards from AngelWorks, the Gillson-Longenbaugh Foundation, and the Marcus Foundation. This work was also supported in part by grants from the National Cancer Institute to SHC (R01CA109322, R01CA127483, R01CA208703, and U54CA210181 CITO pilot grant) and to PYP (R01CA140243, R01CA188610, and U54CA210181 CITO pilot grant). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Trial registration: ClinicalTrials.gov NCT02444741.

Keywords: biomarkers; human; immunotherapy; medicine; patient stratification; translational research.

Figure 1.. Schematic representation of biological mechanisms included in the mathematical model.

These processes are described by four partial differential equations, which are solved to obtain Equation (1). Briefly, the checkpoint inhibitor enters the tumor via diffusion (D_a) leading to time-dependent drug concentration (σ), which then binds to the conjugate receptor on immune cells at rate λ. Immune cells (ψ_k) are drawn into the tumor microenvironment via cytokine-mediated chemotaxis (χ), resulting in immune checkpoint inhibitor-mediated cancer cell kill at rate λ_p. The full mathematical model derivation and its underlying assumptions are provided in a recent modeling and analysis report (Butner et al., 2020).

Figure 2.. Mathematical model fit to individual responses to immune checkpoint inhibition.

Open circles represent data points of clinical response in 10 patients extracted from Topalian et al., 2012, while solid lines represent best curve fits of Equation (1) to those data (with α^–1 = 144 days). Each color represents a different patient. Immunotherapy was begun at t = 0, and tumor volume was designated as the relative change in volume from t = 0 (i.e., tumor volume of 1 at t = 0). The dashed line depicts the cutoff used for classifying patients deemed as responders (partial or complete response) versus nonresponders (stable disease or disease progression) according to the RECIST v1.1 criteria.

Figure 3.. Depiction of average Λ and μ values in patients with response (n = 55) versus nonresponse (n = 134) in the calibration cohort (circular markers), while n = 25 patients had objective response and 39 patients demonstrated stable/progressive disease in the validation cohort (square markers) as determined by RECIST v1.1 criteria.

Open markers represent the average values of patients with response, and solid markers represent patients with stable/progressive disease. Error bars represent the standard error of the mean (SEM). p-Values of separation between groups by Wilcoxon rank sum (two tails): Λ, p=0.119 and p<0.001 for literature (calibration) and non-small cell lung cancer (NSCLC) (validation) cohorts, respectively; μ, p<0.001 for both literature (calibration) and NSCLC (validation) cohorts. Insets: receiver-operator characteristic (ROC) curves for patient response versus model parameters for both cohorts; Λ, literature cohort: sensitivity = 0.381, specificity = 0.945, accuracy = 545; μ, literature cohort: sensitivity = 0.891, specificity = 0.567, accuracy = 0.661; Λ, NSCLC clinical cohort: sensitivity = 0.600, specificity = 0.744, accuracy = 0.688; μ, NSCLC clinical cohort: sensitivity = 0.960, specificity = 0.769, accuracy = 0.844. PR, partial response; CR, complete response. Examples of cancer drug-specific parameter values may be found in Butner et al., 2020.

Figure 4.. Simulated response to immune checkpoint inhibition at different values of α, Λ, and µ.

Data are obtained from Equation (1). Normalized tumor volume ($\rho `$) was determined at t = 200 days. Three different α values were used that represent the minimum, average, and maximum values derived from fitting the calibration cohort, as described in the text. Λ and µ were varied continuously over their respective ranges. Colors also correspond with $\rho `$ as per color map on the right. RECIST v1.1 criteria of response are listed to the right of the color bars.

Figure 5.. Comparison of intratumoral CD8+ T cell count and tumor PD-L1 staining derived from fitting the model to clinical data and values reported in the literature, as described in the text.

(A) Model intratumoral CD8+ T cell count (circles: calibration cohort, p=0.119 [Wilcoxon, two-tail]; squares: validation cohort, p<0.001) was derived from Λ and literature CD8 intratumoral count was taken from immunohistochemical (IHC) staining in Tumeh et al., 2014 in melanoma (diamonds; average CD8 counts including on-treatment values [n = 23]). CD8+ T cell counts from pretreatment biopsies only (n = 46) demonstrated mean values (± SEM) of 2632 ± 518 cells/mm² in patients with response to immunotherapy and 322 ± 133 cells/mm² in nonresponding patients, respectively. Values for CD8+ T cell counts are plotted as averages with error bars representing the standard error. (B) Patient response rates to immunotherapy stratified by PD-L1 staining were derived from µ from the model (calibration: red; validation: blue) and from references (Borghaei et al., 2015; Robert et al., 2015b; Brahmer et al., 2012; Tumeh et al., 2014; Motzer et al., 2015; Powles et al., 2014; Topalian et al., 2012; Garon et al., 2015; Herbst et al., 2014; Kefford et al., 2014; Spira et al., 2015; Taube et al., 2014; Weber et al., 2015) for the literature data (green; n = 975 for 1% cutoff, n = 1492 for 5% cutoff; see Appendix 1—table 1). Response to immune checkpoint inhibition was determined by RECIST v1.1 criteria. PR, partial response; CR, complete response.

Appendix 1—figure 1.. Steps for calibration of the mathematical model with clinical data.

First, checkpoint inhibitor response curves were extracted from the literature. In all cases, immunotherapy treatment began at time t = 0. Second, a tumor-specific proliferation constant (α) was determined for each cancer type by fitting exponential function ($e^{\alpha t}$ to fastest progressing patient in each clinical trial [red line]). Third, individual patient response data were fit to Equation (1) by using the respective α to determine Λ and µ. Λ and µ values were then with compared in patients with partial/complete response versus patients with stable/progressive disease after immunotherapy by using the RECIST v1.1 criteria.

Appendix 1—figure 2.. Model validation, sensitivity studies, and comparison of model parameters to immunohistochemical (IHC) measures.

Model parameters were obtained from a second in-house patient cohort of patients with non-small cell lung cancer (NSCLC) (n = 64), which were compared to values obtained in the calibration cohort in a validation study. To study the sensitivity of the model to changes in model parameter values, key parameters were perturbed ±10% and the resultant simulated expected tumor burden was compared to measured values pre-perturbation. Tumor burden measures were also truncated, and results of truncated and full dataset model fits were compared. Lastly, the full parameter space of the model was examined. In order to compare model parameters to the underlying biology, model parameters were converted to intratumoral CD8+ lymphocyte counts (for Λ) and PD-L1 staining (for μ), which were compared to IHC measures obtained from the literature.

Appendix 1—figure 3.. Parameter validation analysis within the calibration cohort.

In order to examine the robustness of ranges for (A) parameter Λ and (B) parameter μ between partial and complete response (PR/CR) versus stable/progressive disease among different cancer types, a validation study was performed where 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. Analysis was repeated once for each cancer type, and results are shown as mean ± standard deviation (error bars). Parameter ranges were found to vary between individual cancer types, and with μ showing more consistent significant difference between response categories relative to Λ (these results are consistent with results shown in Butner et al., 2020).