Early prediction of clinical response to checkpoint inhibitor therapy in human solid tumors through mathematical modeling
- Mathematics in Medicine Program, Houston Methodist Research Institute, United States
- Department of Radiation Oncology, The University of Texas M.D. Anderson Cancer Center, United States
- Department of Imaging Physics, The University of Texas M.D. Anderson Cancer Center, United States
- Department of Nanomedicine, Houston Methodist Research Institute, United States
- Swansea University Medical School, Singleton Park, United Kingdom
- Department of Surgery, Houston Methodist Cancer Center, United States
- Department of Investigational Cancer Therapeutics, The University of Texas M.D. Anderson Cancer Center, United States
- University of Texas Health Science Center (UTHealth), McGovern Medical School, United States
- Breast Oncology Program, Dana Farber/Brigham and Women's Cancer Center, United States
- Michael E. DeBakey Department of Surgery, Baylor College of Medicine, United States
- Immunotherapy Research Center, Houston Methodist Research Institute, United States
- Cancer Center, Houston Methodist Research Institute, United States
- Rutgers Cancer Institute of New Jersey, United States
- Department of Surgery, Rutgers Robert Wood Johnson Medical School, United States
- Department of Neurology, Harvard Medical School, United States
- Division of Cancer Biology, Department of Radiation Oncology, Rutgers New Jersey Medical School, United States
- Division of Hematology/Oncology, Department of Medicine, Rutgers New Jersey Medical School, United States
Figures
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 (Da) leading to …
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 …
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). …
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Figure 3—source data 1
Numerical data for Figure 3.
- https://cdn.elifesciences.org/articles/70130/elife-70130-fig3-data1-v2.xlsx
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 () was determined at t = 200 days. Three different α values were used that represent the minimum, average, and maximum values derived …
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 …
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Figure 5—source data 1
Numerical data for Figure 5.
- https://cdn.elifesciences.org/articles/70130/elife-70130-fig5-data1-v2.xlsx
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 …
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 …
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 …
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Appendix 1—figure 3—source data 1
Numerical data for Appendix 1—figure 3.
- https://cdn.elifesciences.org/articles/70130/elife-70130-app1-fig3-data1-v2.xlsx
Tables
Table 1
Clinical trials with checkpoint inhibitors used to fit the mathematical model and derived values of tumor proliferation constant, α.
| Reference | Tumor type histopathology | Checkpoint inhibitor monoclonal antibody | Constantα (days–1) | Calculated tumor doubling time (α–1, days) |
|---|---|---|---|---|
| Le et al., 2015 | CRC | Pembrolizumab (anti-PD1) | 0.0622 | 11 |
| Powles et al., 2014 | UCC | Atezolizumab (anti-PD-L1) | 0.016 | 43 |
| Antonia et al., 2015 | SCLC | Nivolumab (anti-PD1) | 0.014 | 50 |
| Topalian et al., 2012 | MM | Nivolumab (anti-PD1) | 0.0069 | 100 |
| Borghaei et al., 2015 | NSCLC | Nivolumab (anti-PD1) | 0.0069 | 100 |
| Motzer et al., 2015 | RCC | Nivolumab (anti-PD1) | 0.0034 | 204 |
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CRC, colorectal carcinoma; UCC, urothelial cell carcinoma; SCLC, small cell lung cancer;MM, malignant melanoma; NSCLC, non-small lung cancer; RCC, renal cell carcinoma.
Table 2
Spearman correlation coefficients between Λ and µ derived from fitting truncated datasets versus full dataset.
t: days. Note that values of 1.000 are due to only a small number of patients (n = 4) that were imaged before t = 30 days in the validation cohort; these either did not have lesion volumes …
| Calibration cohort | Validation cohort | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Λ | t < 60 | t < 120 | t < 200 | t = all days | Λ | t < 60 | t < 120 | t < 200 | t = all days |
| t < 30 | 0.476 | 0.162 | 0.080 | 0.071 | t < 30 | 1.000 | 1.000 | 0.800 | 0.800 |
| t < 60 | 0.416 | 0.309 | 0.306 | t < 60 | 0.812 | 0.658 | 0.823 | ||
| t < 120 | 0.668 | 0.599 | t < 120 | 0.676 | 0.750 | ||||
| t < 200 | 0.730 | t < 200 | 0.771 | ||||||
| µ | t < 60 | t < 120 | t < 200 | t = all days | µ | t < 60 | t < 120 | t < 200 | t = all days |
| t < 30 | 0.942 | 0.928 | 0.922 | 0.910 | t < 30 | 1.000 | 0.800 | 0.800 | 0.800 |
| t < 60 | 0.968 | 0.941 | 0.946 | t < 60 | 0.974 | 0.960 | 0.963 | ||
| t < 120 | 0.946 | 0.922 | t < 120 | 0.971 | 0.961 | ||||
| t < 200 | 0.921 | t < 200 | 0.989 | ||||||
Appendix 1—table 1
Studies used for derivation of pathological markers of immunotherapy response.
| Reference (see main text) | Tumor type | Checkpoint inhibitor | Pathological biomarker | PD-L1 staining cutoff |
|---|---|---|---|---|
| Tumeh et al., 2014 | Melanoma | Pembrolizumab | CD8+ TILs | N/A |
| Kefford et al., 2014 | Melanoma | Pembrolizumab | PD-L1 | 1% |
| Powles et al., 2014 | UCC | Atezolizumab | PD-L1 | 1%, 5%, 10% |
| Herbst et al., 2014 | NSCLC, RCC, melanoma, HNSCC, CRC, gastric and pancreatic cancer | Atezolizumab | PD-L1 | 1%, 5%, 10% |
| Robert et al., 2015b | Melanoma | Nivolumab | PD-L1 | 5% |
| Motzer et al., 2015 | RCC | Nivolumab | PD-L1 | 5% |
| Taube et al., 2014 | NSCLC, RCC, melanoma, PC, CRC | Nivolumab | PD-L1 | 5% |
| Spira et al., 2015 | NSCLC | Atezolizumab | PD-L1 | 1%, 5%, 10% |
| Brahmer et al., 2012 | NSCLC | Nivolumab | PD-L1 | 1%, 5%, 10% |
| Borghaei et al., 2015 | NSCLC | Nivolumab | PD-L1 | 1%, 5%, 10% |
| Weber et al., 2015 | Melanoma | Nivolumab | PD-L1 | 5% |
| Topalian et al., 2012 | Melanoma, RCC, NSCLC, CRC, PC | Nivolumab | PD-L1 | 5% |
| Garon et al., 2015 | NSCLC | Pembrolizumab | PD-L1 | 1%, 50% |
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RCC: renal cell; UCC: urothelial cell carcinoma; CRC: colorectal carcinoma; NSCLC: non-small lung carcinoma; HNSCC: head and neck squamous cell carcinoma; PC: prostate carcinoma; TIL: tumor-infiltrating lymphocytes
Additional files
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Transparent reporting form
- https://cdn.elifesciences.org/articles/70130/elife-70130-transrepform1-v2.pdf
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Appendix 1—figure 3—source data 1
Numerical data for Appendix 1—figure 3.
- https://cdn.elifesciences.org/articles/70130/elife-70130-app1-fig3-data1-v2.xlsx
