Predicting resistance and pseudoprogression: are minimalistic immunoediting mathematical models capable of forecasting checkpoint inhibitor treatment outcomes in lung cancer?
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Updated: Jun 14, 2025

Predictive Immune Modeling of Solid Tumors
Published on: February 25, 2020
Kevin Robert Scibilia1, Pirmin Schlicke2, Folker Schneller3
1Department of Computer Science, TUM School of Computation, Information and Technology, Technical University of Munich, Boltzmannstr. 3, Garching, 85747, Germany.
Background:
The increased application of immune checkpoint inhibitors (ICIs) targeting PD-1/PD-L1 in lung cancer treatment generates clinical need to reliably predict individual patients' treatment outcomes.
Methods:
To bridge the prediction gap, we examine four different mathematical models in the form of ordinary differential equations, including a novel delayed response model. We rigorously evaluate their individual and combined predictive capabilities with regard to the patients' progressive disease (PD) status through equal weighting of model-derived outcome probabilities.
Results:
Fitting the complete treatment course, the novel delayed response model (R2=0.938) outperformed the simplest model (R2=0.865). The model combination was able to reliably predict patient PD outcome with an overall accuracy of 77% (sensitivity = 70%, specificity = 81%), solely through calibration with primary tumor longest diameter measurements. It autonomously identified a subset of 51% of patients where predictions with an overall accuracy of 81% (sensitivity = 81%, specificity = 81%) can be achieved. All models significantly outperformed a fully data-driven machine learning-based approach.
Implications:
These modeling approaches provide a dynamic baseline framework to support clinicians in treatment decisions by identifying different treatment outcome trajectories with already clinically available measurement data.
Limitations And Future Directions:
Conjoint application of the presented approach with other predictive tools and biomarkers, as well as further disease information (e.g. metastatic stage), could further enhance treatment outcome prediction. We believe the simple model formulations allow widespread adoption of the developed models to other cancer types. Similar models can easily be formulated for other treatment modalities.
Insights
Mathematical models predict lung cancer treatment outcomes for immune checkpoint inhibitors (ICIs). A novel delayed response model and combined approach accurately forecast progressive disease (PD) status using tumor measurements, outperforming machine learning.
Area of Science:
- Oncology
- Mathematical Biology
- Computational Medicine
Background:
- Immune checkpoint inhibitors (ICIs) targeting PD-1/PD-L1 are increasingly used for lung cancer.
- Predicting individual patient outcomes with ICIs is a clinical challenge.
Purpose of the Study:
- To develop and evaluate mathematical models for predicting lung cancer patient response to ICIs.
- To assess the predictive capabilities of ordinary differential equation (ODE) models, including a novel delayed response model.
Main Methods:
- Four ODE mathematical models were examined, including a novel delayed response model.
- Models were evaluated individually and in combination for predicting progressive disease (PD) status.
- Calibration used primary tumor longest diameter measurements.
Main Results:
- The novel delayed response model (R²=0.938) outperformed a simpler model (R²=0.865).
- The combined model predicted PD outcome with 77% overall accuracy (70% sensitivity, 81% specificity).
- A subset of 51% of patients achieved 81% accuracy (81% sensitivity, 81% specificity).
- All ODE models surpassed a machine learning approach.
Conclusions:
- ODE modeling provides a dynamic framework for clinical decision-making in lung cancer treatment.
- Models identify distinct treatment outcome trajectories using existing clinical data.
- The approach is adaptable for other cancer types and treatment modalities.
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