Department of Computer Science, TUM School of Computation, Information and Technology, Technical University of Munich, Boltzmannstr. 3, Garching, 85747, Germany.
Department of Mathematics, TUM School of Computation, Information and Technology, Technical University of Munich, Boltzmannstr. 3, Garching, 85747, Germany.
Math Biosci. 2024 Oct;376:109287. doi: 10.1016/j.mbs.2024.109287. Epub 2024 Aug 31.
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.
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.
Fitting the complete treatment course, the novel delayed response model (R=0.938) outperformed the simplest model (R=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.
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.
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.
免疫检查点抑制剂（ICIs）针对 PD-1/PD-L1 在肺癌治疗中的应用日益增多，这就产生了可靠预测个体患者治疗结果的临床需求。
为了弥补预测差距，我们以常微分方程的形式检查了四种不同的数学模型，包括一种新的延迟反应模型。我们通过对模型得出的结果概率进行均等加权，严格评估了它们在患者进展性疾病（PD）状态方面的个体和综合预测能力。
在拟合完整的治疗过程中，新型延迟反应模型（R=0.938）的表现优于最简单的模型（R=0.865）。通过仅使用原发肿瘤最长直径测量值进行校准，模型组合能够可靠地预测患者 PD 结果，整体准确率为 77%（灵敏度=70%，特异性=81%）。它能够自主识别出 51%的患者子集，这些患者的整体准确率为 81%（灵敏度=81%，特异性=81%）。所有模型均显著优于完全基于数据驱动的机器学习方法。
这些建模方法提供了一个动态的基线框架，通过使用已经可用于临床的测量数据来识别不同的治疗结果轨迹，从而为临床医生提供治疗决策支持。
联合使用本文提出的方法与其他预测工具和生物标志物，以及进一步的疾病信息（例如转移性阶段），可以进一步提高治疗结果预测的准确性。我们相信，简单的模型公式允许将开发的模型广泛应用于其他癌症类型。类似的模型可以轻松地应用于其他治疗方式。
