Neural Ordinary Differential Equations for Tumor Dynamics Modeling and Overall Survival Predictions
Mark Laurie (1,2), James Lu (1)
(1) Genentech Inc., USA, (2) Stanford University, USA
Introduction: Tumor dynamic modeling has been widely adopted in supporting the development of oncology drugs. While the existing Tumor Growth Inhibition (TGI) models [1] have served well to date, there is significant challenge in incorporating rich, multi-modal data to provide the actionable insights necessary for personalized therapy. Moreover, there is a need for improving the extraction of tumor metrics from early longitudinal tumor data to enable survival predictions. Deep Learning (DL) offers the potential for building accurate tumor dynamic models while also leveraging high-dimensional data.
Methods: We propose a foundational DL framework, Tumor Dynamic Neural-ODE (TDNODE), based on an encoder-decoder architecture [2] that facilitates automated prediction using observed longitudinal tumor size measurements. We applied TDNODE to the IMPower150 trial [3], which consists of longitudinal tumor measurements collected from n=1106 NSCLC patients in 3 treatment arms (Arm 1 = Atezolizumab + Carboplatin + Paclitaxel; Arm 2 = Atezolizumab + Carboplatin + Paclitaxel + Bevacizumab; Arm 3 = Carboplatin + Paclitaxel + Bevacizumab). We performed an 80-20 split of patients into a training (n=890) and test set (n=216) respectively. Data augmentation on the training set was performed as in [2]. The TDNODE model was implemented using the PyTorch library torchdiffeq, with a 4-dimensional state representation and a 6-dimensional latent parameter representation. Once trained, TDNODE was applied to predict tumor size values on the test set and the predictive performance evaluated. Furthermore, TDNODE metrics were derived by taking the encoder outputs from individual patients’ longitudinal tumor data and used to predict Overall Survival (OS) using an ML model, XGBoost [4]. The ability of the resulting TDNODE-OS model to discriminate patient survival at the individual level was assessed by computing the concordance index (c-index). The 95% prediction interval (PI) of the resulting TDNODE-OS model was derived by bootstrapping data from the training set; the PIs of the ML survival model were compared to the survival data from ~70 test patients in each treatment arm.
Results: On the test set, TDNODE demonstrated an ability to predict future tumor size measurements from 8, 12, 24, 32 weeks of observed post-treatment tumor data, with accuracies of R2=0.76±0.03, 0.78±0.02, 0.87±0.02 and 0.9±0.02 respectively. Furthermore, in contrast to some TGI models, TDNODE showed little to no bias in predicting the future tumor dynamics from early data as confirmed by the residual-vs-time diagnostics plot on the test set. The TDNODE metrics alone enabled an excellent prediction of patient survival via a ML model: on the test set, it yielded a c-index=0.83 which compares favorably with 0.68 using the existing TGI metrics (KG, KS and TTG) [5]. Furthermore, the resulting TDNODE-OS model predicted well the survival curves amongst test patients across all 3 arms, with the data falling within the 95% PIs of the model. Finally, the TDNODE-OS model predicts hazard ratios (HRs) and 95% PI of: Arm 1-vs-3=0.62 [0.47, 0.82], Arm 2-vs-3=0.54 [0.40, 0.72]. These are well aligned with the actual HRs computed from the test set (Arm 1-vs-3=0.64 [0.41, 1.00]; Arm 2-vs-3=0.66 [0.42, 1.02]).
Conclusions: We demonstrated that TDNODE can be effectively applied to oncology clinical trials to derive novel DL-based metrics, which can be used to predict trial HRs. In particular, the TDNODE metrics appear to offer the potential for improved patient level survival prediction than the existing TGI metrics. Furthermore, the derived TDNODE metrics can be explained via the aid of model visualizations. The positive results and explainability attributes of TDNODE have shown it as a DL formalism with promising potential to enable the next generation of oncology disease modeling by improving predictivity and enabling the use of high content data.
References:
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