Predicting cancer dynamics under treatment is challenging due to high inter-patient heterogeneity, lack of predictive biomarkers, and sparse and noisy longitudinal data. Mathematical models can summarize cancer dynamics by a few interpretable parameters per patient. Machine learning methods can then be trained to predict the model parameters from baseline covariates, but do not account for uncertainty in the parameter estimates. Instead, hierarchical Bayesian modeling can model the relationship between baseline covariates to longitudinal measurements via mechanistic parameters while accounting for uncertainty in every part of the model. The mapping from baseline covariates to model parameters can be modeled in several ways. A linear mapping simplifies inference but fails to capture nonlinear covariate effects and scale poorly for interaction modeling when the number of covariates is large. In contrast, Bayesian neural networks can potentially discover interactions between covariates automatically, but at a substantial cost in computational complexity. In this work, we develop a hierarchical Bayesian model of subpopulation dynamics that uses baseline covariate information to predict cancer dynamics under treatment, inspired by cancer dynamics in multiple myeloma (MM), where serum M protein is a well-known proxy of tumor burden. As a working example, we apply the model to a simulated dataset and compare its ability to predict M protein trajectories to a model with linear covariate effects. Our results show that the Bayesian neural network covariate effect model predicts cancer dynamics more accurately than a linear covariate effect model when covariate interactions are present. The framework can also be applied to other types of cancer or other time series prediction problems that can be described with a parametric model.

翻译：预测治疗条件下的癌症动态具有挑战性，主要源于患者间的高度异质性、预测性生物标志物的缺乏，以及稀疏且含噪声的纵向数据。数学模型可通过每位患者少数几个可解释参数来概括癌症动态。随后可训练机器学习方法从基线协变量预测这些模型参数，但此类方法未考虑参数估计中的不确定性。相比之下，分层贝叶斯建模可通过机制参数对基线协变量与纵向测量值之间的关系进行建模，同时考虑模型每个部分的不确定性。从基线协变量到模型参数的映射可通过多种方式建模。线性映射简化了推断过程，但无法捕捉非线性协变量效应，且在协变量数量较多时难以有效建模交互作用。相反，贝叶斯神经网络虽可能自动发现协变量间的交互作用，但需付出计算复杂度显著增加的代价。受多发性骨髓瘤（MM）中癌症动态的启发（其中血清M蛋白是肿瘤负荷的公认替代指标），本研究开发了一个亚群动态的分层贝叶斯模型，利用基线协变量信息预测治疗条件下的癌症动态。作为示例，我们将该模型应用于模拟数据集，并将其预测M蛋白轨迹的能力与具有线性协变量效应的模型进行比较。结果表明，当存在协变量交互作用时，贝叶斯神经网络协变量效应模型比线性协变量效应模型能更准确地预测癌症动态。该框架也可应用于其他类型癌症或其他可用参数模型描述的时序预测问题。