Treatment evaluation in advanced cancer mainly relies on overall survival and tumor size dynamics. Both markers and their association can be simultaneously analyzed by using joint models, and these approaches are supported by many softwares or packages. However, these approaches are essentially limited to linear models for the longitudinal part, which limit their biological interpretation. More biological models of tumor dynamics can be obtained by using nonlinear models, but they are limited by the fact that parameter identifiability require rich dataset. In that context Bayesian approaches are particularly suited to incorporate the biological knowledge and increase the information available, but they are limited by the high computing cost of Monte‐Carlo by Markov Chains algorithms. Here, we aimed to assess the performances of the Hamiltonian Monte‐Carlo (HMC) algorithm implemented in Stan for inference in a nonlinear joint model. The method was validated on simulated data where HMC provided proper posterior distributions and credibility intervals in a reasonable computational time. Then the association between tumor size dynamics and survival was assessed in patients with advanced or metastatic bladder cancer treated with atezolizumab, an immunotherapy agent. HMC confirmed limited sensitivity to prior distributions. A cross‐validation approach was developed and identified the current slope of tumor size dynamics as the most relevant driver of survival. In summary, HMC is an efficient approach to perform nonlinear joint models in a Bayesian framework, and opens the way for the use of nonlinear models to characterize both the rapid dynamics and the intersubject variability observed during cancer immunotherapy treatment.

中文翻译：

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基于哈密顿蒙特卡洛算法的贝叶斯推断在癌症免疫治疗中的非线性关节建模

晚期癌症的治疗评估主要取决于总体生存率和肿瘤大小动态。可以使用联合模型同时分析标记及其关联，并且许多软件或软件包都支持这些方法。然而，这些方法本质上限于纵向部分的线性模型，这限制了它们的生物学解释。通过使用非线性模型可以获得更多的肿瘤动力学生物学模型，但是它们受到参数可识别性需要丰富数据集这一事实的限制。在这种情况下，贝叶斯方法特别适合整合生物学知识并增加可用信息，但是它们受到Markov Chains算法在蒙特卡洛方法中的高计算成本的限制。这里，我们旨在评估在斯坦（Stan）中实施的哈密顿（Hamiltonian）蒙特卡洛（HMC）算法的性能，以便在非线性联合模型中进行推断。该方法在HMC在合理的计算时间内提供正确的后验分布和可信区间的模拟数据上得到了验证。然后，对接受免疫治疗剂阿特唑单抗治疗的晚期或转移性膀胱癌患者的肿瘤大小动力学与生存率之间的关系进行了评估。HMC证实了对先前发行版的敏感性有限。开发了一种交叉验证方法，并将当前肿瘤大小动态变化的斜率确定为与生存最相关的驱动因素。总之，HMC是在贝叶斯框架中执行非线性联合模型的有效方法，