Takahashi Ami, Suzuki Taiji
Department of Mathematical and Computing Science, School of Computing, Tokyo Institute of Technology, Tokyo, Japan.
Biometrics and Data Management, Clinical Statistics, Pfizer R&D Japan, Tokyo, Japan.
Contemp Clin Trials Commun. 2021 Feb 15;21:100753. doi: 10.1016/j.conctc.2021.100753. eCollection 2021 Mar.
We introduce a Bayesian optimization method for estimating the maximum tolerated dose in this article. A number of parametric model-based methods have been proposed to estimate the maximum tolerated dose; however, parametric model-based methods need an assumption that dose-toxicity relationships follow specific theoretical models. This assumption potentially leads to suboptimal dose selections if the dose-toxicity curve is misspecified. Our proposed method is based on a Bayesian optimization framework for finding a global optimizer of unknown functions that are expensive to evaluate while using very few function evaluations. It models dose-toxicity relationships with a nonparametric model; therefore, a more flexible estimation can be realized compared with existing parametric model-based methods. Also, most existing methods rely on point estimates of dose-toxicity curves in their dose selections. In contrast, our proposed method exploits a probabilistic model for an unknown function to determine the next dose candidate without ignoring the uncertainty of posterior while imposing some dose-escalation limitations. We investigate the operating characteristics of our proposed method by comparing them with those of the Bayesian-based continual reassessment method and two different nonparametric methods. Simulation results suggest that our proposed method works successfully in terms of selections of the maximum tolerated dose correctly and safe dose allocations.
在本文中，我们介绍一种用于估计最大耐受剂量的贝叶斯优化方法。已经提出了许多基于参数模型的方法来估计最大耐受剂量；然而，基于参数模型的方法需要一个假设，即剂量-毒性关系遵循特定的理论模型。如果剂量-毒性曲线指定错误，这个假设可能会导致次优的剂量选择。我们提出的方法基于一个贝叶斯优化框架，用于找到未知函数的全局优化器，这些函数评估成本高昂，同时仅使用极少的函数评估。它使用非参数模型对剂量-毒性关系进行建模；因此，与现有的基于参数模型的方法相比，可以实现更灵活的估计。此外，大多数现有方法在剂量选择时依赖于剂量-毒性曲线的点估计。相比之下，我们提出的方法利用未知函数的概率模型来确定下一个剂量候选，在施加一些剂量递增限制的同时不忽略后验的不确定性。我们通过将我们提出的方法与基于贝叶斯的连续重新评估方法以及两种不同的非参数方法进行比较，来研究其操作特性。模拟结果表明，我们提出的方法在正确选择最大耐受剂量和安全剂量分配方面成功有效。
