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引用次数: 0
摘要
受临床试验中剂量-反应或剂量-毒性曲线建模需要的启发,我们开发了一种新的基于马蹄铁的贝叶斯等容回归先验,将二元结果与有序分类预测因子进行建模,其中假定结果概率随预测因子单调非递减。预测因子的连续类别中结果概率的差异集配备了一个多变量先验,该先验在单纯形上具有支持。Dirichlet 分布可以从独立伽马分布随机变量的归一化总和中导出,是先验值的自然选择,但通过数学和模拟论证,我们发现即使在简单的数据配置下,得到的后验值也容易出现下溢和其他数值不稳定性。我们提出了另一种基于马蹄型收缩的先验,在数值上更加稳定。我们证明,这种基于马蹄形的先验不会出现基于 Dirichlet/gamma 先验的数值不稳定性,而且基于马蹄形的后验比基于 Dirichlet 的后验能更有效地估计出潜在的真实曲线。我们在一个预测肺癌患者辐射诱发肺毒性的模型中演示了该先验值的使用,该模型是正常肺组织所受剂量的函数。我们的方法是在 R 软件包 isotonicBayes 中实现的,因此适用于剂量寻找研究或其他剂量反应建模的设计。
Shrinkage priors for isotonic probability vectors and binary data modeling, with applications to dose-response modeling.
Motivated by the need to model dose-response or dose-toxicity curves in clinical trials, we develop a new horseshoe-based prior for Bayesian isotonic regression modeling a binary outcome against an ordered categorical predictor, where the probability of the outcome is assumed to be monotonically non-decreasing with the predictor. The set of differences between outcome probabilities in consecutive categories of the predictor is equipped with a multivariate prior having support over simplex. The Dirichlet distribution, which can be derived from a normalized sum of independent gamma-distributed random variables, is a natural choice of prior, but using mathematical and simulation-based arguments, we show that the resulting posterior is prone to underflow and other numerical instabilities, even under simple data configurations. We propose an alternative prior based on horseshoe-type shrinkage that is numerically more stable. We show that this horseshoe-based prior is not subject to the numerical instability seen in the Dirichlet/gamma-based prior and that the horseshoe-based posterior can estimate the underlying true curve more efficiently than the Dirichlet-based one. We demonstrate the use of this prior in a model predicting the occurrence of radiation-induced lung toxicity in lung cancer patients as a function of dose delivered to normal lung tissue. Our methodology is implemented in the R package isotonicBayes and therefore suitable for use in the design of dose-finding studies or other dose-response modeling contexts.
期刊介绍:
Pharmaceutical Statistics is an industry-led initiative, tackling real problems in statistical applications. The Journal publishes papers that share experiences in the practical application of statistics within the pharmaceutical industry. It covers all aspects of pharmaceutical statistical applications from discovery, through pre-clinical development, clinical development, post-marketing surveillance, consumer health, production, epidemiology, and health economics.
The Journal is both international and multidisciplinary. It includes high quality practical papers, case studies and review papers.