基于反射布朗运动的复发事件建模及其在低血糖中的应用
Recurrent Events Modeling Based on a Reflected Brownian Motion with Application to Hypoglycemia
AI总结：
针对2型糖尿病低血糖事件，提出基于带反射屏障的布朗运动下边界穿越模型，结合协变量和患者脆弱性，用贝叶斯MCMC推断，模拟和DURABLE试验数据验证有效。
摘要：
2型糖尿病患者需要在日常糖尿病自我管理中密切监测血糖水平。尽管许多治疗药物旨在严格控制血糖，但低血糖常常作为一种不良事件出现。在实践中，由于神经源性症状的感知，患者观察低血糖事件比高血糖事件更容易。我们提出将每个患者观察到的低血糖事件建模为具有上反射屏障的反射布朗运动的下边界穿越事件。下边界由临床标准设定。为了捕捉患者异质性和患者内部依赖性，将协变量和患者水平的脆弱性纳入波动率和上反射屏障中。该框架为潜在血糖水平变异性、患者异质性和风险因素对血糖的影响提供了量化。我们基于贝叶斯框架使用马尔可夫链蒙特卡罗方法进行推断。使用两个模型比较标准，即偏差信息准则和伪边际似然的对数，进行模型选择。该方法在模拟研究中得到验证。在分析DURABLE试验中糖尿病患者的数据集时，我们的模型提供了充分的拟合，生成与观察数据相似的数据，并提供了其他模型可能遗漏的见解。
英文摘要：
Patients with type 2 diabetes need to closely monitor blood sugar levels as their routine diabetes self-management. Although many treatment agents aim to tightly control blood sugar, hypoglycemia often stands as an adverse event. In practice, patients can observe hypoglycemic events more easily than hyperglycemic events due to the perception of neurogenic symptoms. We propose to model each patient's observed hypoglycemic event as a lower-boundary crossing event for a reflected Brownian motion with an upper reflection barrier. The lower-boundary is set by clinical standards. To capture patient heterogeneity and within-patient dependence, covariates and a patient level frailty are incorporated into the volatility and the upper reflection barrier. This framework provides quantification for the underlying glucose level variability, patients heterogeneity, and risk factors' impact on glucose. We make inferences based on a Bayesian framework using Markov chain Monte Carlo. Two model comparison criteria, the Deviance Information Criterion and the Logarithm of the Pseudo-Marginal Likelihood, are used for model selection. The methodology is validated in simulation studies. In analyzing a dataset from the diabetic patients in the DURABLE trial, our model provides adequate fit, generates data similar to the observed data, and offers insights that could be missed by other models.
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