Vaccination is widely acknowledged as one of the most effective tools for preventing disease. However, there has been a rise in parental refusal and delay of childhood vaccination in recent years in the United States. This trend undermines the maintenance of herd immunity and elevates the likelihood of outbreaks of vaccine-preventable diseases. Our aim is to identify demographic or socioeconomic characteristics associated with vaccine refusal, which could help public health professionals and medical providers develop interventions targeted to concerned parents. We examine US county-level vaccine refusal data for patients under five years of age collected on a monthly basis during the period 2012--2015. These data exhibit challenging features: zero inflation, spatial dependence, seasonal variation, spatially-varying dispersion, and a large sample size (approximately 3,000 counties per month). We propose a flexible zero-inflated Conway--Maxwell--Poisson (ZICOMP) regression model that addresses these challenges. Because ZICOMP models have an intractable normalizing function, it is challenging to do Bayesian inference for these models. We propose a new hybrid Monte Carlo algorithm that permits efficient sampling and provides asymptotically exact estimates of model parameters.

翻译：疫苗接种被广泛认为是预防疾病的最有效工具之一。然而，近年来美国出现了儿童疫苗接种家长拒绝和推迟现象的增加趋势。这一趋势削弱了群体免疫的维持，并增加了疫苗可预防疾病暴发的可能性。我们的目标是识别与疫苗拒绝相关的人口或社会经济特征，从而帮助公共卫生专业人员和医疗服务提供者制定针对担忧家长的干预措施。我们研究了2012年至2015年间每月收集的美国县级五岁以下患者疫苗拒绝数据。这些数据呈现以下挑战性特征：零膨胀、空间依赖性、季节性变化、空间变异离散性以及大样本量（每月约3000个县）。我们提出了一个灵活的零膨胀Conway–Maxwell–Poisson（ZICOMP）回归模型来应对这些挑战。由于ZICOMP模型具有难以处理的归一化函数，对此类模型进行贝叶斯推断十分困难。我们提出了一种新的混合蒙特卡洛算法，该算法能够实现高效采样，并提供模型参数的渐近精确估计。