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, and spatially-varying dispersion, for data observed on approximately 3,000 counties per month. We propose a flexible zero-inflated Conway--Maxwell--Poisson (ZICOMP) regression model that addresses these challenges. Because the ZICOMP model has an intractable normalizing function, Bayesian inference can be difficult. We propose a new hybrid Monte Carlo algorithm that permits efficient sampling, automatically selects a basis representation for the spatial process via reversible jump MCMC, and provides asymptotically exact approximations of the posterior distribution of the model parameters. We use our approach to learn about characteristics impacting vaccine refusal in the US.

翻译：疫苗接种被广泛认为是预防疾病最有效的工具之一。然而，近年来美国出现父母拒绝或延迟儿童疫苗接种的现象上升趋势。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。本研究旨在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。我们分析了2012至2015年间每月收集的美国县级五岁以下患者的疫苗拒绝数据。这些数据呈现以下挑战性特征：零膨胀、空间依赖性、季节性变化以及空间变异性离散程度，且每月涉及约3000个县。我们提出了一种灵活的零膨胀Conway-Maxwell-Poisson（ZICOMP）回归模型，以应对这些挑战。由于ZICOMP模型存在难以处理的归一化函数，贝叶斯推断存在困难。我们提出了一种新型混合蒙特卡洛算法，该算法可实现高效采样、通过可逆跳跃MCMC自动选择空间过程的基表示，并提供模型参数后验分布的渐近精确近似。我们利用该方法揭示了影响美国疫苗拒绝的特征。