Misclassification in binary outcomes is not uncommon and statistical methods to investigate its impact on policy-driving study results are lacking. While misclassifying binary outcomes is a statistically ubiquitous phenomena, we focus on misclassification in a public health application: vaccinations. One such study design in public health that addresses policy is the cluster controlled randomized trial (CCRT). A CCRT that measures the impact of a novel behavioral intervention on increasing vaccine uptake can be severely biased when the supporting data are incomplete vaccination records. In particular, these vaccine records more often may be prone to negative misclassification, that is, a clinic's record of an individual patient's vaccination status may be unvaccinated when, in reality, this patient was vaccinated outside of the clinic. With large nation-wide endeavors to encourage vaccinations without a gold-standard vaccine record system, sensitivity analyses that incorporate misclassification rates are promising for robust inference. In this work we introduce a novel extension of Bayesian logistic regression where we perturb the clinic size and vaccination count with random draws from expert-elicited prior distributions. These prior distributions represent the misclassification rates for each clinic that stochastically add unvaccinated counts to the observed vaccinated counts. These prior distributions are assigned for each clinic (the first level in a group-level randomized trial). We demonstrate this method with a data application from a CCRT evaluating the influence of a behavioral intervention on vaccination uptake among U.S. veterans. A simulation study is carried out demonstrating its estimation properties.

翻译：二元结局的误分类并不罕见，而研究其对政策驱动型研究结果影响的统计方法尚显不足。尽管二元结局的误分类在统计学上是普遍现象，我们重点关注公共卫生应用中的一个具体案例：疫苗接种。在公共卫生领域，旨在为政策提供依据的研究设计之一是聚类对照随机试验（CCRT）。一项旨在评估新型行为干预措施对提高疫苗接种率影响的CCRT，当其支持数据（疫苗接种记录）不完整时，可能会产生严重偏倚。具体而言，这些疫苗记录往往更容易出现阴性误分类，即诊所记录的个体患者疫苗接种状态可能显示为"未接种"，而实际上该患者已在诊所外完成了接种。在缺乏金标准疫苗记录系统的大规模全国性疫苗接种推广工作中，纳入误分类率的敏感性分析对于获得稳健的推断结果具有重要前景。本研究提出了一种贝叶斯逻辑回归的新扩展方法，通过从专家启发式先验分布中随机抽取数值，对诊所规模和疫苗接种计数进行扰动。这些先验分布代表了每个诊所的误分类率，它们以随机方式将未接种计数添加到观察到的已接种计数中。这些先验分布被分配给每个诊所（组群水平随机试验中的第一层级）。我们通过一项评估行为干预对美国退伍军人疫苗接种率影响的CCRT数据应用来演示该方法，并进行了模拟研究以展示其估计特性。