With the emergence and spread of infectious diseases with pandemic potential, such as COVID- 19, the urgency for vaccine development have led to unprecedented compressed and accelerated schedules that shortened the standard development timeline. In a relatively short time, the leading pharmaceutical companies1, received an Emergency Use Authorization (EUA) for vaccine\prime s en-mass deployment To monitor the potential side effect(s) of the vaccine during the (initial) vaccination campaign, we developed an optimal sequential test that allows for the early detection of potential side effect(s). This test employs a rule to stop the vaccination process once the observed number of side effect incidents exceeds a certain (pre-determined) threshold. The optimality of the proposed sequential test is justified when compared with the ({\alpha}, {\beta}) optimality of the non-randomized fixed-sample Uniformly Most Powerful (UMP) test. In the case of a single side effect, we study the properties of the sequential test and derive the exact expressions of the Average Sample Number (ASN) curve of the stopping time (and its variance) via the regularized incomplete beta function. Additionally, we derive the asymptotic distribution of the relative savings in ASN as compared to maximal sample size. Moreover, we construct the post-test parameter estimate and studied its sampling properties, including its asymptotic behavior under local-type alternatives. These limiting behavior results are the consistency and asymptotic normality of the post-test parameter estimator. We conclude the paper with a small simulation study illustrating the asymptotic performance of the point and interval estimation and provide a detailed example, based on COVID-19 side effect data (see Beatty et al. (2021)) of our suggested testing procedure.

翻译：随着具有大流行潜力的传染病（如COVID-19）的出现和传播，疫苗开发的紧迫性导致了前所未有的压缩和加速进程，缩短了标准开发时间表。在相对较短的时间内，主要制药公司获得了疫苗大规模部署的紧急使用授权（EUA）。为监测（初期）疫苗接种运动期间疫苗的潜在副作用，我们开发了一种最优序贯检验，用于早期检测潜在的副作用。该检验采用一条规则，一旦观察到的副作用事件数量超过某个（预先确定的）阈值，即停止疫苗接种过程。与非随机化固定样本一致最优势（UMP）检验的（α, β）最优性相比，该序贯检验的最优性得到了验证。在单一副作用情形下，我们研究了序贯检验的性质，并通过正则化不完全贝塔函数推导了停止时间的平均样本量（ASN）曲线（及其方差）的精确表达式。此外，我们推导了相对于最大样本量的ASN相对节省的渐近分布。同时，我们构建了检验后参数估计量，并研究了其抽样性质，包括在局部型备择假设下的渐近行为。这些极限行为结果是检验后参数估计量的一致性和渐近正态性。我们通过一个小的模拟研究来展示点估计和区间估计的渐近性能，并基于COVID-19副作用数据（参见Beatty等人（2021））给出了我们建议检验程序的详细实例。