We propose an online false discovery rate (FDR) controlling method based on conditional local FDR (LIS), designed for infectious disease datasets that are discrete and exhibit complex dependencies. Unlike existing online FDR methods, which often assume independence or suffer from low statistical power in dependent settings, our approach effectively controls FDR while maintaining high detection power in realistic epidemic scenarios. For disease modeling, we establish a Dynamic Bayesian Network (DBN) structure within the Susceptible-Infected-Susceptible (SIS) model, a widely used epidemiological framework for infectious diseases. Our method requires no additional tuning parameters apart from the width of the sliding window, making it practical for real-time disease monitoring. From a statistical perspective, we prove that our method ensures valid FDR control under stationary and ergodic dependencies, extending online hypothesis testing to a broader range of dependent and discrete datasets. Additionally, our method achieves higher statistical power than existing approaches by leveraging LIS, which has been shown to be more powerful than traditional $p$-value-based methods. We validate our method through extensive simulations and real-world applications, including the analysis of infectious disease incidence data. Our results demonstrate that the proposed approach outperforms existing methods by achieving higher detection power while maintaining rigorous FDR control.

翻译：我们提出了一种基于条件局部FDR（LIS）的在线错误发现率（FDR）控制方法，专门针对具有离散性和复杂依赖性的传染病数据集设计。不同于现有在线FDR方法——它们常假设独立性或在依赖场景下统计功效较低——我们的方法在真实疫情情景中能有效控制FDR的同时保持高检测效能。在疾病建模方面，我们在易感-感染-易感（SIS）模型（一种广泛应用于传染病的流行病学框架）内建立了动态贝叶斯网络（DBN）结构。该方法除滑动窗口宽度外无需额外调整参数，使其适用于实时疾病监测。从统计学角度，我们证明了该方法在稳态和遍历依赖条件下能确保有效的FDR控制，将在线假设检验扩展至更广泛的依赖性和离散型数据集。此外，通过利用已被证明比传统p值方法更强大的LIS，我们的方法实现了比现有方法更高的统计功效。我们通过广泛模拟和实际应用（包括传染病发病率数据分析）验证了该方法。结果表明，所提方法在严格保持FDR控制的同时实现了更高检测效能，优于现有方法。