发表机构
The Ohio State University; Uppsala University（俄亥俄州立大学; 乌普萨拉大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对Horvitz--Thompson患病率估计的噪声与缺失问题，提出联合局部线性趋势状态空间模型，利用卡尔曼滤波与平滑提高精度，并在模拟和真实数据中验证了效果。
AI 中文摘要
Horvitz--Thompson（HT）估计量可以在重复监测下，通过校正由计划性、基于症状和接触者追踪部分引起的非随机检测，提供传染病每日患病率的无偏估计。然而，由于每个HT估计基于当日可用的检测数据，且可能涉及高度可变的逆概率权重，因此可能带有噪声，精度随时间变化，并在检测暂时中断时变得不可用。每日HT估计量被建模为潜在患病率过程的带噪声观测，日特定观测方差通过删除一组群组刀切法估计。我们的主要规格是联合局部线性趋势状态空间模型，该模型通过添加潜在斜率扩展了仅含水平的随机游走标准模型。卡尔曼滤波器通过借用过去估计的信息来提高精度。在每个时间$t$，过程方差仅使用截至时间$t$的观测来估计或结转，因此所得滤波估计可实时获得。我们还描述了相应的卡尔曼平滑器，作为基于完整观测序列的回顾性扩展。当每日HT估计缺失时，卡尔曼滤波器通过仅预测更新进行，而相应的平滑器则使用后续观测回顾性地重建这些时期。在模拟中，联合卡尔曼滤波器相对于原始每日HT估计量大幅提高了精度，同时保留了主要的时间模式，平滑器提供了更稳定的回顾性总结。在俄亥俄州立大学2020年秋季SARS-CoV-2监测数据中，滤波器和平滑器在无检测日提供了估计，而HT估计量在这些日子既无点估计也无区间估计，并且在有观测日产生了比HT区间更窄的置信区间。
英文摘要
Horvitz--Thompson (HT) estimators can provide unbiased daily estimates of infectious disease prevalence under repeated surveillance by correcting for nonrandom testing induced by scheduled, symptom-based, and contact-tracing components. However, because each HT estimate is based on the testing data available for that day and may involve highly variable inverse probability weights, it can be noisy, have precision that varies over time, and become unavailable during temporary interruptions in testing. The daily HT estimator is modeled as a noisy observation of an underlying prevalence process, with day-specific observation variances estimated using a delete-a-group jackknife. Our primary specification is a joint local linear trend state-space model that extends the standard level-only random walk by adding a latent slope. The Kalman filter improves precision by borrowing information from past estimates. At each time $t$, the process variances are estimated or carried forward using only observations available through time $t$, so the resulting filtered estimate is available in real time. We also describe the corresponding Kalman smoother as a retrospective extension based on the full observed series. When daily HT estimates are missing, the Kalman filter proceeds through prediction-only updates, whereas the corresponding smoother retrospectively reconstructs those periods using later observations. In simulations, the joint Kalman filter substantially improves precision relative to the raw daily HT estimator while preserving the main temporal pattern, and the smoother provides a more stable retrospective summary. In The Ohio State University's fall 2020 SARS-CoV-2 surveillance data, the filter and smoother provide estimates on no-testing days, when the HT estimator provides neither point nor interval estimates, and yield narrower confidence intervals than HT intervals on observed days.
CommentsAbstract shortened to comply with arXiv's 1,920-character limit
