Infectious Disease Surveillance Center, National Institute of Infectious Diseases, Tokyo, Japan.
Graduate School of Medicine, The University of Tokyo, Tokyo, Japan.
BMC Med Res Methodol. 2022 Jul 25;22(1):202. doi: 10.1186/s12874-022-01662-1.
Interrupted time series (ITS) analysis has become a popular design to evaluate the effects of health interventions. However, the most common formulation for ITS, the linear segmented regression, is not always adequate, especially when the timing of the intervention is unclear. In this study, we propose a new model to overcome this limitation.
We propose a new ITS model, ARIMAITS-DL, that combines (1) the Autoregressive Integrated Moving Average (ARIMA) model and (2) distributed lag functional terms. The ARIMA technique allows us to model autocorrelation, which is frequently observed in time series data, and the decaying cumulative effect of the intervention. By contrast, the distributed lag functional terms represent the idea that the intervention effect does not start at a fixed time point but is distributed over a certain interval (thus, the intervention timing seems unclear). We discuss how to select the distribution of the effect, the model construction process, diagnosing the model fitting, and interpreting the results. Further, our model is implemented as an example of a statement of emergency (SoE) during the coronavirus disease 2019 pandemic in Japan.
We illustrate the ARIMAITS-DL model with some practical distributed lag terms to examine the effect of the SoE on human mobility in Japan. We confirm that the SoE was successful in reducing the movement of people (15.0-16.0% reduction in Tokyo), at least between February 20 and May 19, 2020. We also provide the R code for other researchers to easily replicate our method.
Our model, ARIMAITS-DL, is a useful tool as it can account for the unclear intervention timing and distributed lag effect with autocorrelation and allows for flexible modeling of different types of impacts such as uniformly or normally distributed impact over time.
中断时间序列（ITS）分析已成为评估健康干预措施效果的一种流行设计。然而，最常用的 ITS 线性分段回归模型并不总是足够的，尤其是当干预时间不明确时。在本研究中，我们提出了一种新的模型来克服这一限制。
我们提出了一种新的 ITS 模型，ARIMAITS-DL，它结合了（1）自回归综合移动平均（ARIMA）模型和（2）分布滞后函数项。ARIMA 技术允许我们对时间序列数据中经常观察到的自相关进行建模，以及干预的衰减累积效应。相比之下，分布滞后函数项表示干预效果不是从固定时间点开始，而是分布在一定时间间隔内（因此，干预时间似乎不明确）的想法。我们讨论了如何选择效应的分布、模型构建过程、诊断模型拟合以及解释结果。此外，我们的模型作为日本 2019 年冠状病毒病大流行期间紧急声明（SoE）的一个实例进行了实现。
我们用一些实际的分布滞后项来说明 ARIMAITS-DL 模型，以检验 SoE 对日本人口流动的影响。我们确认 SoE 成功地减少了人们的行动（东京减少了 15.0-16.0%），至少在 2020 年 2 月 20 日至 5 月 19 日之间。我们还提供了其他研究人员易于复制我们方法的 R 代码。
我们的模型 ARIMAITS-DL 是一种有用的工具，因为它可以解释干预时间不明确和分布滞后效应，同时考虑到自相关和随时间均匀或正态分布的影响等不同类型的影响的灵活建模。
