Interrupted time series (ITS) is often used to evaluate the effectiveness of a health policy intervention that accounts for the temporal dependence of outcomes. When the outcome of interest is a percentage or percentile, the data can be highly skewed, bounded in $[0, 1]$, and have many zeros or ones. A three-part Beta regression model is commonly used to separate zeros, ones, and positive values explicitly by three submodels. However, incorporating temporal dependence into the three-part Beta regression model is challenging. In this article, we propose a marginalized zero-one-inflated Beta time series model that captures the temporal dependence of outcomes through copula and allows investigators to examine covariate effects on the marginal mean. We investigate its practical performance using simulation studies and apply the model to a real ITS study.

翻译：中断时间序列（ITS）常用于评估考虑结果时间依赖性的健康政策干预效果。当关注的结果为百分比或百分位数时，数据可能呈现高度偏态分布，被限制在$[0, 1]$区间内，且包含大量零值或一值。三部分Beta回归模型通常通过三个子模型分别处理零值、一值和正值。然而，将时间依赖性纳入三部分Beta回归模型具有挑战性。本文提出一种边缘化零一膨胀Beta时间序列模型，该模型通过copula捕捉结果的时间依赖性，并允许研究者检验协变量对边缘均值的影响。我们通过模拟研究评估其实际性能，并将该模型应用于真实的中断时间序列研究案例。