A marginalized three-part interrupted time series regression model for proportional data

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 a 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.