  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.
