Marginalized Three-Part Beta Interrupted Time Series Regression Models for Proportional Data Analysis

• Activity Number: 18 - New Models, Diagnostics, and Considerations in Evaluating Intervention and Policy Effects
• Type: Topic Contributed
• Date/Time: Sunday, August 7, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Health Policy Statistics Section
• Author(s): Shangyuan Ye*
• Companies: Oregon Health and Science University
• Keywords: Interrupted time series; Beta regression; Three-part model; Marginalized model; Copula

Abstract

Interrupted time series (ITS) -- a quasi-experimental design -- is often used to evaluate the effectiveness of a health policy intervention that accounts for the temporal dependence between outcomes. When an aggregated-level percentage is the outcome of interest, 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 which captures the temporal dependence between 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.