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

TL;DR

This paper introduces a new marginalized zero-one-inflated Beta time series model that effectively captures temporal dependence in bounded proportional data, improving analysis of health policy interventions.

Contribution

It develops a novel copula-based three-part regression model for bounded outcomes with zeros and ones, addressing a gap in modeling temporal dependence in such data.

Findings

Model performs well in simulation studies.

Applied successfully to real health policy data.

Provides insights into covariate effects on proportions.

Abstract

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.