Modeling Time Series Regression with Multiple Disruption Events

Abstract: Interrupted time series (ITS) analysis is a quasi-experimental design for evaluating interventions and external shocks when randomized controlled trials are infeasible – for example, when an intervention affects an entire population and no clear control group can be established. Classic ITS focuses on a single intervention at one point in time, with counterfactual predictions used to estimate its effect. This study investigates modeling strategies for an expanded version of ITS, where multiple disruption events occur and multiple series can be observed. We propose a regression-based approach that expands the standard design along two dimensions: first, by allowing multiple disruptions under different assumptions about their relationships; and second, by extending the framework to longitudinal panel data, enabling the joint analysis of related series. The methodology incorporates fixed- and random-effects structures to capture shared patterns across series, and provides statistical procedures to test disruption effects, the presence of random effects, and effect sizes. We implement these contributions in a publicly available R package, designed to support research in domains where interventions and systemic change are central. Finally, we validate this framework through extensive simulations of unknown parameters, and two case studies in public health: regional waiting times for medical services in the United Kingdom during the start and end of the COVID-19 lockdowns, and birth rates in Israel during wars and national safety crises, illustrating the “baby boom” phenomenon.