Optimized segmented regression models for the transition period of intervention effects

Abstract Background The interrupted time series (ITS) design is a widely used approach to examine the effects of interventions. However, the classic segmented regression (CSR) method, the most popular statistical technique for analyzing ITS data, may not be adequate when there is a transitional period between the pre- and post-intervention phases. Methods To address this issue and better capture the distribution patterns of intervention effects during the transition period, we propose using different cumulative distribution functions in the CSR model and developing corresponding optimized segmented regression (OSR) models. This study illustrates the application of OSR models to estimate the long-term impact of a national free delivery service policy intervention in Ethiopia. Results Regardless of the choice of transition length ( $$L$$ L ) and distribution patterns of intervention effects, the OSR models outperformed the CSR model in terms of mean square error (MSE), indicating the existence of a transition period and the validity of our model’s assumptions. However, the estimates of long-term impacts using OSR models are sensitive to the selection of L, highlighting the importance of reasonable parameter specification. We propose a data-driven approach to select the transition period length to address this issue. Conclusions Overall, our OSR models provide a powerful tool for modeling intervention effects during the transition period, with a superior model fit and more accurate estimates of long-term impacts. Our study highlights the importance of appropriate statistical methods for analyzing ITS data and provides a useful framework for future research.