Reflection on modern methods: a common error in the segmented regression parameterization of interrupted time-series analyses.

Interrupted time-series (ITS) designs are a robust and increasingly popular non-randomized study design for strong causal inference in the evaluation of public health interventions. One of the most common techniques for model parameterization in the analysis of ITS designs is segmented regression, which uses a series of indicators and linear terms to represent the level and trend of the time-series before and after an intervention. In this article, we highlight an important error often presented in tutorials and published peer-reviewed papers using segmented regression parameterization for the analyses of ITS designs. We show that researchers cannot simply use the product between their calendar time variable and the indicator variable indicating pre- versus post-intervention time periods to represent the post-intervention linear segment. If researchers use this often-presented parameterization, they will get an erroneous result for the level change in their time-series. We show that researchers must take care to use the product between their intervention variable and the time elapsed since the start of the intervention, rather than the time since the beginning of their study. Thus, the second linear segment of the time-series indexing the post-intervention level and trend should be zero before intervention implementation and begin by counting from zero, rather than counting from the time elapsed since the beginning of the study. We hope that this article can clarify segmented regression parameterization for the analysis of ITS designs and help researchers avoid confusing and erroneous results in the level changes of their time-series.