Controlled interrupted time series, segmented regression and difference-in-difference: a guide bridging econometric terminology for public health researchers

While econometrics and statistics drove modern quasi-experimental methods for causal inference in policy evaluation, public health frequently adopts such tools to evaluate health interventions when randomised controlled trials are not feasible. However, public health researchers unfamiliar with the causal inference literature can become lost due to methodological gaps and non-uniform vocabulary between these disciplines. Contending that terminology is the primary source of misunderstanding for a beginner audience, we provide a clear, structured overview of key concepts and terms for public health evaluations, identifying synonyms and misleading words across fields. We also address issues relating to model specification and the interpretation of model parameter estimates. In doing so, we place specific emphasis on the interrupted time series (ITS) design, one of the most widely applied approaches to policy evaluation in public health when using observational data. Finally, we address a common misconception in the application of autoregressive, integrated, moving average (ARIMA) models, the most frequently used regression technique in ITS analysis.