Interrupted Time Series protocol

The outcome is aggregated into equal time intervals and regressed on three terms: time (the pre-intervention slope), an interruption indicator (1 from the first affected period onward), and time-since-interruption (0 until the interruption, then counting up). Their coefficients are the baseline trend, the change in level — the immediate step at the interruption — and the change in slope — how the trend itself bends afterwards. They answer different questions and can point in opposite directions: a policy can cause a sharp one-off drop that then drifts back up (level change down, slope change up), and reporting only one of the two would describe it wrongly (Wagner 2002; Lopez Bernal 2017).

Two things routinely break it. Seasonality: if the outcome has an annual cycle and the interruption falls at a particular point in that cycle, the cycle is read as a step or a bend. Autocorrelation: adjacent time points resemble each other, which does not bias the coefficients but makes the standard errors too small and the confidence intervals too narrow. Neither is optional to consider.

Why a control series strengthens the claim. An uncontrolled ITS attributes every departure from the extrapolated pre-trend to the intervention — including anything else that happened at the same time, and any secular change that was already bending. A comparison series that shares the secular environment but is not exposed to the intervention lets you difference those out: the estimate becomes the difference in level and slope changes, and a co-intervention affecting both series cancels (Lopez Bernal 2018).