Interrupted Time Series for Public Health

The level change is the immediate, step-like shift in the outcome at the moment the intervention takes effect — the jump up or down right at the interruption. The slope change is how much the underlying trend tilts afterward, that is, whether the outcome starts rising or falling faster or slower than it did before. A policy might cause an abrupt drop with no change in trend, a gradual change in trend with no immediate jump, both, or neither. Wagner and colleagues stress reporting both because they describe fundamentally different effect patterns.

In a time series, observations close together are correlated, so the residuals of an ordinary regression are not independent. Ignoring this leaves the point estimates roughly unbiased but makes standard errors too small, inflating significance and risking false positives. Lopez Bernal, Cummins and Gasparrini recommend testing for autocorrelation (for example with the Durbin-Watson statistic or autocorrelation plots) and accounting for it through autoregressive error models or robust standard errors. Seasonality should be modeled at the same time, since seasonal cycles otherwise contaminate both the trend and the estimated effect.

A single interrupted series can be confounded by anything else that happened around the intervention time. Adding an equivalent series from a population that did not receive the intervention turns the analysis into a controlled interrupted time series: the effect becomes the difference between the treated and control series in their level and slope changes. If both series are subject to the same coincident shocks but only the treated one received the intervention, the comparison removes those shared influences. Lopez Bernal and colleagues regard a well-chosen comparison series as one of the most effective ways to sharpen causal inference from ITS.