Interrupted Time Series Analysis

Core Idea

Interrupted time series (ITS) analysis evaluates the impact of an intervention at a known time point by modeling the outcome trend before and after the intervention. The approach uses segmented regression with four key parameters: the pre-intervention level, the pre-intervention trend (slope), the immediate level change at the intervention point, and the change in trend after the intervention. Unlike DiD, ITS can be applied with a single group (no control series needed), relying instead on the pre-intervention trend to project the counterfactual trajectory that would have occurred without the intervention. The deviation of the observed post-intervention trajectory from this counterfactual provides the estimated intervention effect. ITS must account for autocorrelation in the time series (observations close in time are correlated) and is most convincing when the pre-intervention series is long enough to establish a stable trend.

Explainer

Many health interventions are implemented at a specific point in time — a hospital installs hand sanitizer dispensers, a government bans a pesticide, or a new prescribing guideline takes effect. Interrupted time series analysis is designed for exactly this situation: you have repeated measurements of an outcome over time, and an intervention occurs at a known point, "interrupting" the series. The question is whether the series changes after the intervention in a way that would not have occurred otherwise.

The standard approach is segmented regression, which fits a piecewise linear model with four parameters. The pre-intervention intercept and pre-intervention slope establish the baseline trend. The level change (the coefficient on a step function at the intervention point) captures any immediate jump or drop in the outcome. The trend change (the coefficient on the interaction between time and the post-intervention indicator) captures any change in the ongoing slope after the intervention. The counterfactual — what would have happened without the intervention — is the extrapolation of the pre-intervention trend into the post-intervention period.

Two technical issues require attention. First, time series data exhibit autocorrelation — observations close in time are more similar than distant ones. OLS assumes independence and produces standard errors that are too small when autocorrelation is present. Solutions include Newey-West robust standard errors, generalized least squares with an autoregressive error structure (e.g., AR(1)), or full ARIMA modeling. Second, seasonality is common in health data (influenza peaks in winter, trauma peaks in summer). If the intervention point coincides with a seasonal pattern, the apparent intervention effect may be spurious. Including seasonal indicators (monthly dummy variables or harmonic terms) controls for this.

The main threat to ITS validity is co-intervention — something else changing at the same time as the intervention. A single-group ITS cannot distinguish between the intended intervention and a coincident policy change, staffing shift, or data collection modification. Adding a control series — a comparable population that did not receive the intervention — transforms the design into a controlled ITS, which controls for any temporal event that affects both groups equally. This is closely related to DiD but leverages the full time series rather than collapsing to pre-post means, making it more powerful and more informative about the temporal dynamics of the intervention effect.