Interrupted time series and segmented regression
The analysis question
An interrupted time series compares the observed post-intervention trajectory with a projected continuation of the pre-intervention trajectory under explicit assumptions. Segmented regression can parameterize an immediate level change, a slope change or another prespecified impact pattern. Choose that pattern from how the intervention is expected to work before inspecting the outcome series.
Define the time variables
Let T index observations, let X be 0 before the intervention and 1 from its start T0, and define time since intervention as (T − T0) × X. It is zero at the breakpoint. In the linear identity-link model Y = β0 + β1T + β2X + β3(T − T0)X, β2 is the level change at T0 and β3 is the change in slope. At a later time, the contrast is β2 + β3(T − T0). Different coding or a nonlinear link changes coefficient interpretation; use the cited correction to the original tutorial.
What a level change and a slope change look like
Choose the outcome and error model
- Use a model appropriate to counts, rates, proportions or continuous outcomes. A count model may need a log denominator offset and an overdispersion assessment.
- Check residual temporal dependence and seasonality. Independent-error standard errors can be misleading even when the fitted trajectory looks plausible.
- Document observation spacing, data quality, coding changes, denominator changes and intervention rollout or lag.
- A short or unstable baseline weakens the projected counterfactual. There is no universal number of observations that guarantees adequate power or trend estimation.
Strengthen the design
A credible unaffected comparison series, alternative intervention dates, appropriate negative controls and sensitivity to trend or lag assumptions may help investigate competing explanations. Each has assumptions of its own. A concurrent system-wide change cannot be separated by adding an intervention indicator that occurred at exactly the same time.
Example
Monthly infection counts fall after a hospital protocol. The team prespecifies the expected level or trend change, models patient-days where appropriate, checks seasonal and residual patterns, and examines concurrent surveillance changes before attributing the decline to the protocol.
Record in the workspace
Record the intervention timing and expected impact, time scale, outcome and denominator, counterfactual trend, comparison series, error structure and sensitivity analyses. The code library does not yet provide a validated general ITS implementation; obtain a method-specific implementation and review.
What to watch out for
Segmented regression does not isolate an intervention from every event occurring at the same time. Concurrent changes, seasonality, autocorrelation and changing denominators can undermine the counterfactual trend.
- Interrupted time series regression for the evaluation of public health interventions: a tutorial (opens in a new tab) · Int J Epidemiol · doi 10.1093/ije/dyw098
- Segmented Regression in an Interrupted Time Series Study Design (opens in a new tab) · Anesth Analg · doi 10.1213/ANE.0000000000005269
- Corrigendum to: Interrupted time series regression for the evaluation of public health interventions: a tutorial (opens in a new tab) · Int J Epidemiol · doi 10.1093/ije/dyaa118