Interrupted time-series impact estimation

Model level slope and correlation

Level and slope changes refer to a specified time origin and scale. Choose an appropriate outcome distribution and model serial correlation and seasonality. An offset may be needed for rates with changing populations.

Flow diagram

Interrupted time-series impact estimationF1.S1Define level and slope contrastsF1.S2Select segmented modelF1.S3Model serial and seasonal structureF1.S4Include controls when justifiedF1.S5Specify uncertainty and predictedeffectsF1.N1Impact model specificationScenarioImpact formTrendCorrelationSeasonalityContrastPrimaryimpactLagged impactAlternativetrendF1.N2Illustrative model specificationt indexes equally spaced observations, T₀ isthe first intervention time and Iₜ is 1 fromT₀ onward. β₂ is the immediate level change;β₃ is the slope change; β₁ is thepre-intervention slope.F1.N3Method and protocol evidenceF1.N4Model assumptionsF1.S0 Start flowInterrupted time-series impactestimationF1.S999 End flowEnd flow

Steps

Define level and slope contrasts

Prespecify effect scale, impact form and follow-up horizon.

Select segmented model

Choose a distribution and link appropriate to the outcome and denominators.

Model serial and seasonal structure

Specify autocorrelation, seasonal terms and trend flexibility.

Include controls when justified

Define controlled contrasts rather than assuming any series is a valid control.

Specify uncertainty and predicted effects

Plan model-based contrasts and diagnostics with sensitivity analyses.

Interrupted time-series impact estimation

End flow

Tables and supporting information

Impact model specification

Impact model specificationScenarioImpact formTrendCorrelationSeasonalityContrastPrimaryimpactLagged impactAlternativetrend

Record expected shapes and uncertainty methods; leave estimated effects blank.

Illustrative model specification

t indexes equally spaced observations, T₀ is the first intervention time and Iₜ is 1 from T₀ onward. β₂ is the immediate level change; β₃ is the slope change; β₁ is the pre-intervention slope.

Method and protocol evidence

Attach the protocol, methodological sources and versioned software specification supporting these decisions. Record citations and provenance; do not enter participant identifiers.

Model assumptions

Linear Gaussian segmented regression is only one option; notation must be adapted for count or nonlinear outcomes. This linear identity-link model is illustrative. Counts may need a count model and population offset. Serial correlation, seasonality, transition periods and concurrent shocks must be addressed; a fitted change alone does not identify a causal effect.

Sources