Interrupted time series regression for the evaluation of public health interventions: a tutorial

James Lopez Bernal, Steven Cummins, Antonio Gasparrini, James Lopez Bernal, Steven Cummins, Antonio Gasparrini

Abstract

Interrupted time series (ITS) analysis is a valuable study design for evaluating the effectiveness of population-level health interventions that have been implemented at a clearly defined point in time. It is increasingly being used to evaluate the effectiveness of interventions ranging from clinical therapy to national public health legislation. Whereas the design shares many properties of regression-based approaches in other epidemiological studies, there are a range of unique features of time series data that require additional methodological considerations. In this tutorial we use a worked example to demonstrate a robust approach to ITS analysis using segmented regression. We begin by describing the design and considering when ITS is an appropriate design choice. We then discuss the essential, yet often omitted, step of proposing the impact model a priori. Subsequently, we demonstrate the approach to statistical analysis including the main segmented regression model. Finally we describe the main methodological issues associated with ITS analysis: over-dispersion of time series data, autocorrelation, adjusting for seasonal trends and controlling for time-varying confounders, and we also outline some of the more complex design adaptations that can be used to strengthen the basic ITS design.

Figures

Figure 1
Figure 1
Scatter plot of example dataset. Standardized (Std) rate of ACE over time. White background, pre-intervention period; grey background, post-intervention period; continuous line, pre-intervention trend; dashed line, counterfactual scenario
Figure 2
Figure 2
Examples of impact models used in ITS (a) Level change; (b) Slope change; (c) Level and slope change; (d) Slope change following a lag; (e) Temporary level change; (f) Temporary slope change leading to a level change.
Figure 3
Figure 3
Interrupted time series with level change regression model. Line: predicted trend based on the unadjusted regression model
Figure 4
Figure 4
Model adjusted for seasonality. Solid line: predicted trend based on the seasonally adjusted regression model. Dashed line: de-seasonalized trend

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