Chapter11 Interrupted time series analysis using segmented regression
Segmented regression is another common way for analyzing the impact of an intervention. Two good papers explaining the methods of segmented regression are, for example:
- Bernal, J. L., Cummins, S., & Gasparrini, A. (2017). Interrupted time series regression for the evaluation of public health interventions: a tutorial. International journal of epidemiology, 46(1), 348-355.
- Wagner, A. K., Soumerai, S. B., Zhang, F., & Ross‐Degnan, D. (2002). Segmented regression analysis of interrupted time series studies in medication use research. Journal of clinical pharmacy and therapeutics, 27(4), 299-309.
As explained by the latter, “Segmented regression analysis uses statistical models to estimate level and trend in the pre-intervention segment and changes in level and trend after the intervention (or interventions).”.
More exactly, a segmented regression model is structured as follow:
\[Y = b_0 + b_1Time + b_2Intervention + b_3TimeSinceIntervention + e\]
It includes at least:
- an outcome variable (Y);
- a variable that indicates the time 1,2,…,t passed from the start of the series;
- a dummy variable (0/1) for observation collected before (0) or after (1) the intervention;
- a variable measuring the time 1,2,…,t passed since the intervention has occured, and which is equal to zero before the intervention.
The interpretation of coefficients is as follows:
- \(b_0\) is the baseline level at Time 0;
- The Time (\(b_1\)) coefficient indicates the trend (the slope) before the intervention ( change in outcome associated with a time unit increase).
- The Intervention (\(b_2\)) coefficient indicates the immediate effect (level change) induced by the intervention (from the last observation before the intervention to the first one after).
- The Time Since Intervention (\(b_3\)) coefficient indicates the “sustained effect”, i.e., the change in trend after the intervention (the effect for each time point that passes after the intervention). It measures the difference between the slope of the line before and after the intervention. It is also possible to calculate the slope of the line after the intervention by summing up the coefficients of Time and Time Since Treatment (\(b_1 + b_3\))
A good tutorial on this tecnique can be found at the following link: https://ds4ps.org/pe4ps-textbook/docs/p-020-time-series.html.