Interpretation of coefficients in segmented regression for interrupted time series analyses

Area of Science:

• Epidemiology
• Biostatistics
• Health Services Research

Background:

• Segmented regression is a standard method for interrupted time series (ITS) analysis.
• Two primary equation parametrizations exist for segmented regression.
• Divergent coefficient interpretations between these parametrizations can cause user errors.

Purpose of the Study:

• To clarify coefficient interpretation differences between two segmented regression parametrizations in ITS analysis.
• To illustrate these differences using a real-world policy example.
• To guide accurate interpretation of intervention effects in ITS studies.

Main Methods:

• Derived analytical results for two common segmented regression parametrizations.
• Applied these parametrizations to a dataset evaluating Italy's smoking regulation policy.
• Obtained and compared estimated coefficients and standard errors.

Main Results:

• Both parametrizations model the same underlying segmented regression.
• The immediate intervention effect is estimated differently due to parametrization choices.
• The interpretation of the intervention indicator coefficient critically affects immediate effect calculation.

Conclusions:

• Despite representing the same model, segmented regression parametrizations yield different coefficient interpretations.
• Researchers must carefully interpret coefficients and calculate intervention effects, regardless of parametrization used.
• Awareness of parametrization nuances is crucial for accurate ITS analysis.