Interpretation of coefficients in segmented regression for interrupted time series analyses

Area of Science:

• Epidemiology
• Biostatistics
• Health Policy Analysis

Background:

• Segmented regression is a standard method for interrupted time series (ITS) analysis.
• Two primary equation parametrizations exist for segmented regression.
• Coefficient interpretation differences can lead to user misinterpretations in ITS analysis.

Purpose of the Study:

• To clarify the distinct coefficient interpretations between two common segmented regression parametrizations used in ITS analysis.
• To illustrate how these parametrization differences impact the estimation and interpretation of intervention effects.
• To provide guidance for accurate analysis and reporting in ITS studies.

Main Methods:

• Derived analytical results to compare two segmented regression parametrizations for ITS.
• Applied the parametrizations to a real-world dataset evaluating an Italian smoking regulation policy.
• Focused on continuous outcomes and clarified coefficient interpretation and intervention effect calculation.

Main Results:

• Confirmed both parametrizations model the same underlying segmented regression.
• Demonstrated that the immediate intervention effect is estimated differently due to parametrization.
• Identified the coefficient for intervention implementation as the key differentiator in interpretation and effect calculation.

Conclusions:

• Two common segmented regression parametrizations, though modeling the same ITS, yield different coefficient interpretations.
• Researchers must carefully interpret coefficients and calculate intervention effects, regardless of the chosen parametrization.
• Awareness of these differences is crucial for accurate policy impact assessment in ITS studies.