# Interpretation of coefficients in segmented regression for interrupted time series analyses

## TL;DR

This paper explains how different ways of setting up segmented regression models can lead to different interpretations of the same data in interrupted time series analysis.

## Contribution

The paper clarifies the differences in coefficient interpretation between two common segmented regression parametrizations in ITS analysis.

## Key findings

- Both parametrizations represent the same model but differ in coefficient interpretation.
- The immediate intervention effect is estimated differently depending on the parametrization used.
- Researchers should be cautious when interpreting coefficients and calculating intervention effects.

## Abstract

Segmented regression, a common model for interrupted time series (ITS) analysis, primarily utilizes two equation parametrizations. Interpretations of coefficients vary between the two segmented regression parametrizations, leading to occasional user misinterpretations.

To illustrate differences in coefficient interpretation between two common parametrizations of segmented regression in ITS analysis, we derived analytical results and present an illustration evaluating the impact of a smoking regulation policy in Italy using a publicly accessible dataset. Estimated coefficients and their standard errors were obtained using two commonly used parametrizations for segmented regression with continuous outcomes. We clarified coefficient interpretations and intervention effect calculations.

Our investigation revealed that both parametrizations represent the same model. However, due to differences in parametrization, the immediate effect of the intervention is estimated differently under the two approaches. The key difference lies in the interpretation of the coefficient related to the binary indicator for intervention implementation, impacting the calculation of the immediate effect.

Two common parametrizations of segmented regression represent the same model but have different interpretations of a key coefficient. Researchers employing either parametrization should exercise caution when interpreting coefficients and calculating intervention effects.