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[Preprint]. 2024 Feb 27:rs.3.rs-3972428.
doi: 10.21203/rs.3.rs-3972428/v1.

Interpretation of coefficients in segmented regression for interrupted time series analyses

Affiliations

Interpretation of coefficients in segmented regression for interrupted time series analyses

Yongzhe Wang et al. Res Sq. .

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Abstract

Background: 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.

Methods: 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.

Results: 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.

Conclusions: 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.

Keywords: coefficient interpretation; healthcare policy evaluation; interrupted time series design; observational study; segmented regression.

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Conflict of interest statement

Competing interests All authors declare no conflicts of interest.

Figures

Figure 1
Figure 1
Estimated segmented regression line using the illustration dataset. The scatter points in blue and orange represented the data points in the pre- and post-intervention periods, respectively, while the black lines represented the pre- and post-intervention models. The vertical black dot-dashed line represented the time point of policy (i.e., intervention) implementation. The black dashed line represented the extension of the post-intervention model.

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