Are We in Control? How Best to Include a Control Group in Interrupted Time Series Designs: A Simulation Study

Area of Science:

• Epidemiology
• Biostatistics
• Health Services Research

Background:

• Controlled interrupted time series (CITS) are vital for evaluating public health policies.
• Limited research exists on statistically modeling control groups within CITS and segmented regression.

Purpose of the Study:

• To compare the statistical performance of different segmented regression models for including control groups.
• To assess model robustness under various assumption violations.

Main Methods:

• Simulated and compared four segmented regression models using a real-world dataset.
• Evaluated models under scenarios violating assumptions like non-parallel trends and autocorrelation.
• Included models with restricted cubic splines for time to mitigate assumption violations.

Main Results:

• Standard Difference-in-Difference (DiD) and CITS models showed low bias when assumptions were met.
• Interrupted time series (ITS) of the difference between groups, with time splines, demonstrated the lowest bias and highest coverage, even with violated assumptions.
• This approach is valuable for causal inference across diverse trend patterns.

Conclusions:

• Modeling CITS as an ITS of the difference between series is a robust method for incorporating control groups.
• Using time splines within this ITS framework reduces bias from assumption violations without compromising performance when assumptions hold.