Finite Sample Properties of Quantile Interrupted Time Series Analysis: A Simulation Study

Interrupted Time Series (ITS) analysis represents a powerful quasi-experime-ntal design in which a discontinuity is enforced at a specific intervention point in a time series, and separate regression functions are fitted before and after the intervention point. Segmented linear/quantile regression can be used in ITS designs to isolate intervention effects by estimating the sudden/level change (change in intercept) and/or the gradual change (change in slope). To our knowledge, the finite-sample properties of quantile segmented regression for detecting level and gradual change remains unaddressed. In this study, we compared the performance of segmented quantile regression and segmented linear regression using a Monte Carlo simulation study where the error distributions were: IID Gaussian, heteroscedastic IID Gaussian, correlated AR(1), and T (with 1, 2 and 3 degrees of freedom, respectively). We also compared segmented quantile regresison and segmented linear regression when applied to a real dataset, employing an ITS design to estimate intervention effects on daily-mean patient prescription volumes. Both the simulation study and applied example illustrate the usefulness of quantile segmented regression as a complementary statistical methodolo-gy for assessing the impacts of interventions in ITS designs.