Multiple-group (controlled) interrupted time series analysis with higher-order autoregressive errors: a simulation study comparing Newey–West and Prais–Winsten methods

Previous comparisons of ordinary least squares with Newey–West standard errors (OLS-NW) and Prais–Winsten (PW) regression in multiple-group interrupted time series analysis have been limited to AR(1) errors. Using the recent extension of PW to AR(k) processes, we conducted a Monte Carlo simulation comparing OLS-NW and PW under AR(2) and AR(3) error structures with varying autocorrelation, series lengths, and effect sizes. Difference-in-differences in level and trend were assessed using six performance metrics, with sensitivity, misspecification, and illustrative data analyses. Both methods produced approximately unbiased estimates. OLS-NW generally had higher power but substantially inflated Type I error and poor confidence interval coverage, particularly with stronger autocorrelation and longer series. Under highly persistent autocorrelation, PW maintained near-nominal coverage and Type I error. The inferential trade-off observed under AR(1) not only persisted but intensified, supporting PW when valid statistical inference is the primary objective.ABBREVIATIONS: AR: autoregressive; FGLS: feasible generalized least squares; GLS: generalized least squares; HAC: heteroskedasticity- and autocorrelation-consistent standard errors; ITSA: interrupted time series analysis; MG-ITSA: multiple-group interrupted time series analysis; OLS: ordinary least squares; OLS-NW: ordinary least squares with Newey-West standard errors; PW: Prais-Winsten regression; RMSE: root mean squared error; SG-ITSA: single-group interrupted time series analysis