Background: Multiple group controlled interrupted time series analysis (MG-ITSA) is widely used to evaluate healthcare interventions. Prior studies compared ordinary least squares with Newey-West standard errors (OLS-NW) and Prais-Winsten (PW) regression under first order autoregressive (AR1) errors, but performance under higher order autocorrelation is unclear. Recent extensions of PW to AR(k) processes allow such comparisons. Methods: We conducted a Monte Carlo simulation using an MG-ITSA model with four control units. Data were generated under AR2 and AR3 error structures representing mild, oscillatory, and highly persistent autocorrelation across series lengths from 10 to 100 time points and varying effect sizes. Treatment effects were defined as difference in differences in level and trend. We evaluated power, 95 percent confidence interval coverage, type I error, percent bias, root mean squared error, and empirical standard errors. Sensitivity analyses examined alternative designs. Results: Both methods produced approximately unbiased estimates. OLS-NW showed higher power but inflated type I error and poor coverage, especially with higher AR order and longer series. Under highly persistent autocorrelation, OLS-NW coverage fell to 45 to 50 percent at 100 time points, while PW maintained 91 to 94 percent coverage. Type I error for OLS-NW rose to 50 to 57 percent. PW showed power advantages in some settings. Conclusions: The tradeoff between power and valid inference seen under AR1 errors worsens with higher order autocorrelation. The apparent power advantage of OLS-NW reflects inflated false positives. PW provides more reliable inference and is preferred for hypothesis testing and error control.

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