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.

翻译：背景：多种群控制中断时间序列分析（MG-ITSA）广泛应用于评估医疗干预效果。既往研究在一阶自回归（AR1）误差条件下比较了普通最小二乘法联合Newey-West标准误（OLS-NW）与Prais-Winsten（PW）回归的性能，但在高阶自相关条件下的表现尚不明确。PW方法向AR(k)过程的近期扩展使此类比较成为可能。方法：我们采用包含四个控制单元的MG-ITSA模型进行蒙特卡洛模拟。数据在AR2和AR3误差结构下生成，分别代表轻度、振荡性和高度持久性自相关，时间序列长度从10至100个时间点且效应量可调。治疗效果定义为水平和趋势的倍差估计量。评估指标包括统计功效、95%置信区间覆盖率、第一类错误率、百分比偏倚、均方根误差以及经验标准误。敏感性分析检验了替代设计方案。结果：两种方法均产生近似无偏估计。OLS-NW表现出更高功效，但第一类错误率膨胀且覆盖率较差，尤其在高阶自回归和长序列条件下。在高度持久性自相关情况下，100个时间点时OLS-NW覆盖率降至45%~50%，而PW仍维持91%~94%的覆盖率。OLS-NW的第一类错误率升至50%~57%。某些情境下PW显示出功效优势。结论：AR1误差下观察到的功效与有效推断之间的权衡在高阶自相关中进一步恶化。OLS-NW表面的功效优势反映了假阳性率的膨胀。PW方法能提供更可靠的推断，在假设检验与错误控制中更优。