In praise of Prais-Winsten: An evaluation of methods used to account for autocorrelation in interrupted time series

Interrupted time series are increasingly being used to assess the population impact of public health interventions. These data are usually correlated over time (auto correlated) and this must be accounted for in the analysis. Typically, this is done using either the Prais-Winsten method, the Newey-West method, or autoregressive-moving-average (ARMA) modeling. In this paper, we illustrate these methods via a study of pneumococcal vaccine introduction and explore their performance under 20 simulated autocorrelation scenarios with sample sizes ranging between 20 and 300. We show that in terms of mean square error, the Prais-Winsten and ARMA methods perform best, while in terms of coverage the Prais-Winsten method generally performs better than other methods. All three methods are unbiased. As well as having good statistical properties, the Prais-Winsten method is attractive because it is decision-free and produces a single measure of autocorrelation that can be compared between studies and used to guide sample size calculations. We would therefore encourage analysts to consider using this simple method to analyze interrupted time series.