Evaluation of statistical methods used to meta-analyse results from interrupted time series studies: a simulation study

Background Interrupted time series (ITS) are often meta-analysed to inform public health and policy decisions but examination of the statistical methods for ITS analysis and meta-analysis in this context is limited. Methods We simulated meta-analyses of ITS studies with continuous outcome data, analysed the studies using segmented linear regression with two estimation methods [ordinary least squares (OLS) and restricted maximum likelihood (REML)], and meta-analysed the immediate level- and slope-change effect estimates using fixed-effect and (multiple) random-effects meta-analysis methods. Simulation design parameters included varying series length; magnitude of lag-1 autocorrelation; magnitude of level- and slope-changes; number of included studies; and, effect size heterogeneity. Results All meta-analysis methods yielded unbiased estimates of the interruption effects. All random effects meta-analysis methods yielded coverage close to the nominal level, irrespective of the ITS analysis method used and other design parameters. However, heterogeneity was frequently overestimated in scenarios where the ITS study standard errors were underestimated, which occurred for short series or when the ITS analysis method did not appropriately account for autocorrelation. Conclusions The performance of meta-analysis methods depends on the design and analysis of the included ITS studies. Although all random effects methods performed well in terms of coverage, irrespective of the ITS analysis method, we recommend the use of effect estimates calculated from ITS methods that adjust for autocorrelation when possible. Doing so will likely to lead to more accurate estimates of the heterogeneity variance.