Handling missing values in interrupted time series analysis of longitudinal individual-level data

Background: In the interrupted time series (ITS) approach, it is common to average the outcome of interest at each time point and then perform a segmented regression (SR) analysis. In this study, we illustrate that such ‘aggregate-level’ analysis is biased when data are missing at random (MAR) and provide alternative analysis methods. Methods: Using electronic health records from the UK, we evaluated weight change over time induced by the initiation of antipsychotic treatment. We contrasted estimates from aggregate-level SR analysis against estimates from mixed models with and without multiple imputation of missing covariates, using individual-level data. Then, we conducted a simulation study for insight about the different results in a controlled environment. Results: Aggregate-level SR analysis suggested a substantial weight gain after initiation of treatment (average short-term weight change: 0.799kg/week) compared to mixed models (0.412kg/week). Simulation studies confirmed that aggregate-level SR analysis was biased when data were MAR. In simulations, mixed models gave less biased estimates than SR analysis and, in combination with multilevel multiple imputation, provided unbiased estimates. Mixed models with multiple imputation can be used with other types of ITS outcomes (eg, proportions). Other standard methods applied in ITS do not help to correct this bias problem. Conclusion: Aggregate-level SR analysis can bias the ITS estimates when individual-level data are MAR, because taking averages of individual-level data before SR means that data at the cluster level are missing not at random. Avoiding the averaging-step and using mixed models with or without multilevel multiple imputation of covariates is recommended.