Bayesian Hierarchical Models Incorporating Measurement Error for Interrupted Time Series Design

Interrupted time series (ITS) design is a quasi-experimental approach for evaluating the impact of an intervention in public health research using segmented linear regression (SLR) models. Usually, aggregated data across multiple time points before and after an intervention are compared to detect a change in intercept, slope, or both; however, the use of aggregated data can lead to an ecological fallacy, imprecise estimates, loss of power, and spurious inferences. We formulated three models with/without measurement error in the dependent variable to address different data limitations resulted from aggregation. Adopting the Bayesian hierarchical methodology for three standard SLR models from an ITS design, we compared performances of the varying pre-intervention intercept model (VPIM), varying intercept model (VIM) and measurement error model (MEM) with a non-hierarchical model (NHM) using real-life data and simulation studies. The MEM first estimates true value using observed data and standard deviation, then regresses the independent variables on the estimated true values. The results demonstrated the suitability of the hierarchical models through sustained improvement in model performance and parameter estimates over the NHM. The VPIM and VIM provided precise estimates modeling the population of clusters and pooling information across parameters. The measurement error assumption, along with the Bayesian model’s hierarchical formulation and generative nature, helped stabilize the unstable values of the dependent variable based on observed data and standard deviations.