Immediate level change estimates can be biased when interrupted time series analyses aggregate over time using...

Interrupted time series (ITS) designs are commonly used to evaluate the impact of interventions in public health. In an ITS study, data are collected over time prior and post an interruption (eg, public policy intervention). Data are often aggregated over a time interval using the mean, and these means can then be analyzed using segmented linear regression with a continuous outcome. A commonly calculated effect measure from this model is the immediate level change (change in outcome immediately post-intervention). We investigated whether estimates of immediate level change can be biased depending on the time interval of data aggregation.

We developed an equation to estimate the magnitude of bias in the immediate level change parameter of a segmented linear regression model when data are aggregated over time intervals (eg weekly, monthly, quarterly, and yearly) using the mean. We validated the bias expression using a simulation study. We demonstrated through application to a real-world ITS how the bias can be removed via the simple formula.

We found that the magnitude of bias in the immediate level change parameter is dependent on the time interval of data aggregation and the size of slope change. Longer intervals of aggregation and larger slope changes lead to larger bias. Our simulation study confirmed the validity of the expression for bias.

When aggregating ITS data over time using the mean, researchers need to be aware of the potential for bias in the estimate of the immediate level change parameter, so that they can mitigate its impact. Aggregating data over smaller time intervals, or removing the bias via a formula, provide simple solutions.