Segmented Linear Regression Models for Assessing Change in Retrospective Studies in Healthcare

In retrospective studies, the effect of a given intervention is usually evaluated by using statistical tests to compare data from before and after the intervention. A problem with this approach is that the presence of underlying trends can lead to incorrect conclusions. This study aimed to develop a rigorous mathematical method to analyse temporal variation and overcome these limitations.

We evaluated hip fracture outcomes (time to surgery, length of stay, and mortality) from a total of 2777 patients between April 2011 and September 2016, before and after the introduction of a dedicated hip fracture unit (HFU). We developed a novel modelling method that fits progressively more complex linear sections to the time series using least squares regression. The method was used to model the periods before implementation, after implementation, and of the whole study period, comparing goodness of fit using F-tests.

The proposed method offered reliable descriptions of the temporal evolution of the time series and augmented conclusions that were reached by mere group comparisons. Reductions in time to surgery, length of stay, and mortality rates that group comparisons would have credited to the hip fracture unit appeared to be due to unrelated underlying trends.

Temporal analysis using segmented linear regression models can reveal secular trends and is a valuable tool to evaluate interventions in retrospective studies.