Functional limits of agreement: a method for assessing agreement between measurements of gait curves

Three dimensional measurements of gait is a widely used tool in clinical gait analysis, and the evaluation of the reliability and reproducibility of the method is a recurring topic in the literature. The reliability of gait curve measurements is often assessed by extraction of single points from the gait curves before applying traditional reliability measures for scalars. This approach does, however, not explore the entire gait curves as continuous functions of time. In order to assess agreement between gait curves measured by different measurement methods, or measurers, we propose an extension of the concept of limits of agreement (LoA) to curve data. The LoA represent the estimated variation in the actual observations, which are then to be accompanied by an evaluation of whether this observed variation is within clinically acceptable limits. The generalization of the methodology from scalars to continuous function, e.g. gait curves, can be done using functional data analysis (FDA), a statistical methodology particularly developed for analyzing functional data. The resulting functional limits of agreement (FLoA) are continuous functions from 0 to 100% of the gait cycle, representing the difference in gait curves as measured by different measurement methods. The FLoA are presented in actual degrees for each joint and plane under study. The proposed methodology is demonstrated on real data from an inter-rater repeatability study.