Confidence sets for intraclass correlation coefficients in test–retest curve measurements

Abstract

Evaluating test–retest reliability is crucial in biomechanical research, as it validates experimental results. While methods for reliability of scalar outcome variables are well-established, methods to assess reliability of continuous curve data (such as joint angle trajectories during gait) remain less explored. This study investigates methods for constructing confidence sets for curve-level intraclass correlation coefficients (ICC), which can be expressed as either an ICC curve or an integrated ICC. Currently, no standardised guidelines exist in biomechanics for reporting curve-level ICC uncertainty. Nonparametric bootstrapping techniques are proposed for both the ICC curve’s confidence bands and the integrated ICC’s confidence intervals, and these methods are validated through Monte Carlo simulations, covering various effect sizes and curve characteristics. Additionally, these methods are applied to assess the test–retest reliability of knee kinematics in three different planes during landing of one-leg hops, where less uncertainty is observed for the ICC curve and integrated ICC in the frontal plane compared to other planes. When the entire time domain is of primary empirical interest, we recommend using a rank-based bootstrap confidence band to express ICC uncertainty, as it yields increasingly precise and valid results as the number of individuals increases, with the coverage rate approaching the correct level of 95%. When a single summary metric is of primary interest, we recommend using the integrated ICC along with a typical bootstrap confidence interval based on the normal distribution, as the coverage rate remains adequately accurate and stable at around the correct level of 95% across varying number of individuals.