A thorough analysis of the coefficient of multiple correlation (Cmc) shows multiple problems

Abstract

Introduction: The question of reliability is essential for any measurement method, and when investigating reliability of 3DGA kinematic curves the coefficient of multiple correlations (CMC) [1] is frequently used, despite the reports of methodological issues [2]. Theaimof the current studywas toperformasystematic evaluation of theCMCusing stochastic simulations. The results are exemplified on an inter-rater reliability study of 3DGA data related to marker placement. Patients/materials and methods: Synthetic gait curves were generated from a stochastic model where amplitude, vertical offset and a possible horizontal shift due to random error and timing issues were included as stochastic variables. The model was used hierarchically. First a “true” curve for each subject was sampled; then curves from each of the different test situations, e.g. different tester teams, was sampled using this “true” curve as the mean. The CMC is a measure of similarity of waveforms, e.g. curve data [1], comparing multiple curves from several subjects across test situations, e.g. testers. The CMC was calculated based on the synthetic data with systematic variations in curve amplitude, frequency, vertical curve offset, and number of subjects and number of test situations. Confidence intervals were estimated using bootstrapping. Seven healthy adult volunteers gave written informed consent to take part in the accompanying inter-rater reliability study. The subjects were tested on two consecutive days by two different tester teams. 3DGA data was recorded during bare feet, level walking along a 10m walkway at self-selected comfortable walking speed, using six Vicon MX13 cameras, and the PluginGait model. For each subject, one left cycle from each test situation was selected, based on similarity in walking speed. Results: Joints with large amplitudes, i.e. above 15◦, resulted in CMC>0.9. High sampling frequencies, i.e. above 20 points per gait cycle, also resulted in CMC>0.9. Increasing offsets resulted in decreasing CMC values. For two test situations 20 subjects resulted inwider CIs for the CMC than five subjects on five test situations. In the inter-rater reliability study, the CMC calculations consistently broke down, i.e. could not be computed, for jointswith a lowamplitude. In curves with a visually apparent systematic vertical offset, the CMC was still approximately 0.9. Discussion and conclusions: The CMC is sensitive to the amplitude of the curve, demonstrating how the signal-to-noise ratio is a problem issue. As the CMC does not adjust for the inter-gait-curve correlation between data points, higher sample frequency leads to high CMCs, merely due to high correlation between data in the calculations. The frequently used reliability design of two tester teams was demonstrated to show comparably high CIs. In conclusion, in our study the CMC did not show the statistical properties that are needed for it to be an overall measurement of curve similarity. Other methods than the CMC must be used to assess reliability of 3DGA data. References