CI2 for creating and comparing confidence-intervals for time-series bivariate plots

Abstract

AcknowledgementsThank you to Rory Heaney for collecting the test data. 2 CI2 for creating and comparing confidence-intervals for time-series bivariate plots Highlights CI2 quantifies the confidence-intervals (CI) of bivariate time-series plots. Determines if the CI between two bivariate time-series overlap. Any time-lag between two time-series can be incorporated into the analysis. Knee-ankle angles plots on standard v curved treadmills differ at heel-strike. Matlab code is provided to facilitate standardisation of use of CI2. AbstractCurrently no method exists for calculating and comparing the confidence-intervals (CI) for the time-series of a bivariate plot. The study's aim was to develop 'CI2' as a method to calculate the CI on time-series bivariate plots, and to identify if the CI between two bivariate time-series overlap. The test data were the knee and ankle angles from 10 healthy participants running on a motorised standard-treadmill and non-motorised curvedtreadmill. For a recommended 10+ trials, CI2 involved calculating 95% confidence-ellipses at each time-point, then taking as the CI the points on the ellipses that were perpendicular to the direction vector between the means of two adjacent time-points. Consecutive pairs of CI created convex quadrilaterals, and any overlap of these quadrilaterals at the same time or ±1 frame as a time-lag calculated using cross-correlations, indicated where the two time-series differed. CI2 showed no group differences between left and right legs on both treadmills, but the same legs between treadmills for all participants showed differences of less knee extension on the curved-treadmill before heel-strike. To improve and standardise the use of CI2 it is recommended to remove outlier time-series, use 95% confidence-ellipses, and scale the ellipse by the fixed Chi-square value as opposed to the sample-size dependent F-value. For practical use, and to aid in standardisation or future development of CI2, Matlab code is provided. CI2 provides an effective method to quantify the CI of bivariate plots, and to explore the differences in CI between two bivariate time-series.

The effects of concurrent biomechanical biofeedback on rowing performance at different stroke rates

“…To account for inter-rower differences in times to complete the pull, data were time normalised by cubic spline interpolation to 101 samples-per-pull, and discrete values were expressed as percentages of each time-normalised pull, where 0% represented the catch and 100% represented the finish. These data were used to quantify changes in coordination between elbow and knee motions through assessment of alterations made to the timings and magnitude of their relative motions during the pull, bivariate analysis of these joints was conducted using 'CI2ʹ (Mullineaux, 2017). On bivariate kneeelbow angle-angle plots from each of the Baseline, S3, and Transfer sessions per participant, the 10 consecutive rowing strokes taken were detrended by removing the mean angle from all data points and 95% confidence intervals (CI) were created using ellipses and quadrilaterals at each time point.…”

Error and anomaly detection for intra-participant time-series data

“…As stage 1 of the method is based on a non-parametric statistic, it is less susceptible to distribution assumptions, but as stage 2 is based on a parametric statistic, there is a greater need to consider the number of trials required. In a technique exploring the bivariate plots of intra-participant data (Mullineaux 2017 ), it is recommended that a minimum of 10 trials are used as this leads to a sufficiently low bias between the actual area and ellipse quantified area (Jackson et al 2011 ). Given the complexity of assessing how many trials are required in biomechanical research, and independently of the number of subjects as applicable to this situation on intra-participant data, for typical simulation criteria a total of 9 ± 8 trials are required (mean ± 95% confidence intervals; Forrester 2015 ).…”

“…A requirement for many time-series analyses is that the data are of the same length, hence data are often time normalised when multiple trials are collated to create the average trial or to conduct time-series analysis (e.g. vector coding, Tepavac and Field-Fote 2001 ; CI2, Mullineaux 2017 ; and; outlier detection, Sangeux and Polak 2014 ). On the assumption of a ‘typical’ time-series for each participant, this time-normalising should lead to a reduced temporal variability and, where the temporal variability is still high, rectification or time-warping has been proposed (Kale et al 2003 ).…”

Hip joint kinematics and segment coordination variability according to pain and structural disease severity in hip osteoarthritis

“…An ellipse was fitted to these points using the equations previously described 26 , with the size scaling adjusted according to the Chi-squared value. 27 The area of the ellipse at each data point represented a bivariate measure of coordination variability, whereby a larger ellipse area indicated greater coordination variability. Ellipse area was calculated at each point across timenormalised (i.e.…”