Quantifying sources of variability in gait analysis

Highlights

• We proposed corrected methods to estimate variance components.

• We showed that ICC and CMC can be derived from variance components.

• We discussed methods to estimate variability on the curve level.

Abstract

Measurements from gait analysis are affected by many sources of variability. Schwartz et al. [1] illustrated an experimental design and methods to estimate these variance components. However, the derivation contains errors which could severely bias the estimation of some components. Therefore, in this paper, we presented correction to this method using ANOVA and Likelihood methods. Furthermore, we demonstrated how commonly used reliability indices like CMC and ICC may be derived from the variance components. We advocate the use of the variance components, in preference to reliability indices, because the variance components are easier to interpret, with understandable units.

Introduction

Measurements from gait analysis are variable. The sources of the variability may be intrinsic or extrinsic. Intrinsic variability corresponds to the variability of the subject under investigation, for example the variability between strides of the same individual, or between individuals [2]. Extrinsic variability corresponds to the variability of the gait analysis measurement process, for example marker replacement between sessions, and between assessors, or different marker placement protocols and processing workflows. Having the ability to differentiate and quantify these different sources of variability, or as we call it, variance components, is important for estimating the reliability and repeatability of gait analysis, comparing different methods and protocols, training assessors, and sharing data between laboratories. To this purpose, three statistics are commonly used in the literature, namely, the Coefficient of Multiple Correlation (CMC) as defined in Kadaba et al. [3], the Intra-Class Correlation coefficient (ICC) [4], and the explicit quantification of variances following the method proposed by Schwartz et al. [1].

CMC has been a popular choice because it is designed to handle curves rather than point data. However, several authors have highlighted issues with CMC, such as its strong dependence on sample size, or range of motion (ROM) [2], [5]. As we will elaborate below, we concur with Røislien et al. [5] that CMC in its current form should not be used in these studies. ICC is a similar index but works on the individual time point. However, as we will show below, both these indices may be derived from the variance component estimates themselves. Therefore, in our view, the most appropriate and fundamental framework is that of Schwartz et al. [1], which estimate the variance components directly.

The method of Schwartz et al. [1] has been adopted in several studies [6], [7], [8], [9], [10], [11], [12]. However, their proposed variance component estimators are biased, and as we will demonstrate, this bias may be severe. Our primary objective is to present a corrected set of variance component estimators. In addition, we will present methods to derive the ICC and CMC from the estimated variance components. Finally, we will discuss methods to move beyond point-based calculation for curve data.