Short CommunicationA simple method to choose the most representative stride and detect outliers
Introduction
Clinical gait analysis collects several strides for each patient. Clinical decision making is preferably based on all the strides collected so that the clinician may visually appreciate both the patient's pattern and variability. The researcher, however, may only be interested in the patient's most representative stride, for example in order to assemble data from several patients. This may be done by averaging the gait curves point/time wise or, choosing one stride visually or automatically [1]. Averaging gait curves point/time wise may remove important features from the shape of the curves [2] and choosing the most representative curve visually may be time consuming and has objectivity issues [1]. Recently, a statistical method was proposed to find the most representative stride [1]. However, the method requires specific software to perform the principal component decomposition (i.e. Matlab with the statistical toolbox).
Kinematic variables derive from one multi-segment kinematic chain and are often grouped in the gait profile [3] which link together pelvic tilt, obliquity and rotation, hip flexion, abduction and rotation, knee flexion, ankle dorsiflexion and foot progression angles. Ideally the most representative stride should be chosen as the most representative of the patient's gait pattern across all the variables that constitute the gait profile.
The notion of centrality for multivariate data may be expressed as depth [4]. The deepest value being the most representative of the multivariate dataset. The first objective of this technical note was to propose a measure of depth for kinematic data that may be calculated for a single kinematic variable or for all the kinematic variables of the gait profile.
The second objective of this technical note was to propose a robust test to detect outliers. Clinicians or researchers are often interested in detecting curves that have a different shape from the rest of the data automatically. These outliers may need to be removed from the dataset in order to calculate a better estimate of the gait pattern variability. Alternatively, outlying data may also need to be analysed separately to identify the potential causes for the abnormal pattern.
Section snippets
Materials and methods
In 2001, Fraiman and Muniz [5] defined a functional depth (FD) that we adapted below for a kinematic variable K as:with Ki(t) the ith kinematic curve and D() the empirical distribution function at the time t. FD is minimum for the deepest curve and maximum for the most distant curve. FD has a ceiling effect and is not expressed in the same unit as the kinematic data. We proposed to modify the definition of centrality and derived the functional median
Results
Fig. 1 presents the total functional median depth on the data provided in Ref. [1]. Both algorithms chose the same representative stride. The rank, from most representative to least representative was also identical. The score for stride 2 was 2.6 which means that this stride may have been considered as an outlier for a cut-off value of 2.
Fig. 2 presents the total functional median depth on the patient. The algorithm identified an outlier over the gait profile (Rscore = 6.1). For this stride, the
Discussion and conclusion
We presented a new algorithm to identify the most representative curve based on a functional measure of depth. The novelty of our approach lies in its computational simplicity and the provision of a method to detect outliers.
Our algorithm was compared to a validated statistical method and displayed exact agreement on the one dataset provided by the authors [1]. We do not expect the two methods to always agree exactly since they may have different sensitivity to variation in shape and position
Acknowledgement
This work has been partially funded through a Clinical Science theme grant from the Murdoch Childrens Research Institute.
Conflict of interest statement: The authors declare that there are no conflicts of interest.
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