Simultaneous estimation of effects of gender, age and walking speed on kinematic gait data

Abstract

Analysis of variations in normal gait has received considerable attention over the last years. However, most such analyses are carried out on one explanatory variable at a time, and adjustments for other possibly influencing factors are often done using ad hoc methods. As a result, it can be difficult to know whether observed effects are actually a result of the variable under study. We wanted to simultaneously statistically test the effect of gender, age and walking speed on gait in a normal population, while also properly adjusting for the possibly confounding effects of body height and weight. Since point-by-point analysis does not take into account the time dependency in the data, we turned to functional data analysis (FDA). In FDA the whole gait curve is represented not by a set of points, but by a mathematical function spanning the whole gait cycle. We performed several multiple functional regression analyses, and the results indicate that walking speed is the main factor influencing gait in the reference material at our motion analysis laboratory. This effect is also largely unaffected by the presence of other variables in the model. A gender effect was also apparent in several planes and joints, but this effect was often more outspoken in the multiple than in the univariate regression analyses, highlighting the importance of adjusting for confounders like body height and weight.

Introduction

Analysis of variations in normal gait has received considerable attention over the last years, and studies have shown that factors such as walking speed [1], [2], [3], [4], age [5], [6] and gender [4], [7], [8] all influence gait. A shortcoming of many such studies is that they only look into one possible explanatory variable at a time. Such models can often be too simple, making it difficult to establish whether observed differences are the result of the variable under study, and not of some other variable not included in the model. For example; since women tend to be smaller than men; given that one could properly adjust gait data for body height and weight, would apparent gender differences still be present, or is ‘gender’ merely a surrogate measure for ‘size’?

Depending on the research question, this latter problem could both be seen as a model with more than one explanatory variable, and as a model with one explanatory variable plus an adjustment for possible confounding effects. In the analysis of gait, several ad hoc methods exist for such adjustment. However, all ad hoc methods, for example controlling for body size by scaling walking speed by leg length [7], are deemed to be suboptimal; without perfectly deterministic relationships between the variable and the scaling factor, noise is entered into the model by the researcher.

Some of the above problems might be overcome by conducting an experimental study, matching on confounding factors. However, in addition to the practical challenges, this might not have a meaningful interpretation. Who does one match, say, a reference material with? And what would such a matching tell us? Also, a variable used for matching cannot be investigated further as an explanatory factor for the dependent variable [9].

In summary, univariate analyses are often insufficient for the statistical analysis of gait. One needs to be able to statistically test several possible explanatory variables simultaneously, while also properly adjusting for confounders. A natural choice for such analyses is multiple regression models, the two most common being linear and logistic multiple regression, for continuous and binary dependent variables, respectively. When the dependent variable is a gait curve (GC), however, classical regression models are no longer applicable. One possible solution is to pick out a single point [8], or range of motion (ROM) [4] to represent a GC. A downside of this approach is that it is difficult to verify and quantify whether the chosen point can be said to truly represent the whole curve [10]. Also, using a single point to represent a GC implies throwing away most of the meticulously gathered information.

A way around the problem of information reduction is to extract more points than one. However, two, or more, points taken from the same GC will be correlated, and results from statistical tests must be adjusted accordingly. This is rarely done [11]. Point-by-point regression on the whole curve [7] is therefore not a particularly good solution. Confidence intervals based on this approach tend to give overly optimistic results [12], e.g., estimates do not truthfully describe the actual amount of variation present, and give a false impression of precision. This might be just as bad as a certain degree of conservative scepticism; potentially giving treatment advice based on a too narrow confidence band can lead to ethically questionable practice. Confidence intervals generated by bootstrapping of the whole lines improve coverage results [10], [12]. Unfortunately, it is not straightforward how bootstrapping can be applied to assess whether the observed variability in the data can be ascribed to one ore more covariates, or how to adjust for confounders.

In order to apply multiple regression analysis for gait data we turned to functional data analysis (FDA) [13]. Here, instead of representing a GC by a set of points, each GC is represented as a continuous, mathematical function of time; the dependent variable for each trial is turned into one, functional object. As a result classical statistical techniques can be applied with proper modifications.

The aim of this work was to simultaneously statistically test whether the three factors gender, age and walking speed significantly affect kinematic gait data in a reference population. We also wanted to properly adjust for the possibly confounding effects of body height and weight.