Bootstrap prediction and confidence bands: a superior statistical method for analysis of gait data

Gait analysis studies typically utilize continuous curves of data measured over the gait cycle, or a portion of the gait cycle. Statistical methods which are appropriate for use in studies involving a single point of data are not adequate for analysis of continuous curves of data. This paper determines the operating characteristics for two methods of constructing statistical prediction and confidence bands. The methods are compared, and their performance is evaluated using cross-validation methodology with a data set of the sort commonly evaluated in gait analysis. The methods evaluated are the often-used point-by-point Gaussian theory intervals, and the simultaneous bootstrap intervals of Sutherland et al. The Development of Mature Walking, MacKeith Press, London, 1988 and Olshen et al. Ann. Statist. 17 (1989) 1419-40. The bootstrap bands are shown to provide appropriate coverage for continuous curve gait data (86% coverage for a targeted coverage of 90%). The Gaussian bands are shown to provide inadequate coverage (54% for a targeted coverage of 90%). The deficiency in the Gaussian method can lead to inaccurate conclusions in gait studies. Bootstrap prediction and confidence bands are advocated for use as a standard method for evaluating gait data curves because the method is non-parametric and maintains nominal coverage levels for entire curves of gait data.