This paper presents statistical tools to assess reliability in gait analysis. Gait analysis involves measuring continuous curves over a gait cycle. Three main problems are encountered in clinical practice: (1) determining if a patient's gait curves belong to a given population, (2) classifying a new subject, and (3) comparing two populations. The paper introduces intra-class correlation coefficients to measure reliability, confidence bands to define population curves, and analysis of variance with confidence bands to compare population means. These tools can help clinicians interpret gait data and determine if a patient's gait is pathological or normal.

1.      
     
              
         
                  
                
                
              

                  
                     
                     
paper presents three statistical tools for solving these problems: (i) intra-class correlation coefficients, (ii) confidence bands for a population
(iii) a combination of analysis of variance and confidence bands for the difference between the means and shows how they can be used in
 
     
 Gait analysis; Reliability; Confidence band; Bootstrap prediction
         
           
                   
                   
        ever, curves are scattered and a criteria must be defined to
                 
       
                  
                      
        numerical parameter, confidence intervals are typically used
                  
        the analogue of confidence intervals are confidence bands.
             The most popular method of constructing confidence bands
                 
               
                    
three types of problem are encountered. The first one con-        
                
               
         pointed out that such a confidence band should not be used
       
   
probability compared to the 95% pre-specified probability.
         
              
          


2.            
                  
of the knee flexion angle for the right and left lower limb)            
                
        hip flexion/extension, hip abduction/adduction, hip rotation,
   knee flexion/extension, knee varus/valgus, foot alignment,
           foot rotation and ankle flexion/extension (these traces are
               
              
           
        
  inary results of the knee flexion/extension in the sagittal
         
     
             
        
                   
                  
                    
                
        reproducible i.e. sufficiently similar to consider that their
                  
ied a clinical case: the mean curve of knee flexion/extension            
               
                  
          
        
       
         
                    
              
          
              
  
      Under these conditions, the intra-class correlation coeffi-
          
       
United Kingdom) for motion analysis, using five infrared     
         The coefficient         
spherical, retro-reflective markers (2.5 cm in diameter) were          
used to define different segments of the pelvis and lower           
               
practitioner) on anatomically well-defined points of the  
       
  
          
                
                 
ial planes were recorded by the cameras placed in defined         
                     
                         
                     
              
            The identification of        
                coefficients. These coefficients were com-
                  was identified
                   
                 

3.            
Fig. 1. (A) Knee flexion angle vs. percent of gait cycle for a young subject with nine reliable cycles (right side). (B) Knee flexion angle vs. percent
                       
          

4.            
          The pre-specified probability is denoted by 1  
      the confidence interval of the population (range of normal
values) is defined by:   
   
        
          
         
      fixing any hypothesis for the distribution of   
              
          
                      
                
                   
           defined by: 
                        
      
                  
                
    
2.4. Confidence bands            
         
For a numerical parameter, confidence intervals are used           
                 
values or to perform group comparisons (confidence interval which enables us to build the CBP and confidence bands
                  
procedures for building such confidence intervals exist and    
                 
              
             
For gait curves, the analogue of confidence intervals is           
confidence bands: these are regions delimited by two curves       
defined at each time point. The confidence band of a pop-
            be the number of mis-classified subjects. Initialise
           
in the confidence band with a pre-specified probability (in             
                   
corresponding confidence band defines the region that con- 
tains the true mean curve with a pre-specified probability.          
The reliability of the method used to build a confidence          
band depends on its capacity to preserve the pre-specified       
probability. The method currently used to build a confidence         
band consists in computing a confidence interval at each  
         For example, if the sample size is 30 and if we found five
           mis-classified curves, then the estimated true coverage
                 
      
             
         
pre-specified probability and the true coverage probability.        
In the present study, confidence bands were established       
              
                 
                 
           two groups YRG and ERG. The fixed effects were side
                
                  
case of a confidence interval for a single measure    chose a first-order, autoregressive covariance pattern to
                   

5.            
                  
             
               
groups (young–elderly), the fixed effects were time (51         
                    
parisons at each time point (post hoc analysis) were first per-          
        
       
         3.2. Confidence bands and population comparisons
quently, the confidence band for the difference between the
        Using a linear, mixed model, no significant effect of side
                  
                   
          The confidence band for the difference between the means
                       
                     
                   
         falls entirely within the confidence bands, thus confirming
to a significant difference between the two groups at these            
                    
           
     
  represents the 95% confidence bands of the
         
       
           
used to estimate the confidence bands’ reliability. For the
                
                  
        from the pre-specified probability in the two groups: 73.3%
                   
     -value for the knee flex-         
ion angle was fixed at 0.95 for the control population. Ex-            
     -value less than 0.95 confirmed         
               
Fig. 2. Confidence band for the difference between the means of two sides (right–left) in the young reference group, computed using the bootstrap
        

6.            
Fig. 3. (A) Confidence bands and mean for the young group. LCI and UCI designate the 95% lower confidence band and 95% upper confidence band,
                    
grey line represents the mean. The thin continuous line represents a curve of a young control subject completely included within the bootstrap confide
band and incompletely within the Gaussian point-by-point band. (B) Confidence band for the difference between the means of the two independent groups
                  
                      
             tified differences between the groups for four points (from
                    
                     
    does not fall within the CBDM, thus confirming the result
                  
and ERG were significantly different (             
                

7.            
Fig. 4. Mean (dotted grey line) and confidence band for the elderly reference group (dotted dark lines) and change in knee flexion ankle for a Parkinsonia
                     
     
             
       
                    
tice. The trace of knee flexion angle of a Parkinsonian pa-          
                  
the ERG group’s mean curve with a confidence band. When         
the patient had not received any treatment, knee flexion was         
reduced: the curve was near the lower limit of the confi-         
              
at the maximum flexion time. After acute administration of         
                  
now totally included within the confidence band. After sub- it is necessary to build confidence bands to characterise the
                   
the confidence band.        
for building confidence bands is based on computation of a
confidence interval at each time point by applying Gaussian
           
            
                
          coverage probability was very different to the pre-specified
                
          delimited by the point-by-point confidence band was too
                     
            building a population’s confidence band. Our study confirms
                  
                 
ficient (ICC), which is considered to be the “gold standard”          
                  
For the knee flexion angle, a minimum level for ICC (0.95) method, the confidence bands established using the boot-
                  
         probabilities were in accordance with the pre-specified
                   
                  
               
                   

8.            
                    
                     
              
                    
                
 ) and hence can resolve this difficulty. Bootstrap          
                
                 
           second time to confirm the presence or absence of aberrant
                 
                   
          important to examine the clinical significance of this phe-
                   
                    
No significant differences were found between the confi-         
                    
the confidence bands characterising the normal regions of          
         the precision with which we estimate the confidence band.
                    
                      
                
          
We recommend the use of confidence bands for testing          
               
                    
         most severely influenced by disabling motor fluctuations.
                  
test reveals a significant difference, the confidence bands        
                   
tification of regions where differences exist. Such a tech-           
                 
               
ever, the confidence bands were computed using a Gaussian          
         analysed the influence of a new, therapeutic neurosurgical
                 
                  
               
        of the subthalamic nuclei (STN) induced a more beneficial
                
          
                 
                 
lower limbs for the mean curves of knee flexion during a        
gait cycle for both groups (YRG and ERG), confirming clas-            
       determine the influence of therapies on joint position in a
                    
knee flexion (which appeared to be reduced in the ERG) is define these gait improvements more precisely. We can then
                  
                
          
       
the gait cycle). The CBDM confirmed this difference more 
         
                 
                 
             

9.            
programs are available on request to the first author. E-mail: [7] Carpenter J, Bithell J. Bootstrap confidence intervals: when, which,
          

         
    
          
   
           [10] Sadeghi H, Allard P, Shafie K, Mathieu PA, Sadeghi S, Prince F, et
Backus SI. Bootstrap prediction and confidence bands: a superior          
           
           
                     
        
             
                     
              
                  
                      
  Perina M, et al. Influence of pallidal stimulation and   
[6] Akaike H. A new look at the statistical model identification. IEEE        
     