Duhamel, 2004 statistical tools for clinical gait analysis

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Duhamel, 2004 statistical tools for clinical gait analysis

  1. 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. 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. 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. 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. 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 comparisonsquently, 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 confirmingto 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. 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. 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. 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. 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              

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