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