Abstract
We tried to establish an age-predictive equation from kinematic and kinetic parameters during walking using the 2007 Okada database of Japanese elderly. Some predictive equations were established for each gender (109 males and 139 females)—once for all variables, second for the stepwise variable selection method. The range of motion (ROM) of knee and hip and step length are the stable parameters in age-predictive models for both genders. Although the model achieved the Minimum Akaike's Information Criterion Estimate (MAICE), it did not reflect sufficiently the regimes of variable selection.
Introduction
When we estimate somebody's chronological age, we use their facial features or the way they move as the basis of the estimate. In this sense, we are solving an inverse problem adopting the statistical thinking of regression analysis with the kinematic variables as the explanatory or independent variables and age as the dependent variable. In this study, we establish the age-predictive regression equation from kinematic and kinetic parameters during walking, such as walking velocity, step length, step frequency, joint angles, joint angular velocities, joint torques, joint torque powers, as well as work done by the joints of the lower limbs using the walking data base among Japanese adults youth to elderly. 3 Because we consider a large number of age-related parameters in multiple regression analysis when predicting chronological age (with the predicted age as the walking age of the individuals), forward stepwise regression analysis was adopted to establish the predictive equation for the chronological age.
Methods
The study sample was composed of males and females older than 60 years from the Okada 3 database for walking among Japanese adults. The study population, recruited by screening a population-based sample aged 65 years and older, comprised 109 men and 139 women who represent healthy Japanese men and women.
In the present study, the following kinematic and kinetic parameters were used: walking velocity (coded as WV), step length (W10), step frequency (W11), joint angles (W1, W2, W3), joint angular velocities, joint torques, joint torque powers (W4, W5, W6), as well as work (W7, W8, W9) done by the joints of the lower limbs. We used the 12 variables from the above parameters with codes in parentheses for the 109 males and 139 females in the study. Regression analysis was executed first in the case where all variables were entered simultaneously, and in the second case, stepwise for variable selection procedure according to Akaike's Information Criterion (AIC). We called the former the whole variable entry method and the latter the forward stepwise regression analysis. These statistical analyses were executed by the SPSS (ver. 16) statistical software package.
Results
Although the description of the kinematics (motion) and the kinetics (moment and power) of normal gait is important, as stated by many researchers, we tried to build an age-predictive linear model from a variety of parameters of normal gait based on a database of healthy older adults with attention to the association of these parameters. The descriptive statistics of 12 independent walking variables and the dependent variables are shown in Table 1. The average age was 72.06 (standard deviation [SD] ± 4.36) for males, ranging from 65.28 to 86.32 years old, and 71.69 (SD ± 1.05) for females, ranging from 65.17 to 82.46 years old. The mean values of walking velocity of the preceding study by McGibbon and Krebs 4 were less than the present data (1.13 vs. 1.383 m/sec for elderly males, 1.20 vs. 1.314 m/sec for elderly females, respectively). In general, the interrelationship with age in females is higher than with males. For the males, several walking variables showed only a small correlation coefficient with age.
SD, standard deviation; MAICE, minimum Aikake's Information Criterion estimate; ROM, range of motion; r, simple correlation coefficient.
Whole variable model
The 12 variables (coded as WV, W1–W11) were used for the actual regression analysis as the independent variables. The regression coefficient (b p) and standardized regression coefficient, the constant term, and multiple correlation coefficient (R) of the regression equation of which all of the 12 variables were treated as independent variables and are indicated for the two genders in Table 1.
The regression equation composed of all of the 12 variables was y = 0.954*WV +0.017*W1 −0.274*W2 +0.222*W3 +1.199*W4 −0.953*W5 −0.730*W6 +7.158*W7 − 32.81*W8 +3.598*W9 −23.345*W10 −0.542*W11 +91.34 for the males. The multiple correlation coefficient, R of this regression equation was 0.435 (R 2 = 0.189). The regression equation for the females was y = −12.708*WV −0.085*W1 −0.121*W2 +0.090*W3 +0.851*W4 −1.407 *W5 −0.902*W6 −5.792*W7 −8.164*W8 +8.268*W9 −16.596*W10 +6.494*W11 +87.618. R of this regression equation for females was 0.561 (R 2 = 0.314).
When the standardized partial regression coefficients (βp) of these regression equations are ordered according to their absolute value, we obtain W10 > W8 > W2 > W3 > W4 > W5 > W7 > W6 > W4 > W9 > WV > W11 > W1 for the males. On the other hand, for the standardized partial regression coefficient (βp) for the females we obtained WV > W10 > W11 > W5 > W2 > W4 > W9 > W3 > W7 > W1 > W6 > W8. The order of the βp differed significantly, as did the multiple correlation coefficient R, between the genders due to the different structure of the equations. The walking variable especially contributed considerably in the equation for the females to express their age, and the goodness-of-fit for the equations was superior to that of the males. Therefore, we tried a prudent selection of the variables in the stepwise method.
Stepwise model
To obtain an optimal equation with a smaller number of independent variables, but with a higher multiple correlation coefficient (R), several statistical information criteria were applied in our regression analysis. AIC, which is based upon Kullback–Leibler information and considered to be the most effective criterion, is known to achieve the trade-off between suitability and reliability for statistical models. 5 –7 Some scientists empirically support the availability of AIC for regression analysis. 8 –10 Furthermore, the MAICE (Minimum AIC Estimate) is equivalent to 2.0 of F-to-enter or F-to-remove. 11 –13
If we set the MAICE as the criterion for variable selection, we established y = 91.301 −0.258*W2 −19.04*W10 +0.188*W3 −24.72*W8 +0.848*W4 (R = 0.415, R 2 = 0.172) as the optimal for males. For females, it was y = 98.763 −38.347*W10 −0.115*W2 +0.077*W3 (R = 0.525, R 2 = 0.276).
From the viewpoint of the selection criterion for independent variables and the diversity of the variables, the above-mentioned equation was the optimal age-predictive model based on the walking parameters of each gender. However, the parameter regimes (kinematics, kinetics, and so on) of these models were too small to describe the entire walking posture.
In a second approach, we choose to retain the variables with F values larger than 1.0, and to eliminate those with F value smaller than 0.9. As result of the stepwise regression analysis, the following age-predictive equations for both genders were obtained. For the males, y = −0.267*W2 −22.238*W10 +0.197*W3 −32.479*W8 +0.792*W4 −0.852*W5 +93.38 (R = 0.420, R 2 = 0.177, R adjusted for degrees of freedom [df ] = 0.126). For the females, we obtained y = −42.006*W10 −0.105*W2 +0.065*W3 −0.065*W1 −0.092*W5 +8.997*W9 −0.902*W6 +100.69 (R = 0.552, R 2 = 0.305, R adjusted for df = 0.268).
Discussion
Altough we tried regression analysis of all variables, the tolerance of multicollinearity was exceeded. The correlation level with other variables rose too much in a prior diagnosis of the multicollinearity, especially for WV and step length (W10). To avoid the multicollinearity, the stepwise variable selection method is recommended. 8,11 As the result of the second stepwise regression analysis setting (a lower F value to enter or to remove criteria), more than half of the variables used appeared in the models for both genders. However, the age-predictive model for females contained seven variables, one more than the model for the males. Especially, the contributions of the range of motion of the knee joint and hip joint to the age were high; the former showed a negative, the latter a positive correlation with age. Adopting the MAICE, the age-predictive model for each gender was composed of three or four variables, and moreover, relatively it saved the parameters.
Three variables (W2, W3, and W10) of the model appeared in common for both genders in these stepwise methods.That is, range of motion (ROM) of knee and hip are important variables to describe the age-related changes of human walking movement as well as step length. The interaction of ROM of two joints—the knee, with a negative regression coefficient, and the hip, with a positive regression coefficient—in walking step is an excellent marker of aging in the elderly.
In spite of low correlation coefficient (r) of W2 or W3 with AGE, stepwise regression analysis shows that combinations of these variables have increased the explanatory potential. It is supposed to be a synergistic or mutually potentiating effect of two variables, although some researchers of biomechanics are skeptical of the effect.
Furthermore, multicollinearlity detection and its treatment, as well as examination of the residuals, should be discussed in future studies. Whereas more than 110 separate variables are included in the Okada database, 3 the use of the component score due to principal component analysis is necessary for an effective interpretation.