Validity of Knee Flexion and Extension Peak Torque Prediction Models
B e primary purpose of this study was to test the validity of predictive models relating &okineticknee torque production to anthropomelric and demographic variables. Subjects were 2-3 healtbyfemale and 15 healtby male volunteers bemeen the ages of 10 and 77years. We measured suhjects'peak knee flex-ion and extension torque production at two angular velocities. For each torque dependent vardle, we calculated a Pearson product-moment correlation coeficient between the measured torque z~aluesand the z~aluesobtained with prediction equations The dzjierence bemeen the squared value of the correlation coeficients and the regression multiple?I z wlues obtained for an original group of 134 subjects ranged behueen .05 a n d . 10for the torque dependent variables. The raults indicate the zialidity of the regression models at the level specijied by the multiple regression R ' values. Clinicians can use the prediction equations praented in thb article to establbh rehabilitation goals for patients and can estimate the error involued in applying each prediction equation. [Gross MT, Credle.lK, Hopkins LA, et al. Validity of knee flexion and extension peak torque prediction models. Pbys Ther 70:3lo. 19901
Michael T Gross Jennifer K Credle L Annette Hopkins Tracy M Kollins
Key Words: Kinesiologvlbiomechanics, lower extremity;Muscle atropby;Muscle perjomnce, lower extremity; Rehabilitation.
In a previous study, Gross and colleagues reported on the relationship between isokinetic knee torque production and multiple anthropometric and demographic variables.' Subjects in that shldy were 70 healthy female and 64 healthy male volunteers between the ages of 10 and 80 years. They measured subjects' peak knee
flexion and extension torque production at two angular velocities. Stepwise regression analyses were used to examine the relationship between each torque dependent variable and the following potential predictor variables: age, gender, side of lower extremity dominance, height, weight, percentage of body fat, and thgh girth.
M Gross, PT, PhD, is Assistant Professor, Division of Physical Therapy, The University of North Carolina at Chapel Hill, CD #7135, Medical School Wing E 222H, Chapel Hill, NC 27599 (IJSA). J Credle, IT,BS, is Staff Physical Therapist, Department of Physical Therapy, Presbyterian Hospital,
200 Hawthorne Lane, Charlotte, NC 28233. I. Hopkins, PT,HS, is Staff Physical Therapist, Department of Physical Therapy, Rex Hospital, 4420 Lake Boont Trail, Raleigh, NC 27607.
T Kollins, PT, BS, is Staff Physical Therapist, Department of Physical Therapy, Presbyterian Hospital. Ms Credle, Ms Hopkins, and Ms Kollins were studen& in the baccalaureate physical therapy program, Division of Physical Therapy, The IJniversity of North Carolina at Chapel Hill, at the time this study was conducted.
Ibis article ulas submitted Fehruaq~Ci, 1989; ulas ulilh the autbon for ralision for file ueek; and ulas accepttd July 12, 1989.
Physical TherapyNolume 70, Number 1January 1990 Downloaded from https://academic.oup.com/ptj/article-abstract/70/1/3/2728557 by Washington University in St. Louis user on 23 March 2018
In the preliminary study by Gross and colleagues, the authors generated two sets of models designed to predict preinjury knee strength. They proposed clinicians could use one set of models (Type A models) by assessing predictor variables prior to o r immediately following injury. The second set of models (Type B models) involves the assessment of predictor variables postinjury, excluding an assessment of percentage of body fat and thigh ginh. Percentage of body fat and thigh ginh were excluded from Type B models because the authors recognized these variables might be influenced by the amount of time elapsed after injury. The Type A and Type B prediction models are provided in Table 1. The results of the preliminary study indicated a significant relationship between peak knee torque production and specific combinations of anthropometric and
3 / 17
demographic variables (multiple R = .78-87). The authors proposed the models could be used to establish rehabilitation goals for patients. Predictive models for muscular performance may be useful in instances when clinicians are unable to quantitatively assess a patient's muscular performance immediately after injury. Such assessment may not be feasible because of the unavailability of instrumentation or because patient status may prevent the assessment of either the affected or unaffected body part. Assessment of the unaffected body part following injury may not provide a valid indicator of preinjury status if generalized atrophy has occurred secondary to reduced activity levels. The primary purpose of the present study was to test the validity of the predictive models relating isokinetic knee torque production to anthropometric and demographic variables. We also were interested in determining the absolute error between predicted torque values and torque values produced by subjects during testing sessions.
Method Subjects The subjects for this study were 23 healthy female and 15 healthy male volunteers between the ages of 10 and 77 years. The mean age of the female subjects was 45.6 years (s = 20.8), and the mean age of the male subjects was 42.5 years (s = 21.8). Descriptive statistics for subject anthropometric and demographic variables are shown in Table 2 and are grouped by age and sex. The 38 subjects in this study will be referred to as the test group to distinguish them from the original group of 134 subjects who participated in the preliminary investigation. Subjects signed statements of informed consent prior to participation, and the
'1 in
=
-
Table 1 . Prediction Equationf Generated t.'ollowing Am(ysis of Original Group of Subjects (n = 134)' Type A models
ETS = -89.820 -
(0.010 x age2) - (15.210 x gender)
+ (1.787 x height)
+ (0.601 x weight) + (3.504 x thigh girth) - (1.219 x % body fat) FTS = -64.249 - (0.004 x age2) - (9.419 x gender) + (1.388 x height) + (0.295 x weight) + (3.015 x thigh girth) - (1.226 x % body fat) ETF = -52.066 + (0.456 x age) - (0.014 x age2) - (16.834 x gender) + (1.503 x height) + (0.483 x weight) - (0.424 x 96 body fat) age2) - (8.980 x gender) + (1.151 x height) + (0.276 x weight) + (2.373 x thigh girth) - (1.037 x % body fat)
FTF = -51.314 - (0.004 x Type B models
ETS = -80.723 -
+ (0 639 x
(0.010 x age2) - (22.736 x gender) weight)
FTS = -65.148 - (0.004 x
+ (0.295 x weight) ETF = -72.869 + (0.469 x + (1.921 x
height)
height)
+ (2.032 x
height)
age) - (0.014 x age2) - (21.263 x gender)
+ (0.403 x weight)
FTF = -55.519 - (0.004 x
+ (0.262 x
age2) - (17.735 x gender)
+ (2.331 x
age2) - (16.266 x gender)
+ (1.728 x
height)
weight)
aType A model = equation designed for meawrenient of predictor variables prior to or immediately following injury; Type B model = equation designed for measurement of predictor variables following injury. (ETS = peak knee extension torque in foot-pounds [ I It-lb = 1 356 Nam] at 60a/sec;FTS = peak knee flexion torque [ft.lb] at 60°/sec; ETF = peak knee extension torque [ftelb] at 180°/sec; FTF = peak knee flexion torque [ft.lb] at 18O0/sec.)(Gender entered as male = 1, female = 2; weight in pounds [ I Ih = 0.4536 kg]; height in inches [ I in = 2.54 cm]; thigh girth in inches; percentage of body fat as decimal fraction multiplied by 100 [eg, 0.185 x 100 = 18.5% body fat].)
project was approved by the Committee on the Protection of the Rights of Human Subjects at The University of North Carolina at Chapel Hill. We conducted a screening interview of potential subjects to ensure that each participant met the following inclusion criteria: 1. No history of lower extremity fracture. 2. No history of a neurological condition affecting lower extremity function. 3. No lower extremity muscular strain or ligamentous sprain during the two years to prior to testing that limited normal activity for more than 48 hours.
2.54 cm.
4. No history of knee joint arthritis o r contracture.
Procedure A detailed description of the instru-
mentation, procedure, and reliability testing protocol used in this study is provided in the previous study by Gross et al.1 The instrumentation and testing procedure for the test group were identical to those used with the original group of subjects in the preliminary investigation. We will provide, therefore, only an abbreviated description of the testing procedure. We first measured subject height to the nearest 0.5 in* and subject weight to the nearest 0.5 lb.+ The dominant leg was determined by asking each subject which leg would be preferred for kicking a ball. The principal investigator (MTG) measured thigh girth (to the nearest 0.5 in) for each leg at a point midway between the greater trochanter and the proximal pole of
Physical TherapyNolume 70, Number IAanuary 1990 Downloaded from https://academic.oup.com/ptj/article-abstract/70/1/3/2728557 by Washington University in St. Louis user on 23 March 2018
-
Table 2. Meam and Standard Ueuiationf for Subject Characterktics of Test Group (n = 38) and Peak Torque valued' by Age Group and Sex Age Group (yr) 10-20 Varlable
A@ X
M (n=4)
20-40
F (n=6)
M (n=12)
40-60
F (n=14)
60-80
M (n=6)
F M (n=10) (n=8)
F (n=16)
(YO
S
Height - (in)c X S
W€jght X
(Ib)d
S
Th&h girth (in) X S
%_body fat X S
ET_S(ft-lb)" X S
apparatus* with hips and knees flexed at approximately 90 degrees. We stabilized each subject with thigh, pelvic, and chest straps. Prior to testing, we followed computer software procedures"~ correct all torque values for the effects of gravity acting on the mass of the lower leg and the mass of the Cybexm11 dynamometer arm. These procedures involve positioning the dynamometer input arm at the true horizontal as the computer monitors the torque signal voltage (TI) and the position signal voltage at this position. The examiner then attaches the subject's lower leg to the horizontal dynamometer input arm, and the subject relaxes the test leg as the computer monitors the torque voltage signal (T2) and the position voltage signal at this position. The final procedure involves allowing the subject to relax the lower leg freely at 90 degrees of knee flexion as the computer monitors torque (T3) and position signals. The algorithm used for gravity correction (GC) of torque values is
Fl_S(ftalb:~ X S
ET_F (ft -lb:) X
7
S
FT_F(ft-lb:~ X S
Values represent total of 76 observations (both legs of each subject).
' 1 in = 2.54 cm
"1 Ib = 0.4536 kg.
'ETS = peak knee extension torque at 6O0/sec; FTS = peak knee flexion torque at 60°/sec; E7F = peak knee extension torque at 180°/sec; FTF = peak knee flexion torque at 180°1sec.
the patella, with the subject in the supine position, the knee extended, and the lower leg relaxed.2 The principal investigator also performed skinfold measurements (to the nearest 0.5 mm) over the biceps brachii muscle, the triceps brachii muscle, the subscapular region, and the iliac crest in the manner described by Durnin and Rahaman. Percentage-of-body-fatcal-
where TCF is the tor ue calibration factor (in foot-pounds I per volt) and 0 is the degrees of knee flexion. The GC torque values are determined for each position in the range of motion and are added to extension torques and subtracted from flexion torques produced by the subject.
=
,356 N , m,
culations were recorded to the nearest 0.1%. We tested the dominant and nondominant legs of each subject at test velocities of 60" and 180°/sec. The order of dominant-nondominant leg testing and the order of test velocities were randomized for each subject. Each subject sat in the Cybexm I1 testing
*Cybex, Div of Lumex, Inc, 2100 Smithtown Ave, Ronkonkoma, NY 11779. g~soscan11, Isotechnologies Inc, PO Box 1239, Elizabeth Brady Rd, Hillsborough, NC 27278.
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Each subject performed one practice ' series of five submaximal knee extension-flexion repetitions at the first test velocity to become familiar with the testing condition and to minimize any practice effect. Following two minutes of rest, the subject performed three maximal knee extension-flexion efforts. Following another two minutes of rest, the subject performed a second series of three maximal knee extension-flexion efforts at the same angular test velocity. The examiner recorded the largest of the six peak knee extension torque values and the largest of the six peak knee flexion torque values recorded during the two data-collection series at the first test velocity. We used identical procedures for the second test
velocity for the same lower extremity. We then repositioned the subject and conducted the same testing protocol for the contralateral leg.
Preliminary Data Analysis The cross-validation design and analysis procedure used in this study have been described by several a ~ t h o r s . 4 ~ The four variables measured for each subject in this study were peak knee flexion and extension torque performed at 60" and 180°/sec. For each variable, we calculated 1) a Pearson product-moment correlation coefficient (r) between the measured torque values and the torque values obtained with the Type A prediction equation and 2) a Pearson productmoment correlation coefficient between the measured torque values and the torque values obtained with the Type B prediction equation. We assessed the validity of the prediction equations by qualitatively comparing the squared value of the correlation coefficients (Pearson r 2 ) with the curresponding multiple regression K~ values obtained for the original group of subjects. The multiple regression R2 value represents the percentage of dependent-variable variance explained by the regression model. We also calculated the absolute difference between the torque values generated by each subject and the predicted torque values. 'The predicted torque values were based on the regressioil equations derived from the original group of subjects. Absolute differences were calculated for each torque value for both model types. The calculated absolute difference will be referenced as absolute error. The purpose of calculating absolute error values was to provide an estimate of error involved in applying the regression models to the new test group. The following sample computation demonstrates the calculation of absolute error values. Sample subject data are as follows: age = 32.5 years (to the nearest month), male (coded I), height = 70 in, weight = 160 lb, and peak knee extension torque at 180°/sec = 110.7 ft-lb. We will use the
third equation under the Type R models heading in Table 1 to predict peak knee extension torque at 180°/sec.The equation is as follows: ETF = -72.869 + (0.469 X age) (0.014 x age2) - (21.263 x gender) + (1.921 x height) + (0.403 X weight) (2)
Substitution for the five predictor variables would occur as follows:
torque values generated by each subject and predicted torque values based on the newly generated regression equations. These differences were calculated for each torque value for both model types. The purpose of calculating absolute error values was to provide clinicians with an estimate of error involved in using the new regression equations to predict preinjury torque values for rehabilitation goals.
Results
ETF = 105.3 ft-lb
(3)
Computation of absolute error would be as follows: Absolute Error = l~redictedTorque Value - Measured Torque value1 Absolute Error = 1105.3 ft-lb - 110.7ftelbl Absolute Error = 5.4 ft-lb (4)
Post hoc Data Analysis Cross-validation analysis involves an assessment of shrinkage, or differences between the original group's multiple regression R2 values and the corresponding Pearson 12 values. If these differences are small, indicating a small amount of shrinkage, the recommended post hoc procedure is to combine the original group (n = 134) and the test group (n = 38), followed by the derivation of regression equations based on the newly pooled sample (N = 172). This recommendation is based on the greater stability of regression equations derived from larger samples.4.5 We proceeded with apost hoc analysis for the pooled sample of 172 subjects by using each torque variable in a separate stepwise regression procedure for a Type A model and for a Type B model. This regression analysis strategy is described in detail in the previously reported study involving the original group of subjects.' We continued with thepost hoc analysis for the pooled sample by calculating the absolute error between
Table 2 also includes descriptive statistics for all peak torque values. Table 3 provides a comparison of the multiple regression R2 values obtained for the original group of subjects and the Pearson r 2 values, comparing predicted and obtained torque values. Table 3 also provides comparisons for each Type A and each Type B model by identifying the absolute difference (IAR2()between corresponding multiple regression R2 and Pearson r2 values. The results of the preliminary data analysis qualitatively indicate a small amount of shrinkage, or small absolute differences (IAR21) between the screening sample multiple regression R2 values and the corresponding Pearson r values. Table 4 provides descriptive statistics for the absolute error between torque values measured from each test group subject and predicted torque values. Predicted torque values are based on the regression equations derived from an analysis of the original group of subjects. The multiple regression analysis of the pooled sample for Type A models examined the relationship between peak torque production and variables that could be assessed prior to or immediately following injury. The results of each of the four stepwise regression procedures for Type A models are given in Tables 5 to 8. The prediction models generated for each of the four torque variables are also included in Tables 5 to 8. These models indicate that 59% to 73% of the variance (final incremental R2 value) of peak knee extension and
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-
Table 3. Comparison of Original Group (n = 1154) Multgle Regression R' values' and Test Group (n = 38) Pearson r' Valuesfor Tvpe A and Type R Models" Orlglnal Group Multlple R 2
Test Group Pearson r2
1
ETS
.75
.68
.07
FTS
.72
.66
.06
ETF
.75
.70
.05
.64
.55
.09
ETS
.74
.66
.08
FTS
.69
.62
.07
ETF
.74 .61
.69 .51
.05 .10
Dependent Varlable
~
~
Type A models
FTF
Type B models
FTF
"Type A model = equation designed for measurement of predictor variables prior to o r immediatelv following injury; Type B model = equation designed for measurement of predictor variables following injury. (ETS = peak knee extension torque at 60°/sec; FTS = peak knee flexion torque at 60°/sec; ETF = peak knee extension torque at 18O0/sec;FE = peak knee flexion torque at 18O0lsec.) b l A ~ L I= absolute difference between multiple regression R' and Pearson r 2 values
--
Table 4. Absolute Error (in Footpoundsr Between Predicted and Measured Peak Torque Values,forTest Group (n = 38) for Type A and Type B ~ o d e L @ Generated from Analysa of . Original Group (n = 1.34)' -
Dependent Varlable
X
s
-
flexion torque can be explained by using combinations of the following variables: age, age squared, gender, height, weight, percentage of body fat, and thigh girth.
The multiple regression analysis for Type H models examined the relationship between peak torque and variables that could be assessed following injury. This analysis assumes that preinjury body weight could be ~ obtained 1 ~by clinicians either by patient history or from medical records, and the analysis excludes an assessment of percentage of body fat and thigh girth. The regression analysis results for Type B models for knee extension torque at 60°/sec and at 180°/sec were identical to the results for the Type A models for these two variables. The regression analysis results for Type I3 models for knee flexion torque at 60°/sec and at 180°/ sec are given in Tables 9 and 10, respectively. The prediction models generated for knee flexion torque at 60°/sec and at 180°/sec are also included in Tables 9 and 10, respectively. The regression analysis results for Type B models indicate that 59% to 73% of the variance of peak knee extension and flexion torque can be explained by using combinations of the following variables: age, age squared, gender, height, and weight.
Table 5. Regression Ana1.y.si~for Relationsh@Between Peak Knee Extension Torque at GOO/sec(ETS) and Variables that Could Be Asesed Prior to or Immediatety Following Injuly
Type A models ETS
Order Varlables Entered Into Model
FTS ETF
Coefficient of Each Varlable for Flnal Model
Multiple R
Multlple R2
Incremental R2
FTF
Type B models
Height
2.1 14
,680
,463
,463
Weight
,553
,815
.665
,102
ETS FTS ETF
Gender
-25.681
,842
,709
,044
FTF
Age Constant
,966 - 70.703
,845
,715
,006
SS
MS
F
P
482661.33 192745.87
96532.27 570.25
169.28
,000
?'me . . A model = equation designed for measurement of predictor variables prior to o r immediatelv followine
B e primary purpose of this study was to test the validity of predictive models relating &okineticknee torque production to anthropomelric and demographic variables. Subjects were 2-3 healtbyfemale and 15 healtby male volunteers bemeen the ages of 10 and 77years. We measured suhjects'peak knee flex-ion and extension torque production at two angular velocities. For each torque dependent vardle, we calculated a Pearson product-moment correlation coeficient between the measured torque z~aluesand the z~aluesobtained with prediction equations The dzjierence bemeen the squared value of the correlation coeficients and the regression multiple?I z wlues obtained for an original group of 134 subjects ranged behueen .05 a n d . 10for the torque dependent variables. The raults indicate the zialidity of the regression models at the level specijied by the multiple regression R ' values. Clinicians can use the prediction equations praented in thb article to establbh rehabilitation goals for patients and can estimate the error involued in applying each prediction equation. [Gross MT, Credle.lK, Hopkins LA, et al. Validity of knee flexion and extension peak torque prediction models. Pbys Ther 70:3lo. 19901
Michael T Gross Jennifer K Credle L Annette Hopkins Tracy M Kollins
Key Words: Kinesiologvlbiomechanics, lower extremity;Muscle atropby;Muscle perjomnce, lower extremity; Rehabilitation.
In a previous study, Gross and colleagues reported on the relationship between isokinetic knee torque production and multiple anthropometric and demographic variables.' Subjects in that shldy were 70 healthy female and 64 healthy male volunteers between the ages of 10 and 80 years. They measured subjects' peak knee
flexion and extension torque production at two angular velocities. Stepwise regression analyses were used to examine the relationship between each torque dependent variable and the following potential predictor variables: age, gender, side of lower extremity dominance, height, weight, percentage of body fat, and thgh girth.
M Gross, PT, PhD, is Assistant Professor, Division of Physical Therapy, The University of North Carolina at Chapel Hill, CD #7135, Medical School Wing E 222H, Chapel Hill, NC 27599 (IJSA). J Credle, IT,BS, is Staff Physical Therapist, Department of Physical Therapy, Presbyterian Hospital,
200 Hawthorne Lane, Charlotte, NC 28233. I. Hopkins, PT,HS, is Staff Physical Therapist, Department of Physical Therapy, Rex Hospital, 4420 Lake Boont Trail, Raleigh, NC 27607.
T Kollins, PT, BS, is Staff Physical Therapist, Department of Physical Therapy, Presbyterian Hospital. Ms Credle, Ms Hopkins, and Ms Kollins were studen& in the baccalaureate physical therapy program, Division of Physical Therapy, The IJniversity of North Carolina at Chapel Hill, at the time this study was conducted.
Ibis article ulas submitted Fehruaq~Ci, 1989; ulas ulilh the autbon for ralision for file ueek; and ulas accepttd July 12, 1989.
Physical TherapyNolume 70, Number 1January 1990 Downloaded from https://academic.oup.com/ptj/article-abstract/70/1/3/2728557 by Washington University in St. Louis user on 23 March 2018
In the preliminary study by Gross and colleagues, the authors generated two sets of models designed to predict preinjury knee strength. They proposed clinicians could use one set of models (Type A models) by assessing predictor variables prior to o r immediately following injury. The second set of models (Type B models) involves the assessment of predictor variables postinjury, excluding an assessment of percentage of body fat and thigh ginh. Percentage of body fat and thigh ginh were excluded from Type B models because the authors recognized these variables might be influenced by the amount of time elapsed after injury. The Type A and Type B prediction models are provided in Table 1. The results of the preliminary study indicated a significant relationship between peak knee torque production and specific combinations of anthropometric and
3 / 17
demographic variables (multiple R = .78-87). The authors proposed the models could be used to establish rehabilitation goals for patients. Predictive models for muscular performance may be useful in instances when clinicians are unable to quantitatively assess a patient's muscular performance immediately after injury. Such assessment may not be feasible because of the unavailability of instrumentation or because patient status may prevent the assessment of either the affected or unaffected body part. Assessment of the unaffected body part following injury may not provide a valid indicator of preinjury status if generalized atrophy has occurred secondary to reduced activity levels. The primary purpose of the present study was to test the validity of the predictive models relating isokinetic knee torque production to anthropometric and demographic variables. We also were interested in determining the absolute error between predicted torque values and torque values produced by subjects during testing sessions.
Method Subjects The subjects for this study were 23 healthy female and 15 healthy male volunteers between the ages of 10 and 77 years. The mean age of the female subjects was 45.6 years (s = 20.8), and the mean age of the male subjects was 42.5 years (s = 21.8). Descriptive statistics for subject anthropometric and demographic variables are shown in Table 2 and are grouped by age and sex. The 38 subjects in this study will be referred to as the test group to distinguish them from the original group of 134 subjects who participated in the preliminary investigation. Subjects signed statements of informed consent prior to participation, and the
'1 in
=
-
Table 1 . Prediction Equationf Generated t.'ollowing Am(ysis of Original Group of Subjects (n = 134)' Type A models
ETS = -89.820 -
(0.010 x age2) - (15.210 x gender)
+ (1.787 x height)
+ (0.601 x weight) + (3.504 x thigh girth) - (1.219 x % body fat) FTS = -64.249 - (0.004 x age2) - (9.419 x gender) + (1.388 x height) + (0.295 x weight) + (3.015 x thigh girth) - (1.226 x % body fat) ETF = -52.066 + (0.456 x age) - (0.014 x age2) - (16.834 x gender) + (1.503 x height) + (0.483 x weight) - (0.424 x 96 body fat) age2) - (8.980 x gender) + (1.151 x height) + (0.276 x weight) + (2.373 x thigh girth) - (1.037 x % body fat)
FTF = -51.314 - (0.004 x Type B models
ETS = -80.723 -
+ (0 639 x
(0.010 x age2) - (22.736 x gender) weight)
FTS = -65.148 - (0.004 x
+ (0.295 x weight) ETF = -72.869 + (0.469 x + (1.921 x
height)
height)
+ (2.032 x
height)
age) - (0.014 x age2) - (21.263 x gender)
+ (0.403 x weight)
FTF = -55.519 - (0.004 x
+ (0.262 x
age2) - (17.735 x gender)
+ (2.331 x
age2) - (16.266 x gender)
+ (1.728 x
height)
weight)
aType A model = equation designed for meawrenient of predictor variables prior to or immediately following injury; Type B model = equation designed for measurement of predictor variables following injury. (ETS = peak knee extension torque in foot-pounds [ I It-lb = 1 356 Nam] at 60a/sec;FTS = peak knee flexion torque [ft.lb] at 60°/sec; ETF = peak knee extension torque [ftelb] at 180°/sec; FTF = peak knee flexion torque [ft.lb] at 18O0/sec.)(Gender entered as male = 1, female = 2; weight in pounds [ I Ih = 0.4536 kg]; height in inches [ I in = 2.54 cm]; thigh girth in inches; percentage of body fat as decimal fraction multiplied by 100 [eg, 0.185 x 100 = 18.5% body fat].)
project was approved by the Committee on the Protection of the Rights of Human Subjects at The University of North Carolina at Chapel Hill. We conducted a screening interview of potential subjects to ensure that each participant met the following inclusion criteria: 1. No history of lower extremity fracture. 2. No history of a neurological condition affecting lower extremity function. 3. No lower extremity muscular strain or ligamentous sprain during the two years to prior to testing that limited normal activity for more than 48 hours.
2.54 cm.
4. No history of knee joint arthritis o r contracture.
Procedure A detailed description of the instru-
mentation, procedure, and reliability testing protocol used in this study is provided in the previous study by Gross et al.1 The instrumentation and testing procedure for the test group were identical to those used with the original group of subjects in the preliminary investigation. We will provide, therefore, only an abbreviated description of the testing procedure. We first measured subject height to the nearest 0.5 in* and subject weight to the nearest 0.5 lb.+ The dominant leg was determined by asking each subject which leg would be preferred for kicking a ball. The principal investigator (MTG) measured thigh girth (to the nearest 0.5 in) for each leg at a point midway between the greater trochanter and the proximal pole of
Physical TherapyNolume 70, Number IAanuary 1990 Downloaded from https://academic.oup.com/ptj/article-abstract/70/1/3/2728557 by Washington University in St. Louis user on 23 March 2018
-
Table 2. Meam and Standard Ueuiationf for Subject Characterktics of Test Group (n = 38) and Peak Torque valued' by Age Group and Sex Age Group (yr) 10-20 Varlable
A@ X
M (n=4)
20-40
F (n=6)
M (n=12)
40-60
F (n=14)
60-80
M (n=6)
F M (n=10) (n=8)
F (n=16)
(YO
S
Height - (in)c X S
W€jght X
(Ib)d
S
Th&h girth (in) X S
%_body fat X S
ET_S(ft-lb)" X S
apparatus* with hips and knees flexed at approximately 90 degrees. We stabilized each subject with thigh, pelvic, and chest straps. Prior to testing, we followed computer software procedures"~ correct all torque values for the effects of gravity acting on the mass of the lower leg and the mass of the Cybexm11 dynamometer arm. These procedures involve positioning the dynamometer input arm at the true horizontal as the computer monitors the torque signal voltage (TI) and the position signal voltage at this position. The examiner then attaches the subject's lower leg to the horizontal dynamometer input arm, and the subject relaxes the test leg as the computer monitors the torque voltage signal (T2) and the position voltage signal at this position. The final procedure involves allowing the subject to relax the lower leg freely at 90 degrees of knee flexion as the computer monitors torque (T3) and position signals. The algorithm used for gravity correction (GC) of torque values is
Fl_S(ftalb:~ X S
ET_F (ft -lb:) X
7
S
FT_F(ft-lb:~ X S
Values represent total of 76 observations (both legs of each subject).
' 1 in = 2.54 cm
"1 Ib = 0.4536 kg.
'ETS = peak knee extension torque at 6O0/sec; FTS = peak knee flexion torque at 60°/sec; E7F = peak knee extension torque at 180°/sec; FTF = peak knee flexion torque at 180°1sec.
the patella, with the subject in the supine position, the knee extended, and the lower leg relaxed.2 The principal investigator also performed skinfold measurements (to the nearest 0.5 mm) over the biceps brachii muscle, the triceps brachii muscle, the subscapular region, and the iliac crest in the manner described by Durnin and Rahaman. Percentage-of-body-fatcal-
where TCF is the tor ue calibration factor (in foot-pounds I per volt) and 0 is the degrees of knee flexion. The GC torque values are determined for each position in the range of motion and are added to extension torques and subtracted from flexion torques produced by the subject.
=
,356 N , m,
culations were recorded to the nearest 0.1%. We tested the dominant and nondominant legs of each subject at test velocities of 60" and 180°/sec. The order of dominant-nondominant leg testing and the order of test velocities were randomized for each subject. Each subject sat in the Cybexm I1 testing
*Cybex, Div of Lumex, Inc, 2100 Smithtown Ave, Ronkonkoma, NY 11779. g~soscan11, Isotechnologies Inc, PO Box 1239, Elizabeth Brady Rd, Hillsborough, NC 27278.
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Each subject performed one practice ' series of five submaximal knee extension-flexion repetitions at the first test velocity to become familiar with the testing condition and to minimize any practice effect. Following two minutes of rest, the subject performed three maximal knee extension-flexion efforts. Following another two minutes of rest, the subject performed a second series of three maximal knee extension-flexion efforts at the same angular test velocity. The examiner recorded the largest of the six peak knee extension torque values and the largest of the six peak knee flexion torque values recorded during the two data-collection series at the first test velocity. We used identical procedures for the second test
velocity for the same lower extremity. We then repositioned the subject and conducted the same testing protocol for the contralateral leg.
Preliminary Data Analysis The cross-validation design and analysis procedure used in this study have been described by several a ~ t h o r s . 4 ~ The four variables measured for each subject in this study were peak knee flexion and extension torque performed at 60" and 180°/sec. For each variable, we calculated 1) a Pearson product-moment correlation coefficient (r) between the measured torque values and the torque values obtained with the Type A prediction equation and 2) a Pearson productmoment correlation coefficient between the measured torque values and the torque values obtained with the Type B prediction equation. We assessed the validity of the prediction equations by qualitatively comparing the squared value of the correlation coefficients (Pearson r 2 ) with the curresponding multiple regression K~ values obtained for the original group of subjects. The multiple regression R2 value represents the percentage of dependent-variable variance explained by the regression model. We also calculated the absolute difference between the torque values generated by each subject and the predicted torque values. 'The predicted torque values were based on the regressioil equations derived from the original group of subjects. Absolute differences were calculated for each torque value for both model types. The calculated absolute difference will be referenced as absolute error. The purpose of calculating absolute error values was to provide an estimate of error involved in applying the regression models to the new test group. The following sample computation demonstrates the calculation of absolute error values. Sample subject data are as follows: age = 32.5 years (to the nearest month), male (coded I), height = 70 in, weight = 160 lb, and peak knee extension torque at 180°/sec = 110.7 ft-lb. We will use the
third equation under the Type R models heading in Table 1 to predict peak knee extension torque at 180°/sec.The equation is as follows: ETF = -72.869 + (0.469 X age) (0.014 x age2) - (21.263 x gender) + (1.921 x height) + (0.403 X weight) (2)
Substitution for the five predictor variables would occur as follows:
torque values generated by each subject and predicted torque values based on the newly generated regression equations. These differences were calculated for each torque value for both model types. The purpose of calculating absolute error values was to provide clinicians with an estimate of error involved in using the new regression equations to predict preinjury torque values for rehabilitation goals.
Results
ETF = 105.3 ft-lb
(3)
Computation of absolute error would be as follows: Absolute Error = l~redictedTorque Value - Measured Torque value1 Absolute Error = 1105.3 ft-lb - 110.7ftelbl Absolute Error = 5.4 ft-lb (4)
Post hoc Data Analysis Cross-validation analysis involves an assessment of shrinkage, or differences between the original group's multiple regression R2 values and the corresponding Pearson 12 values. If these differences are small, indicating a small amount of shrinkage, the recommended post hoc procedure is to combine the original group (n = 134) and the test group (n = 38), followed by the derivation of regression equations based on the newly pooled sample (N = 172). This recommendation is based on the greater stability of regression equations derived from larger samples.4.5 We proceeded with apost hoc analysis for the pooled sample of 172 subjects by using each torque variable in a separate stepwise regression procedure for a Type A model and for a Type B model. This regression analysis strategy is described in detail in the previously reported study involving the original group of subjects.' We continued with thepost hoc analysis for the pooled sample by calculating the absolute error between
Table 2 also includes descriptive statistics for all peak torque values. Table 3 provides a comparison of the multiple regression R2 values obtained for the original group of subjects and the Pearson r 2 values, comparing predicted and obtained torque values. Table 3 also provides comparisons for each Type A and each Type B model by identifying the absolute difference (IAR2()between corresponding multiple regression R2 and Pearson r2 values. The results of the preliminary data analysis qualitatively indicate a small amount of shrinkage, or small absolute differences (IAR21) between the screening sample multiple regression R2 values and the corresponding Pearson r values. Table 4 provides descriptive statistics for the absolute error between torque values measured from each test group subject and predicted torque values. Predicted torque values are based on the regression equations derived from an analysis of the original group of subjects. The multiple regression analysis of the pooled sample for Type A models examined the relationship between peak torque production and variables that could be assessed prior to or immediately following injury. The results of each of the four stepwise regression procedures for Type A models are given in Tables 5 to 8. The prediction models generated for each of the four torque variables are also included in Tables 5 to 8. These models indicate that 59% to 73% of the variance (final incremental R2 value) of peak knee extension and
Physical TheralpyNolume 70, Number l/January 1990 Downloaded from https://academic.oup.com/ptj/article-abstract/70/1/3/2728557 by Washington University in St. Louis user on 23 March 2018
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Table 3. Comparison of Original Group (n = 1154) Multgle Regression R' values' and Test Group (n = 38) Pearson r' Valuesfor Tvpe A and Type R Models" Orlglnal Group Multlple R 2
Test Group Pearson r2
1
ETS
.75
.68
.07
FTS
.72
.66
.06
ETF
.75
.70
.05
.64
.55
.09
ETS
.74
.66
.08
FTS
.69
.62
.07
ETF
.74 .61
.69 .51
.05 .10
Dependent Varlable
~
~
Type A models
FTF
Type B models
FTF
"Type A model = equation designed for measurement of predictor variables prior to o r immediatelv following injury; Type B model = equation designed for measurement of predictor variables following injury. (ETS = peak knee extension torque at 60°/sec; FTS = peak knee flexion torque at 60°/sec; ETF = peak knee extension torque at 18O0/sec;FE = peak knee flexion torque at 18O0lsec.) b l A ~ L I= absolute difference between multiple regression R' and Pearson r 2 values
--
Table 4. Absolute Error (in Footpoundsr Between Predicted and Measured Peak Torque Values,forTest Group (n = 38) for Type A and Type B ~ o d e L @ Generated from Analysa of . Original Group (n = 1.34)' -
Dependent Varlable
X
s
-
flexion torque can be explained by using combinations of the following variables: age, age squared, gender, height, weight, percentage of body fat, and thigh girth.
The multiple regression analysis for Type H models examined the relationship between peak torque and variables that could be assessed following injury. This analysis assumes that preinjury body weight could be ~ obtained 1 ~by clinicians either by patient history or from medical records, and the analysis excludes an assessment of percentage of body fat and thigh girth. The regression analysis results for Type B models for knee extension torque at 60°/sec and at 180°/sec were identical to the results for the Type A models for these two variables. The regression analysis results for Type I3 models for knee flexion torque at 60°/sec and at 180°/ sec are given in Tables 9 and 10, respectively. The prediction models generated for knee flexion torque at 60°/sec and at 180°/sec are also included in Tables 9 and 10, respectively. The regression analysis results for Type B models indicate that 59% to 73% of the variance of peak knee extension and flexion torque can be explained by using combinations of the following variables: age, age squared, gender, height, and weight.
Table 5. Regression Ana1.y.si~for Relationsh@Between Peak Knee Extension Torque at GOO/sec(ETS) and Variables that Could Be Asesed Prior to or Immediatety Following Injuly
Type A models ETS
Order Varlables Entered Into Model
FTS ETF
Coefficient of Each Varlable for Flnal Model
Multiple R
Multlple R2
Incremental R2
FTF
Type B models
Height
2.1 14
,680
,463
,463
Weight
,553
,815
.665
,102
ETS FTS ETF
Gender
-25.681
,842
,709
,044
FTF
Age Constant
,966 - 70.703
,845
,715
,006
SS
MS
F
P
482661.33 192745.87
96532.27 570.25
169.28
,000
?'me . . A model = equation designed for measurement of predictor variables prior to o r immediatelv followine
