Copyright 1992 by The Geroiilological Society of America
Journal of Gerontology; MEDICAL SCIENCES
1992. Vol. 47, No. 6.MI97-M203
Equations for Predicting Stature in White and Black Elderly Individuals Wm. Cameron Chumlea1 and Shumei Guo1-2 'The Division of Human Biology, Department of Community Health, and 'Department of Mathematics and Statistics, Wright State University School of Medicine, Dayton, Ohio.
A SSESSING nutritional status is important to the health •**• care of the elderly in order to help determine levels of nutritional support and to monitor the effects of nutritional intervention. Anthropometric measurements are part of a nutritional assessment, but standard techniques are not totally suitable for assessing elderly persons who are handicapped or those with limited mobility (1). The accurate use of anthropometry in a nutritional assessment depends upon a subject who is able to stand, sit, or be positioned so that measurements can be taken accurately, reliably, and without difficulty (1). In many instances, elderly individuals, especially the nonambulatory and very old, are unable to assume the body position needed for a measurement, nor are they able to assist the observer by maintaining the position of a limb. In such cases, common measures are unreliable, inaccurate, or even impossible. This is especially true for stature, the measure of which is not only affected by mobility but the increased prevalence of skeletal deformities with old age. Values for stature are needed for elderly persons in order to apply equations for estimating basal energy expenditure and subsequent nutrient need and to calculate indices of nutritional status such as weight-for-stature or weight divided by stature squared. If stature cannot be measured in an elderly person, then a surrogate value must be predicted in some manner. Useful methods of predicting stature in the elderly should make use of body measurements that are actual constituents or indices of stature, and that can be collected regardless of an individual's level of mobility. Also, the accuracy of prediction is needed so that the calculated values in a clinical setting can be evaluated within known confidence limits to adjust nutritional recommendations. Equations for predicting stature from recumbent anthropometric measurements have been developed from a limited
sample of elderly persons living in Southwest Ohio (2,3). The precision of these equations in estimating stature in other samples of the elderly has been good (4,5), but the validation sample and the equations were not nationally representative. Recumbent anthropometric techniques reduce the effects of mobility problems in the elderly and are accurate, reliable, and as valid as corresponding standard measurements for assessing the nutritional status of the elderly (6-8). Monitoring the nutritional status of elderly persons or identifying those with unusual amounts of adipose or muscle tissue or weight, or in need of nutritional therapy, is important for their health (9,10). The purpose of the present study was to develop generalized equations for predicting stature for the elderly from nationally representative samples for the United States population. Nationally representative equations would reduce the sample specificity problem of prediction equations from small unrepresentative samples and increase the precision and confidence in the predicted stature for an individual. METHODS
Sample National Health Examination Survey. — The sample used to develop the predictive equations in the report was selected from elderly subjects in Cycle I of the National Health Examination Survey (NHES) conducted by the National Center for Health Statistics (NCHS) from 1960 to 1970. The target population in the NHES consisted of all noninstitutionalized, civilian residents of the continental United States (11). Briefly, a national probability sample was identified, and the individuals were interviewed and their participation requested. Those who agreed to participate came to a mobile M197
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In an anthropometric nutritional assessment, elderly individuals are frequently unable to assume the positions needed for many measurements. This is especially true for stature, which is affected by mobility and skeletal deformities, and as a result measurements may be unreliable and inaccurate. An alternative is to use a surrogate value of stature. We developed predictive equations using data from elderly subjects in Cycle I of the National Health Examination Survey (NHES). The developed equations were cross-validated using two separate independent and more contemporary samples of elderly White men and women. The possible predictor variables were knee height and buttocks-knee length in the men and knee height and age in the women. For both the men and the women, the majority of the variance in stature was accounted for by knee height. Selected equation models were cross-validated, and a single equation was recommended for each elderly group that included knee height rather than buttocks-knee length as predictor variables. This selection was based upon the performance of the equations, and also upon the practical ease of collecting the possible predictor variables. Included with the recommended equations are the RMSEs and the standard errorfor predicting stature for an individual (SEI). The successful application of the recommended equations with two recent sets of elderly persons indicates the current utility of the recommended equations in White elderly Americans.
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Fels elderly sample. —This independent sample consisted of 106 men and 130 women 65 to 91 years of age from a study at the Fels Research Institute (now the Division of Human Biology, Department of Community Health, Wright State University School of Medicine). These participants were residents at three church-affiliated institutions and a Veterans' Affairs residence center in Southwestern Ohio. These were ambulatory individuals, but physical examinations were not conducted. A more complete description of the health and nutritional status of this sample has been reported (6). Aging Process Study. — This independent sample consisted of 12 men and 190 women, 65 to 95 years of age, who were participants in the Aging Process Study (APS). This is a prospective study of nutritional status of the elderly at the University of New Mexico School of Medicine in Albuquerque. These participants can be described as a sample of well educated, health-conscious individuals who are more affluent than the average elderly person. A more complete description of the health and nutritional status of the APS has been reported (12,13). Measurements The measurements from Cycle I used in the analyses were stature, weight, sitting height, knee height, buttocks-knee length, biacromial breadth, and waist circumference. De-
scriptions of the measurement techniques have been published elsewhere (14,15). The techniques were identical or similar to methods for corresponding measurements listed in the Anthropometric Standardization Reference Manual (1) or corresponding measurements taken in the first, second, and third National Health and Nutrition Examination Surveys (NHANES) and in the Hispanic Health and Nutrition Examination Survey (16,17). Briefly, stature was measured on a specially designed stadiometer. A movable tape measure on the side of the headpiece was photographed recording the subject's stature. The measure of stature was recorded from the photograph. Sitting height was measured with a portable GPM stadiometer mounted in its base as the subject sat on a table. Waist circumference was measured at the level of the umbilicus with a steel tape measure. Biacromial breadth was measured at the corresponding lateral borders of the appropriate bony landmarks with a GPM sliding caliper. Knee height was measured with the subject sitting with the sole of the foot on the floor and the knee and ankle joints at 90° angles. The anthropometer was placed next to the lower leg, and the distance measured from the floor to the top of the thigh immediately above the condyles of the femur. Buttocksknee length was measured with the subject sitting as for the knee height measurement. A GPM sliding caliper measured the distance from the maximum protrusion of the buttocks to the lower border of the patella with the caliper held parallel to the length of the thigh and parallel to the floor (18). Other body measurements were taken in the NHES, but they were not considered in this study because they were related primarily to body fatness or to human engineering questions. The reliability for many of these measurements has been reported (18-21). In general, reliability for these data are good and compare favorably with reliability for corresponding measurements in NHANES II and Hispanic HANES (17,22). In the Fels and APS cross-validation samples, stature and knee height were measured using the same equipment and methodology (1,3). However, knee height was measured recumbently in both samples using a Mediform sliding caliper (3). Descriptive statistics and measurement reliability for the body measurements of these samples have been reported (7,23). Statistics Sampling weights for each individual were used to adjust the data to account for unequal probabilities of selection, for nonresponse and coverage errors so that all the individual data used in these analyses represented national probability estimates (24). Weighted descriptive statistics were computed for the variables in the NHES sample. Means, standard deviations, and minimum, median, and maximum values were calculated for weighted values of the variables. The weighted mean was defined as follows:
2 w,x, Xw —
i= l n
2 w, i= 1
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examination center (MEC) located in their community where all tests were conducted (11). The national probability sample for Cycle I consisted of 7,710 individuals 18.00 to 79.99 years of age. Of these subjects, 6,672 were examined in the MECs. The sample used in the present analysis consisted of individuals 60 to 79.99 years of age. This included 438 White men, 453 White women, 50 Black men, and 60 Black women. The NHES data were used because it is the only nationally representative survey that collected body measurements appropriate for predicting stature. Similar measurements have not been included in other subsequent national surveys, which precluded the use of more recent data. The NHES sample used in this report was randomly divided into validation and cross-validation groups in such a way that the number of individuals in each stratum was balanced by sex and race. The validation group was used to develop the predictive equations, and the cross-validation group was used to cross-validate the derived equations. An additional cross-validation was conducted using two separate independent and more contemporary samples of elderly White men and women. These samples were used in the cross-validation analyses because the elderly subjects in the NHES were measured almost 30 years ago. Many of these individuals would have been born during the last two decades of the 19th century. Contemporary elderly individuals at corresponding ages to those in the NHES sample were born in the second and third decades of the 20th century and thus represent a subsequent generation. The application of the prediction equations to these two groups would address any possible secular effects of the NHES sample on the equations. Similar samples of Black elderly individuals were not available.
EQUATIONS FOR PREDICTING STATURE
In this formula, Xj was the observation for the ith individual and Wj was the weight for X(. The standard deviation for the weighted mean CTW was calculated from the following formula:
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In this equation, Yf was the observed value (stature) for the ith subject in the cross-validation sample, and Y, was the corresponding predicted values obtained from the derived equations in the validation sample (25). RESULTS
Y =
+ e
In this equation, Y was a column vector of observed stature, x was the design matrix with each column containing observed values of predictor variables, b was a column vector whose elements consist of regression coefficients, and e was a column vector of random errors which was assumed to be normally distributed with a mean of 0 and variance of CT2I. The weighted least squares estimator B was calculated by the following equation: P = (XWX)-XWY The variance of (3 was calculated by the following formula: var(p) = (XWX)-'a 2 The root mean square error or RMSE was calculated by the following formula:
RMSE =
Cross-validation. — The accuracy of selected best equations from the validation groups was tested by applying these equations to the NHES cross-validation samples. A measure of the accuracy of an equation was calculated as follows:
pure error =
2 W.CY.-t,) 2 i= 1 n 2 W,
Validation. — An all-possible-subsets regression analysis was conducted to determine which variable or set of variables were the best predictors of stature. These variables were knee height, buttocks-knee length, and age. This analysis was done separately for Whites and Blacks. To determine the extent of possible age effects, the analyses were rerun, forcing in age as a predictor variable. This made no significant effect upon the parameters of the equations except in the White women. The selection of the best possible predictor variables was based upon the values of R2, the root mean square error (RMSE), and distributions of the residuals for the predictive equations from the all-possible-subsets regression. The values for R2, RMSE, and coefficient of variation (CV) for prediction equations for White and Black elderly men and women in the NHES sample are presented in Table 3. For both the men and the women, the majority of the variance in stature was accounted for by knee height. For the men, the inclusion of age made no improvement in the predictive power of the equations. The combination of knee height and buttocks-knee length as predictor variables in the men increased the R2 value, and the RMSE decreased by 0.3 to 0.4 cm. For the women, the inclusion of age with knee height also did not improve the predictive power of the equation. However, the partial F-value for age was significant (p < .001) in the White women. Buttocks-knee length in the women did little to improve the predictive ability of knee height alone. In both sexes, the combination of knee height, buttocks-knee length, and age did not improve the predictive ability of the equations over the other paired combinations, but there was a significant effect of age in the White women. Thus, the possible predictor variables were knee height and buttocks-knee length in the men and knee height and age in the women. Because differences in the parameters of the possible equations were small depending upon the combination of predictor variables, two model equations were selected from each elderly group for crossvalidation. The selected models are identified by superscripts in Table 3. Cross-validation. — These selected equation models were cross-validated by comparing the pure errors (the mean
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Validation. — Regression equations were computed using every possible combination of the predictor variables in the validation group. From these regression equations, a final set of predictor variables was selected on the basis of minimum residual mean square error. An all-possible-subsets of weighted regression procedures was adopted to select the best predictive equation. The procedure evaluates every possible combination of predictor variables. The best equations of 1 predictor, 2 predictor, and 3 predictor variables were selected on the basis of minimum root mean square errors (RMSE). A set of recommended equations was selected for general use. These equations are parsimonious and relatively accurate in predicting stature with easy-to-measure predictor variables (25). The regression equation for predicting stature was as follows:
Descriptive statistics for the weighted values of the predictor variables for the total NHES sample are presented by race and sex in Table 1. The validation and cross-validation groups were balanced with regard to age and race, and this stratification resulted in the same number of observations in each group above and below the median age. There were no statistically significant race- or sex-specific differences between mean values for corresponding measurements in the validation and cross-validation groups. Descriptive statistics for the values of the predictor variables for the Fels and APS samples are presented by sex in Table 2.
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Table 1. Descriptive Statistics for Weighted Values of Elderly Men and Women in the NHES Sample (Validation and Cross-Validation Groups Combined) Men
Women Black (n - 5 0 )
White (#i = 438)
White (/; = 453)
Black (n = 60)
Variable
Mean
SO
Mean
SD
Mean
SD
Mean
SD
Age (years) Stature (cm) Weight (kg) Biacromial breadth (cm) Waist circum. (cm) Sitting height (cm) Knee height (cm) Buttocks-knee length (cm)
68.1 170.0 72.9 39.6 89.2 90.7 53.2 59.0
5.0 7.0 12.7 2.1 11.4 3.6 2.7 2.9
68.5 169.7 67.0 39.8 85.5 87.9 54.0 60.0
14.7 6.2 12.2 2.2 10.9 3.6 3.0 2.7
68.1 156.8 66.9 35.3 76.5 84.8 49.0 56.5
5.0 6.8 12.9 1.9 11.7 3.6 2.6 2.9
67.7 156.8 70.6 36.3 79.9 82.3 50.3 58.6
5.2 7.1 16.7 1.8 13.3 3.8 3.0 3.2
Men
Women APS
Fels
Fels
APS
Variable
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Stature (cm) Weight (kg) Knee height (cm)
169.5 73.2 53.3
6.9 13.4 2.7
163.6 57.8 49.1
10.9 10.2 3.4
156.3 62.3 49.4
6.0 12.0 2.3
164.3 67.5 50.6
10.1 12.5 3.7
Table 3. Best Possible Prediction Equations for Stature in the Validation Groups White Women
White Men Predictor Variables *Knee height tKnee height, buttocksknee length tKnee height/age Knee height/buttocksknee length/age
2
2
Black Men CV
Rl
RMSE
CV
0.51
4.73
2.80
0.62
4.28
2.74
2.65 2.63
0.69 0.51
3.78 4.80
2.24 2.84
0.62 0.62
4.33 4.35
2.78 2.79
2.61
0.72
3.67
2.17
0.62
4.41
2.82
CV
R
0.68
4.06
2.39
2.38 2.42
0.64 0.65
4.15 4.13
2.33
0.65
4.09
RMSE
CV
R
0.68
4.12
2.42
0.70 0.68
3.99 4.11
0.70
3.97
Black Women
RMSE
RMSE
R
2
*Model 1, all groups. tModel 2, White Men and Black Men only. tModel 2, White Women and Black Women only.
of the squared differences of the observed and predicted values) in the NHES cross-validation groups with the RMSEs for the corresponding model equations in the validation groups. These comparisons are presented in Table 4. The performance of the equation models in the NHES crossvalidation groups was very good. Except for the White women, the equation models predicted slightly better or the errors were smaller in the NHES cross-validation groups than in the NHES validation groups. In the White women, the predictive errors for the cross-validation group were slightly larger than for the validation group. These results indicate that in this nationally representative group of elderly subjects 60 to 79 years of age, the developed best equations have the same predictive power as in the sample from which the equations were developed. This should considerably reduce the sample specificity problem in the use of these equations within the specified age range. Since the selected equations performed so well in the
Table 4. Measures of Performance of the Selected Equations for Stature in the Validation and Cross-Validation Groups RMSE*
Pure Error
White Men Model 1 Model 2
4.12 3.99
3.62 3.41
Black Men Model I Model 2
4.73 3.78
3.20 3.17
White Women Model 1 Model 2
4.06 4.13
5.36 4.48
Black Women Model 1 Model 2
4.28 4.35
3.82 3.83
*RMSE - root mean square error.
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Table 2. Descriptive Statistics for Values of Elderly Men and Women in the Fels Elderly and Aging Process Study (APS) Samples
EQUATIONS
FOR PREDICTING
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STATURE
Table 5. Recommended Equations for Predicting Stature in Elderly Men and Women 60 to 80 Years of Age and Cross-Validation
Equation: Stature =
RMSE SEI Pure error Fels Men Fels Women APS Men APS Women
White Men
White Women
Black Men
Black Women
59.01 + 2.08 knee height
95.79 + 1.37 knee height
58.72 + 1.96 knee height
0.68 3.91 cm 7.84 cm
75.00 + 1 . 9 1 knee height — 0.17 age 0.59 4.40 cm 8.82 cm
0.51 4.18cm 8.44 cm
0.70 4.06 cm 8.26 cm
3.93 cm — 3.32 cm —
— 3.48 cm — —
— — — —
— — — —
DISCUSSION
Where comparisons are possible, these NHES data are similar to age-, race-, or sex-specific values for corresponding measurements in data from the NHANES I and II (16,26,27). The weighting of the NHES data converted the individual values to values that took into account the proportion that the individual represented of the total population of all White or Black individuals at the same ages in the United States at the time the data were collected. This changes the data set from a collection of individuals to a sample that is representative of the United States population (24). The best equations for predicting stature in the NHES elderly are presented in Table 3. The selected predictor variables were the same for Whites and Blacks: knee height and buttocks-knee length and age. Knee height and buttocksknee length account for almost the entire length of the legs where the majority of the variation in adult stature between individuals and the sexes is reported to occur (28). The relationship of stature to knee height and buttocks-knee length was different statistically between these elderly men and women (Table 3). In the men, stature was predicted well from knee height alone, but the inclusion of buttocks-knee
length made a difference in the values of the R2 and RMSEs. In the women, the inclusion of buttocks-knee length had no effect upon the precision of the equation, but the inclusion of age had an effect for White women only. However, the coefficients for age were negative for both White and Black women. This negative relationship with age in the women and the absence of an age effect in the men possibly reflects the greater effect of the aging process on the skeleton in women than men or the effects of selective survival in the women. These findings are similar to results reported previously for equations to predict stature in the elderly (2). In the earlier prediction equations, knee height was the best predictor of stature for elderly White men, but buttocks-knee length was not measured. In the elderly White women studied earlier, knee height and age were the selected variables, and the coefficient for age was similar to the present value (Table 3). The decision was made to select a single recommended equation for predicting stature in each elderly group. This selection was based upon the performance of the selected equation models, and also upon consideration of the practical ease of collecting the possible predictor variables. A predictive equation developed in a research setting may have excellent performance in cross-validation, but if the predictor variables used in the equation are difficult to measure, this will increase their unreliability and inaccuracy. As a result, the performance of the equation in a practical setting for an individual or a group will deteriorate to an unknown degree. Knee height is easy to measure in either a sitting or a recumbent manner in almost all elderly persons regardless of mobility status. Also, current reliability data are available for knee height as reference for researchers and clinicians. This is not the case for buttocks-knee length. Therefore, the decision was made to recommend equation models that included knee height rather than buttocks-knee length as a predictor variable. Included with the recommended equations (Table 5) are the RMSEs and the standard error for predicting stature for an individual (SEI). The RMSE is used when the equation is applied to groups of individuals. Plus or minus twice the RMSE produces the 95% confidence limits for the prediction of stature for the group from which the equation was developed. For an independent group of individuals to which an equation is applied, there is a 95% chance that ± twice the
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cross-validation (Table 4), it was possible to combine the NHES validation and cross-validation data sets and develop a final set of recommended equations. These equations are presented in Table 5 with the results of the cross-validation of the recommended equations for Whites in the Fels and APS samples. For the Fels and APS cross-validation groups, the pure errors of the recommended equations (Table 5) are similar to the corresponding pure errors of the NHES crossvalidation groups (Table 4). For the Fels men, the value of the pure error is the same as the RMSE of the validation groups, and for the Fels women the pure error is smaller than the RMSE and pure error of both NHES samples. For the APS men, the pure error is smaller than the RMSE and pure errors of the other comparison groups. However, the pure error for the APS women is one-third larger than the RMSE and pure errors of the other comparison groups. Crossvalidations in these two recent samples indicate that for elderly men the recommended equations have the same predictive power as for the validation sample of NHES men. The same is true for the Fels women, but the predictive power is poorer for the APS elderly women than for the NHES women.
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This report has presented the development of predictive equations for stature for White and Black elderly Americans. The equations were developed from nationally representative data, and the measurements were collected from ambulatory elderly persons using standard techniques. The use of recumbent anthropometric measurements in these equations should not expand the errors of prediction over those presented because of the small measurement errors for recumbent knee-height (7). However, the heterogeneity of the
conditions afflicting elderly persons will contribute to increasing the errors of prediction. Also, because of the very limited sample of Black elderly persons used to develop the equations, caution should be taken in interpreting or applying these results to other Black elderly Americans. Because of the small sample sizes, the recommended equations for Blacks will be less reliable for more individuals than the equations for the Whites. To some degree, the data and recommended equations are out-of-date because the data are about 25 years old, but there are no other data sets that contain the required variables. In the National Health and Nutrition Examination Studies I and II (NHANES I and II), the body measurements were related to growth and nutritional status. Knee-height is being collected from elderly subjects in NHANES III, but these data will not be available until late in the 1990s. However, the successful application of the recommended equations with two contemporary sets of elderly persons does indicate the current utility of the recommended equations in White elderly Americans. ACKNOWLEDGMENTS
This work was generously supported by Ross Laboratories, Columbus, Ohio, and Grants HD-12252, HD-27063, and AG-02049 from the National Institutes of Health. The authors appreciate the kind assistance of Dr. Philip J. Garry for allowing the use of data from the Aging Process Study, University of New Mexico, School of Medicine, Albuquerque, New Mexico. Address correspondence to Dr. Wm. Cameron Chumlea, Division of Human Biology, Wright State University, School of Medicine, 1005 Xcnia Avenue, Yellow Springs, OH 45387. REFERENCES
1. Lohman TG, Roche AF, Martorell R. eds. Anthropometric standardization reference manual. Champaign, IL: Human Kinetics Books, 1988. 2. Chumlea WC, Roche AF, Steinbaugh ML. Estimation of stature from knee height for persons 60 to 90 years of age. J Am Geriatr Soc 1985;33:116-20. 3. Chumlea WC, Roche AF, Mukherjee D. Nutritional assessment in the elderly through anthropometry. 2nd ed. Columbus, OH: Ross Laboratories, 1987. 4. Muncie HL, Sobal J, Hoopes JM, Tenney JH, Warren JW. A practical method of estimating stature of bedridden female nursing home patients. J Am Geriatr Soc 1987;35:285-9. 5. Murphy S, Cherot EK, Clement L, West KP. Measurement of knee height in frail, elderly nursing home residents. Am J Clin Nutr 1991 ;54:611-2. 6. Chumlea WC, Steinbaugh ML, Roche AF, Gopalaswamy N. Nutritional anthropometric assessment in elderly persons 65 to 90 years of age. J Nutr Elderly 1985;4:39-51. 7. Chumlea WC, Roche AF, Steinbaugh ML, Mukherjee D. Errors of measurement for methods of recumbent nutritional anthropometry in the elderly. J Nutr Elderly 1985;5:3-11. 8. Chumlea WC, Roche AF, Mukherjee D. Some anthropometric indices of body composition for elderly adults. J Gerontol 1986;41:36-9. 9. Mitchell CO, Lipschitz DA. The effects of age and sex on the routinely used measurements to assess the nutritional status of hospitalized patients. Am J Clin Nutr 1982;36:340-9. 10. Fischer JE. Nutritional assessment before surgery. Am J Clin Nutr 1982;35:1128-31. 11. Gordon T, Miller HW. Cycle I of the health examination survey sample and response. Rockville, MD: National Center for Health Statistics, 1964 (Vital and health statistics: series 11; no. 1). 12. Garry PJ, Goodwin JS, Hunt WC, Hooper EM, Leonard AG. Nutrition
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RMSE will cover the true mean stature of that group (25). For an independent group, the closer the value of the pure error is to the corresponding RMSE is an indication of the confidence in the predicted statures for the independent group. However, the closeness of predicted statures of an independent group to the respective true values will also depend upon how similar are the mean and distribution of knee height to the corresponding mean and distribution of knee height of the group from which the equation was derived. This association was easily demonstrated in the application of the recommended equations to the Fels and APS samples (Table 5). The pure errors for the Fels and APS men were very similar to the corresponding RMSE value. The pure error for the Fels women was smaller than the corresponding RMSE, but the pure error for the APS women was about 2.1 cm larger. The small pure errors for the Fels men and women were because their means and standard deviations for knee height and stature were very similar to corresponding values for knee height and stature in the NHES sample (Tables 1 and 2). In the APS sample, the pure error for the men was smaller than that of the RMSE of the NHES sample as were the means for knee height and the stature, but the corresponding standard deviations of the APS men were larger than those of the NHES sample. In addition, the APS sample of men consisted of only 12 individuals, which affected the results. For the APS women, however, the pure error was larger than the RMSE of the NHES sample as was their mean knee height, stature, and corresponding standard deviations. The application of the recommended equations to the Fels and APS samples indicates how characteristics of a sample can affect the outcome of the predictions. The clinical importance of these recommended equations (Table 5) appears in the application to a single individual. The SEl provides the distributions of the errors that can be expected in applying these equations to estimate the stature of an elderly man or woman if the measured knee height was equal to the respective mean knee height in Table 1. Plus or minus twice the SEl of the predicted stature provides the confidence limits for an individual which have a 95% chance including the individual's true stature. An individual's predicted stature will differ from the true stature as a function of the difference between the measured knee height and the corresponding mean knee height in Table 1. If the individual's knee height is close to the mean knee height of the group from which the equation was derived, then the accuracy of the prediction is greater. Therefore, in the clinical application of these equations one should consider the individual's knee height, the predicted stature, and the SEL These factors should be used in any decision to adjust a predicted stature value to fine tune its clinical use.
EQUATIONS FOR PREDICTING STATURE
13. 14.
15.
16.
17.
19.
20.
21.
22. 23.
24.
25. 26.
27.
28.
12-17 years, United States. Rockville, MD: National Center for Health Statistics, 1974 (Vital and health statistics: series 11; no. 132 IDHEW publication no. (HRA) 74-1614]). Marks GC, Habicht, J-P, Mueller WH. Reliability, dependability and precision of anthropometric measurements. Am J Epidemiol 1989; 130:578-87. Chumlea WC, Rhyne RL, Garry PJ, Hunt WC. Changes in anthropometric indices of body composition with age in a healthy elderly population. Am J Hum Biol 1989; 1:457-62. Landis RJ, Lepkowski JM, Eklund SA, Stehouwer SA. A statistical methodology for analyzing data from a complex survey: the first national health and nutrition examination survey. Data from the National Health Survey. Hyattsville, MD: National Center for Health Statistics, 1982 (Vital and health statistics: series 2; no. 92. |DHHS publication no. (PHS) 82-1366]). Kleinbaum DG, Kupper LL. Applied regression analysis and other multivariate methods. North Scituate, MA: Duxbury Press, 1978. Abraham S, Johnson CL, Najjar MF. Weight and height of adults 1874 years of age. Rockville, MD: National Center for Health Statistics, 1979 (Vital and health statistics: series 11; no. 211 [DHEW publication no. (PHS) 79-1659]). Johnson CL, Fulwood R, Abraham S, Byrner JD. Basic data on anthropometric measurements and angular measurements of the hip and knee joints for selected age groups, 1-74 years of age, United States, 1971-1975. Hyattsville, MD: National Center for Health Statistics, 1981 (Vital and health statistics: series II; no. 219 |DHHS publication no. (PHS) 81-1669J). Tanner JM. Growth at adolescence. Oxford: Blackwell Scientific Publications, 1972.
Received November 11, 1991 Accepted April 15, 1992
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18.
status in a healthy elderly population: Dietary and supplemental intakes. Am J Clin Nutr 1982;36:319-31. Garry PJ, Hunt WC, VanderJagt DJ, Rhyne RL. Clinical chemistry reference intervals for healthy elderly subjects. Am J Clin Nutr 1989;50:1219-30. Stoudt HW, Damon A, McFarland RA, Roberts J. Skinfold, body girths, biacromial diameter, and selected anthropometric indices of adults. Rockville, MD: National Center for Health Statistics, 1970 (Vital and health statistics: series 11; no. 35). Stoudt HW, Damon A, McFarland RA, Roberts J. Weight, height, and selected body dimensions of adults; United States 1960-1962. Rockville, MD: National Center for Health Statistics, 1965 (Vital and health statistics: series 11; no. 8). Najjar MF, Rowland M. Anthropometric reference data and prevalence of overweight. Hyattsville, MD: National Center for Health Statistics, 1987 (Vital and health statistics: series 11; no. 238 [DHEW publication no. (PHS) 87-16885]). Chumlea WC, Guo S, Kuczmarski RJ, Johnson CL, Leahy CK. Reliability for anthropometry in the hispanic health and nutrition examination survey (HHANES). Am J Clin Nutr 1990,51:902-7. Malina RM, Hamill PVV, Lemeshow S. Selected body measurements of children 6-11 years, United States. Rockville, MD: National Center for Health Statistics, 1973 (Vital and health statistics: series ll;no. 123 IDHEW publication no. (HSM) 73-1605J). Mueller WH, Malina RM. Relative reliability of circumferences and skinfolds as measures of body fat distribution. Am J Phys Anthrop 1987;72:437-9. Johnston FE, Hamill PVV, Lemeshow S. Skinfold thickness of children 6-11 years, United States. Rockville, MD: National Center for Health Statistics, 1972 (Vital and health statistics: series 11; no. 120 [DHEW publication no. (HSM) 73-1602J). Johnston FE, Hamill PVV, Lemeshow S. Skinfold thickness of youths
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Journal of Gerontology; MEDICAL SCIENCES
1992. Vol. 47, No. 6.MI97-M203
Equations for Predicting Stature in White and Black Elderly Individuals Wm. Cameron Chumlea1 and Shumei Guo1-2 'The Division of Human Biology, Department of Community Health, and 'Department of Mathematics and Statistics, Wright State University School of Medicine, Dayton, Ohio.
A SSESSING nutritional status is important to the health •**• care of the elderly in order to help determine levels of nutritional support and to monitor the effects of nutritional intervention. Anthropometric measurements are part of a nutritional assessment, but standard techniques are not totally suitable for assessing elderly persons who are handicapped or those with limited mobility (1). The accurate use of anthropometry in a nutritional assessment depends upon a subject who is able to stand, sit, or be positioned so that measurements can be taken accurately, reliably, and without difficulty (1). In many instances, elderly individuals, especially the nonambulatory and very old, are unable to assume the body position needed for a measurement, nor are they able to assist the observer by maintaining the position of a limb. In such cases, common measures are unreliable, inaccurate, or even impossible. This is especially true for stature, the measure of which is not only affected by mobility but the increased prevalence of skeletal deformities with old age. Values for stature are needed for elderly persons in order to apply equations for estimating basal energy expenditure and subsequent nutrient need and to calculate indices of nutritional status such as weight-for-stature or weight divided by stature squared. If stature cannot be measured in an elderly person, then a surrogate value must be predicted in some manner. Useful methods of predicting stature in the elderly should make use of body measurements that are actual constituents or indices of stature, and that can be collected regardless of an individual's level of mobility. Also, the accuracy of prediction is needed so that the calculated values in a clinical setting can be evaluated within known confidence limits to adjust nutritional recommendations. Equations for predicting stature from recumbent anthropometric measurements have been developed from a limited
sample of elderly persons living in Southwest Ohio (2,3). The precision of these equations in estimating stature in other samples of the elderly has been good (4,5), but the validation sample and the equations were not nationally representative. Recumbent anthropometric techniques reduce the effects of mobility problems in the elderly and are accurate, reliable, and as valid as corresponding standard measurements for assessing the nutritional status of the elderly (6-8). Monitoring the nutritional status of elderly persons or identifying those with unusual amounts of adipose or muscle tissue or weight, or in need of nutritional therapy, is important for their health (9,10). The purpose of the present study was to develop generalized equations for predicting stature for the elderly from nationally representative samples for the United States population. Nationally representative equations would reduce the sample specificity problem of prediction equations from small unrepresentative samples and increase the precision and confidence in the predicted stature for an individual. METHODS
Sample National Health Examination Survey. — The sample used to develop the predictive equations in the report was selected from elderly subjects in Cycle I of the National Health Examination Survey (NHES) conducted by the National Center for Health Statistics (NCHS) from 1960 to 1970. The target population in the NHES consisted of all noninstitutionalized, civilian residents of the continental United States (11). Briefly, a national probability sample was identified, and the individuals were interviewed and their participation requested. Those who agreed to participate came to a mobile M197
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In an anthropometric nutritional assessment, elderly individuals are frequently unable to assume the positions needed for many measurements. This is especially true for stature, which is affected by mobility and skeletal deformities, and as a result measurements may be unreliable and inaccurate. An alternative is to use a surrogate value of stature. We developed predictive equations using data from elderly subjects in Cycle I of the National Health Examination Survey (NHES). The developed equations were cross-validated using two separate independent and more contemporary samples of elderly White men and women. The possible predictor variables were knee height and buttocks-knee length in the men and knee height and age in the women. For both the men and the women, the majority of the variance in stature was accounted for by knee height. Selected equation models were cross-validated, and a single equation was recommended for each elderly group that included knee height rather than buttocks-knee length as predictor variables. This selection was based upon the performance of the equations, and also upon the practical ease of collecting the possible predictor variables. Included with the recommended equations are the RMSEs and the standard errorfor predicting stature for an individual (SEI). The successful application of the recommended equations with two recent sets of elderly persons indicates the current utility of the recommended equations in White elderly Americans.
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Fels elderly sample. —This independent sample consisted of 106 men and 130 women 65 to 91 years of age from a study at the Fels Research Institute (now the Division of Human Biology, Department of Community Health, Wright State University School of Medicine). These participants were residents at three church-affiliated institutions and a Veterans' Affairs residence center in Southwestern Ohio. These were ambulatory individuals, but physical examinations were not conducted. A more complete description of the health and nutritional status of this sample has been reported (6). Aging Process Study. — This independent sample consisted of 12 men and 190 women, 65 to 95 years of age, who were participants in the Aging Process Study (APS). This is a prospective study of nutritional status of the elderly at the University of New Mexico School of Medicine in Albuquerque. These participants can be described as a sample of well educated, health-conscious individuals who are more affluent than the average elderly person. A more complete description of the health and nutritional status of the APS has been reported (12,13). Measurements The measurements from Cycle I used in the analyses were stature, weight, sitting height, knee height, buttocks-knee length, biacromial breadth, and waist circumference. De-
scriptions of the measurement techniques have been published elsewhere (14,15). The techniques were identical or similar to methods for corresponding measurements listed in the Anthropometric Standardization Reference Manual (1) or corresponding measurements taken in the first, second, and third National Health and Nutrition Examination Surveys (NHANES) and in the Hispanic Health and Nutrition Examination Survey (16,17). Briefly, stature was measured on a specially designed stadiometer. A movable tape measure on the side of the headpiece was photographed recording the subject's stature. The measure of stature was recorded from the photograph. Sitting height was measured with a portable GPM stadiometer mounted in its base as the subject sat on a table. Waist circumference was measured at the level of the umbilicus with a steel tape measure. Biacromial breadth was measured at the corresponding lateral borders of the appropriate bony landmarks with a GPM sliding caliper. Knee height was measured with the subject sitting with the sole of the foot on the floor and the knee and ankle joints at 90° angles. The anthropometer was placed next to the lower leg, and the distance measured from the floor to the top of the thigh immediately above the condyles of the femur. Buttocksknee length was measured with the subject sitting as for the knee height measurement. A GPM sliding caliper measured the distance from the maximum protrusion of the buttocks to the lower border of the patella with the caliper held parallel to the length of the thigh and parallel to the floor (18). Other body measurements were taken in the NHES, but they were not considered in this study because they were related primarily to body fatness or to human engineering questions. The reliability for many of these measurements has been reported (18-21). In general, reliability for these data are good and compare favorably with reliability for corresponding measurements in NHANES II and Hispanic HANES (17,22). In the Fels and APS cross-validation samples, stature and knee height were measured using the same equipment and methodology (1,3). However, knee height was measured recumbently in both samples using a Mediform sliding caliper (3). Descriptive statistics and measurement reliability for the body measurements of these samples have been reported (7,23). Statistics Sampling weights for each individual were used to adjust the data to account for unequal probabilities of selection, for nonresponse and coverage errors so that all the individual data used in these analyses represented national probability estimates (24). Weighted descriptive statistics were computed for the variables in the NHES sample. Means, standard deviations, and minimum, median, and maximum values were calculated for weighted values of the variables. The weighted mean was defined as follows:
2 w,x, Xw —
i= l n
2 w, i= 1
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examination center (MEC) located in their community where all tests were conducted (11). The national probability sample for Cycle I consisted of 7,710 individuals 18.00 to 79.99 years of age. Of these subjects, 6,672 were examined in the MECs. The sample used in the present analysis consisted of individuals 60 to 79.99 years of age. This included 438 White men, 453 White women, 50 Black men, and 60 Black women. The NHES data were used because it is the only nationally representative survey that collected body measurements appropriate for predicting stature. Similar measurements have not been included in other subsequent national surveys, which precluded the use of more recent data. The NHES sample used in this report was randomly divided into validation and cross-validation groups in such a way that the number of individuals in each stratum was balanced by sex and race. The validation group was used to develop the predictive equations, and the cross-validation group was used to cross-validate the derived equations. An additional cross-validation was conducted using two separate independent and more contemporary samples of elderly White men and women. These samples were used in the cross-validation analyses because the elderly subjects in the NHES were measured almost 30 years ago. Many of these individuals would have been born during the last two decades of the 19th century. Contemporary elderly individuals at corresponding ages to those in the NHES sample were born in the second and third decades of the 20th century and thus represent a subsequent generation. The application of the prediction equations to these two groups would address any possible secular effects of the NHES sample on the equations. Similar samples of Black elderly individuals were not available.
EQUATIONS FOR PREDICTING STATURE
In this formula, Xj was the observation for the ith individual and Wj was the weight for X(. The standard deviation for the weighted mean CTW was calculated from the following formula:
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In this equation, Yf was the observed value (stature) for the ith subject in the cross-validation sample, and Y, was the corresponding predicted values obtained from the derived equations in the validation sample (25). RESULTS
Y =
+ e
In this equation, Y was a column vector of observed stature, x was the design matrix with each column containing observed values of predictor variables, b was a column vector whose elements consist of regression coefficients, and e was a column vector of random errors which was assumed to be normally distributed with a mean of 0 and variance of CT2I. The weighted least squares estimator B was calculated by the following equation: P = (XWX)-XWY The variance of (3 was calculated by the following formula: var(p) = (XWX)-'a 2 The root mean square error or RMSE was calculated by the following formula:
RMSE =
Cross-validation. — The accuracy of selected best equations from the validation groups was tested by applying these equations to the NHES cross-validation samples. A measure of the accuracy of an equation was calculated as follows:
pure error =
2 W.CY.-t,) 2 i= 1 n 2 W,
Validation. — An all-possible-subsets regression analysis was conducted to determine which variable or set of variables were the best predictors of stature. These variables were knee height, buttocks-knee length, and age. This analysis was done separately for Whites and Blacks. To determine the extent of possible age effects, the analyses were rerun, forcing in age as a predictor variable. This made no significant effect upon the parameters of the equations except in the White women. The selection of the best possible predictor variables was based upon the values of R2, the root mean square error (RMSE), and distributions of the residuals for the predictive equations from the all-possible-subsets regression. The values for R2, RMSE, and coefficient of variation (CV) for prediction equations for White and Black elderly men and women in the NHES sample are presented in Table 3. For both the men and the women, the majority of the variance in stature was accounted for by knee height. For the men, the inclusion of age made no improvement in the predictive power of the equations. The combination of knee height and buttocks-knee length as predictor variables in the men increased the R2 value, and the RMSE decreased by 0.3 to 0.4 cm. For the women, the inclusion of age with knee height also did not improve the predictive power of the equation. However, the partial F-value for age was significant (p < .001) in the White women. Buttocks-knee length in the women did little to improve the predictive ability of knee height alone. In both sexes, the combination of knee height, buttocks-knee length, and age did not improve the predictive ability of the equations over the other paired combinations, but there was a significant effect of age in the White women. Thus, the possible predictor variables were knee height and buttocks-knee length in the men and knee height and age in the women. Because differences in the parameters of the possible equations were small depending upon the combination of predictor variables, two model equations were selected from each elderly group for crossvalidation. The selected models are identified by superscripts in Table 3. Cross-validation. — These selected equation models were cross-validated by comparing the pure errors (the mean
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Validation. — Regression equations were computed using every possible combination of the predictor variables in the validation group. From these regression equations, a final set of predictor variables was selected on the basis of minimum residual mean square error. An all-possible-subsets of weighted regression procedures was adopted to select the best predictive equation. The procedure evaluates every possible combination of predictor variables. The best equations of 1 predictor, 2 predictor, and 3 predictor variables were selected on the basis of minimum root mean square errors (RMSE). A set of recommended equations was selected for general use. These equations are parsimonious and relatively accurate in predicting stature with easy-to-measure predictor variables (25). The regression equation for predicting stature was as follows:
Descriptive statistics for the weighted values of the predictor variables for the total NHES sample are presented by race and sex in Table 1. The validation and cross-validation groups were balanced with regard to age and race, and this stratification resulted in the same number of observations in each group above and below the median age. There were no statistically significant race- or sex-specific differences between mean values for corresponding measurements in the validation and cross-validation groups. Descriptive statistics for the values of the predictor variables for the Fels and APS samples are presented by sex in Table 2.
CHUMLEA AND GUO
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Table 1. Descriptive Statistics for Weighted Values of Elderly Men and Women in the NHES Sample (Validation and Cross-Validation Groups Combined) Men
Women Black (n - 5 0 )
White (#i = 438)
White (/; = 453)
Black (n = 60)
Variable
Mean
SO
Mean
SD
Mean
SD
Mean
SD
Age (years) Stature (cm) Weight (kg) Biacromial breadth (cm) Waist circum. (cm) Sitting height (cm) Knee height (cm) Buttocks-knee length (cm)
68.1 170.0 72.9 39.6 89.2 90.7 53.2 59.0
5.0 7.0 12.7 2.1 11.4 3.6 2.7 2.9
68.5 169.7 67.0 39.8 85.5 87.9 54.0 60.0
14.7 6.2 12.2 2.2 10.9 3.6 3.0 2.7
68.1 156.8 66.9 35.3 76.5 84.8 49.0 56.5
5.0 6.8 12.9 1.9 11.7 3.6 2.6 2.9
67.7 156.8 70.6 36.3 79.9 82.3 50.3 58.6
5.2 7.1 16.7 1.8 13.3 3.8 3.0 3.2
Men
Women APS
Fels
Fels
APS
Variable
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Stature (cm) Weight (kg) Knee height (cm)
169.5 73.2 53.3
6.9 13.4 2.7
163.6 57.8 49.1
10.9 10.2 3.4
156.3 62.3 49.4
6.0 12.0 2.3
164.3 67.5 50.6
10.1 12.5 3.7
Table 3. Best Possible Prediction Equations for Stature in the Validation Groups White Women
White Men Predictor Variables *Knee height tKnee height, buttocksknee length tKnee height/age Knee height/buttocksknee length/age
2
2
Black Men CV
Rl
RMSE
CV
0.51
4.73
2.80
0.62
4.28
2.74
2.65 2.63
0.69 0.51
3.78 4.80
2.24 2.84
0.62 0.62
4.33 4.35
2.78 2.79
2.61
0.72
3.67
2.17
0.62
4.41
2.82
CV
R
0.68
4.06
2.39
2.38 2.42
0.64 0.65
4.15 4.13
2.33
0.65
4.09
RMSE
CV
R
0.68
4.12
2.42
0.70 0.68
3.99 4.11
0.70
3.97
Black Women
RMSE
RMSE
R
2
*Model 1, all groups. tModel 2, White Men and Black Men only. tModel 2, White Women and Black Women only.
of the squared differences of the observed and predicted values) in the NHES cross-validation groups with the RMSEs for the corresponding model equations in the validation groups. These comparisons are presented in Table 4. The performance of the equation models in the NHES crossvalidation groups was very good. Except for the White women, the equation models predicted slightly better or the errors were smaller in the NHES cross-validation groups than in the NHES validation groups. In the White women, the predictive errors for the cross-validation group were slightly larger than for the validation group. These results indicate that in this nationally representative group of elderly subjects 60 to 79 years of age, the developed best equations have the same predictive power as in the sample from which the equations were developed. This should considerably reduce the sample specificity problem in the use of these equations within the specified age range. Since the selected equations performed so well in the
Table 4. Measures of Performance of the Selected Equations for Stature in the Validation and Cross-Validation Groups RMSE*
Pure Error
White Men Model 1 Model 2
4.12 3.99
3.62 3.41
Black Men Model I Model 2
4.73 3.78
3.20 3.17
White Women Model 1 Model 2
4.06 4.13
5.36 4.48
Black Women Model 1 Model 2
4.28 4.35
3.82 3.83
*RMSE - root mean square error.
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Table 2. Descriptive Statistics for Values of Elderly Men and Women in the Fels Elderly and Aging Process Study (APS) Samples
EQUATIONS
FOR PREDICTING
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STATURE
Table 5. Recommended Equations for Predicting Stature in Elderly Men and Women 60 to 80 Years of Age and Cross-Validation
Equation: Stature =
RMSE SEI Pure error Fels Men Fels Women APS Men APS Women
White Men
White Women
Black Men
Black Women
59.01 + 2.08 knee height
95.79 + 1.37 knee height
58.72 + 1.96 knee height
0.68 3.91 cm 7.84 cm
75.00 + 1 . 9 1 knee height — 0.17 age 0.59 4.40 cm 8.82 cm
0.51 4.18cm 8.44 cm
0.70 4.06 cm 8.26 cm
3.93 cm — 3.32 cm —
— 3.48 cm — —
— — — —
— — — —
DISCUSSION
Where comparisons are possible, these NHES data are similar to age-, race-, or sex-specific values for corresponding measurements in data from the NHANES I and II (16,26,27). The weighting of the NHES data converted the individual values to values that took into account the proportion that the individual represented of the total population of all White or Black individuals at the same ages in the United States at the time the data were collected. This changes the data set from a collection of individuals to a sample that is representative of the United States population (24). The best equations for predicting stature in the NHES elderly are presented in Table 3. The selected predictor variables were the same for Whites and Blacks: knee height and buttocks-knee length and age. Knee height and buttocksknee length account for almost the entire length of the legs where the majority of the variation in adult stature between individuals and the sexes is reported to occur (28). The relationship of stature to knee height and buttocks-knee length was different statistically between these elderly men and women (Table 3). In the men, stature was predicted well from knee height alone, but the inclusion of buttocks-knee
length made a difference in the values of the R2 and RMSEs. In the women, the inclusion of buttocks-knee length had no effect upon the precision of the equation, but the inclusion of age had an effect for White women only. However, the coefficients for age were negative for both White and Black women. This negative relationship with age in the women and the absence of an age effect in the men possibly reflects the greater effect of the aging process on the skeleton in women than men or the effects of selective survival in the women. These findings are similar to results reported previously for equations to predict stature in the elderly (2). In the earlier prediction equations, knee height was the best predictor of stature for elderly White men, but buttocks-knee length was not measured. In the elderly White women studied earlier, knee height and age were the selected variables, and the coefficient for age was similar to the present value (Table 3). The decision was made to select a single recommended equation for predicting stature in each elderly group. This selection was based upon the performance of the selected equation models, and also upon consideration of the practical ease of collecting the possible predictor variables. A predictive equation developed in a research setting may have excellent performance in cross-validation, but if the predictor variables used in the equation are difficult to measure, this will increase their unreliability and inaccuracy. As a result, the performance of the equation in a practical setting for an individual or a group will deteriorate to an unknown degree. Knee height is easy to measure in either a sitting or a recumbent manner in almost all elderly persons regardless of mobility status. Also, current reliability data are available for knee height as reference for researchers and clinicians. This is not the case for buttocks-knee length. Therefore, the decision was made to recommend equation models that included knee height rather than buttocks-knee length as a predictor variable. Included with the recommended equations (Table 5) are the RMSEs and the standard error for predicting stature for an individual (SEI). The RMSE is used when the equation is applied to groups of individuals. Plus or minus twice the RMSE produces the 95% confidence limits for the prediction of stature for the group from which the equation was developed. For an independent group of individuals to which an equation is applied, there is a 95% chance that ± twice the
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cross-validation (Table 4), it was possible to combine the NHES validation and cross-validation data sets and develop a final set of recommended equations. These equations are presented in Table 5 with the results of the cross-validation of the recommended equations for Whites in the Fels and APS samples. For the Fels and APS cross-validation groups, the pure errors of the recommended equations (Table 5) are similar to the corresponding pure errors of the NHES crossvalidation groups (Table 4). For the Fels men, the value of the pure error is the same as the RMSE of the validation groups, and for the Fels women the pure error is smaller than the RMSE and pure error of both NHES samples. For the APS men, the pure error is smaller than the RMSE and pure errors of the other comparison groups. However, the pure error for the APS women is one-third larger than the RMSE and pure errors of the other comparison groups. Crossvalidations in these two recent samples indicate that for elderly men the recommended equations have the same predictive power as for the validation sample of NHES men. The same is true for the Fels women, but the predictive power is poorer for the APS elderly women than for the NHES women.
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This report has presented the development of predictive equations for stature for White and Black elderly Americans. The equations were developed from nationally representative data, and the measurements were collected from ambulatory elderly persons using standard techniques. The use of recumbent anthropometric measurements in these equations should not expand the errors of prediction over those presented because of the small measurement errors for recumbent knee-height (7). However, the heterogeneity of the
conditions afflicting elderly persons will contribute to increasing the errors of prediction. Also, because of the very limited sample of Black elderly persons used to develop the equations, caution should be taken in interpreting or applying these results to other Black elderly Americans. Because of the small sample sizes, the recommended equations for Blacks will be less reliable for more individuals than the equations for the Whites. To some degree, the data and recommended equations are out-of-date because the data are about 25 years old, but there are no other data sets that contain the required variables. In the National Health and Nutrition Examination Studies I and II (NHANES I and II), the body measurements were related to growth and nutritional status. Knee-height is being collected from elderly subjects in NHANES III, but these data will not be available until late in the 1990s. However, the successful application of the recommended equations with two contemporary sets of elderly persons does indicate the current utility of the recommended equations in White elderly Americans. ACKNOWLEDGMENTS
This work was generously supported by Ross Laboratories, Columbus, Ohio, and Grants HD-12252, HD-27063, and AG-02049 from the National Institutes of Health. The authors appreciate the kind assistance of Dr. Philip J. Garry for allowing the use of data from the Aging Process Study, University of New Mexico, School of Medicine, Albuquerque, New Mexico. Address correspondence to Dr. Wm. Cameron Chumlea, Division of Human Biology, Wright State University, School of Medicine, 1005 Xcnia Avenue, Yellow Springs, OH 45387. REFERENCES
1. Lohman TG, Roche AF, Martorell R. eds. Anthropometric standardization reference manual. Champaign, IL: Human Kinetics Books, 1988. 2. Chumlea WC, Roche AF, Steinbaugh ML. Estimation of stature from knee height for persons 60 to 90 years of age. J Am Geriatr Soc 1985;33:116-20. 3. Chumlea WC, Roche AF, Mukherjee D. Nutritional assessment in the elderly through anthropometry. 2nd ed. Columbus, OH: Ross Laboratories, 1987. 4. Muncie HL, Sobal J, Hoopes JM, Tenney JH, Warren JW. A practical method of estimating stature of bedridden female nursing home patients. J Am Geriatr Soc 1987;35:285-9. 5. Murphy S, Cherot EK, Clement L, West KP. Measurement of knee height in frail, elderly nursing home residents. Am J Clin Nutr 1991 ;54:611-2. 6. Chumlea WC, Steinbaugh ML, Roche AF, Gopalaswamy N. Nutritional anthropometric assessment in elderly persons 65 to 90 years of age. J Nutr Elderly 1985;4:39-51. 7. Chumlea WC, Roche AF, Steinbaugh ML, Mukherjee D. Errors of measurement for methods of recumbent nutritional anthropometry in the elderly. J Nutr Elderly 1985;5:3-11. 8. Chumlea WC, Roche AF, Mukherjee D. Some anthropometric indices of body composition for elderly adults. J Gerontol 1986;41:36-9. 9. Mitchell CO, Lipschitz DA. The effects of age and sex on the routinely used measurements to assess the nutritional status of hospitalized patients. Am J Clin Nutr 1982;36:340-9. 10. Fischer JE. Nutritional assessment before surgery. Am J Clin Nutr 1982;35:1128-31. 11. Gordon T, Miller HW. Cycle I of the health examination survey sample and response. Rockville, MD: National Center for Health Statistics, 1964 (Vital and health statistics: series 11; no. 1). 12. Garry PJ, Goodwin JS, Hunt WC, Hooper EM, Leonard AG. Nutrition
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RMSE will cover the true mean stature of that group (25). For an independent group, the closer the value of the pure error is to the corresponding RMSE is an indication of the confidence in the predicted statures for the independent group. However, the closeness of predicted statures of an independent group to the respective true values will also depend upon how similar are the mean and distribution of knee height to the corresponding mean and distribution of knee height of the group from which the equation was derived. This association was easily demonstrated in the application of the recommended equations to the Fels and APS samples (Table 5). The pure errors for the Fels and APS men were very similar to the corresponding RMSE value. The pure error for the Fels women was smaller than the corresponding RMSE, but the pure error for the APS women was about 2.1 cm larger. The small pure errors for the Fels men and women were because their means and standard deviations for knee height and stature were very similar to corresponding values for knee height and stature in the NHES sample (Tables 1 and 2). In the APS sample, the pure error for the men was smaller than that of the RMSE of the NHES sample as were the means for knee height and the stature, but the corresponding standard deviations of the APS men were larger than those of the NHES sample. In addition, the APS sample of men consisted of only 12 individuals, which affected the results. For the APS women, however, the pure error was larger than the RMSE of the NHES sample as was their mean knee height, stature, and corresponding standard deviations. The application of the recommended equations to the Fels and APS samples indicates how characteristics of a sample can affect the outcome of the predictions. The clinical importance of these recommended equations (Table 5) appears in the application to a single individual. The SEl provides the distributions of the errors that can be expected in applying these equations to estimate the stature of an elderly man or woman if the measured knee height was equal to the respective mean knee height in Table 1. Plus or minus twice the SEl of the predicted stature provides the confidence limits for an individual which have a 95% chance including the individual's true stature. An individual's predicted stature will differ from the true stature as a function of the difference between the measured knee height and the corresponding mean knee height in Table 1. If the individual's knee height is close to the mean knee height of the group from which the equation was derived, then the accuracy of the prediction is greater. Therefore, in the clinical application of these equations one should consider the individual's knee height, the predicted stature, and the SEL These factors should be used in any decision to adjust a predicted stature value to fine tune its clinical use.
EQUATIONS FOR PREDICTING STATURE
13. 14.
15.
16.
17.
19.
20.
21.
22. 23.
24.
25. 26.
27.
28.
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Received November 11, 1991 Accepted April 15, 1992
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