Validation of anthropometric equations for predicting body mass and height in older women

Abstract To investigate the cross-validity of two equations widely used in national research to predict body mass and height in older Brazilians. Additionally, the importance of possible differences between observed and predicted BMI will be investigated with the help of equations. BM and HEI were measured using mechanical scales and portable stadiometers in a sample of 200 older women (66.6 ± 5.43 years) living in Maceió / AL - Brazil. To verify the validity of equations, the following variables were used: Student's t-test, constant error (CE), total error (TE) and standard error of estimation (SEE). To verify agreement between actual and predicted values, the Bland-Altman test was used. The comparison between BM and HEI values obtained through equations and those verified in measurements showed statistically significant differences (p <0.05). CE between predicted and measured values, TE of tested equations, as well as SEE for the prediction of variables: BM (1.66; 0.11 and 6.33), HEI (-0.02; 0.02 and 0.10) and BMI (1.47; 0.10 and 3.24) allowed determining relative values very close to actual ones (2.6%, 1.31% and 5.3% for BM, HEI and BMI respectively); however, values were not statistically significant. The equations analyzed should not be used in a general way for the population of older Brazilian women with characteristics similar to those analyzed in this study. Therefore, further studies should be carried out with the objective of constructing specific equations for the population of older women and hospitalized patients, especially the most fragile ones.


INTRODUCTION
In 2018, the Brazilian population was estimated at 207.8 million people, including 21,872 million, the equivalent of 10.5%, aged 65 years and over, which indicates that the Brazilian elderly population increased by 6% 1 .
Given such change in the demographic profile, the concern of society with the health of the elderly population has increased, especially regarding problems related to morphological (body composition) and physiological changes, falls, especially nutritional deficits that may compromise the health and well-being of this age group 2 . Among previously described factors, nutritional status (NS) can be considered a determining variable for successful longevity 3 ; so, it has been the subject of interest to the scientific community.
NS evaluation, in addition to being important for assessing the nutritional conditions of older adults, also helps professionals during nutritional and exercise prescription for people of all age groups, being part of health maintenance or improvement strategies 4-6, , and drug dosage [7][8][9] .
Several anthropometric measurements, such as body mass (BM), height (HEI), perimeters, skinfolds, bone lengths and diameters, among others, have been widely used for NS evaluation in epidemiological studies with the objective of prescribing diets, exercise or medication dosage 10,11 . Regarding NS evaluation, Body Mass Index (BMI) obtained through the ratio between body mass and square height (BMI = BM / HEI²) and expressed in kg/m², is the measure most widely used in epidemiological studies 3 . However, under some conditions, such as lower limb amputations, the presence of disabling diseases, wheelchair use and bedridden patients, such measures are often impracticable or impossible.
Given the above, regression equations using different anthropometric measures as predictive variables, such as bone length, wingspan or half-wingspan and foot length have been often used, which are capable of predicting BM and HEI in the elderly population. In this context, since they use easy and accessible measurements (knee height (KH), triceps (TSF) and subscapular (SSF) skinfolds and brachial (PBR) and leg perimeters (PPER), two equations, originally proposed by Chumlea et al. 10,11 , have been used in scientific studies to predict BM and HEI.
Interestingly, Monteiro et al. 12 reported that although they were developed using a sample of Americans aged 65-104 years, without considering the influences of possible intervening variables such as ethnicity, genetics, cultural aspects and nutritional habits, among others, such equations have been widely used in Brazil and worldwide.
In addition to being scarce, studies investigating the validity of such equations in samples of Brazilian older women are inconclusive 13 . The above, associated with the approximation of values, due to possible HEI and BM errors, particularly in bedridden subjects, may lead to errors in dietary and exercise prescriptions, as well as in therapeutic planning 4 .
This study was conducted with the objective of evaluating the cross-val-idation of two equations 10,11 widely used in national and international nutritional studies to predict BM and HEI in older women. Additionally, it was also intended to evaluate the importance of differences caused by the use of equations for BMI calculation.

METHODS
To compose the sample, 200 volunteers with minimum age of 60 years (60-86 years, 66.60 ± 5.43 years) were conveniently selected from a population of 800 women, participants of leisure physical activity programs offered by various institutions in the city of Maceió, who were functionally independent and without diagnosis of bone diseases, amputations or recent fractures, among other diseases that could interfere with performance in tests or that could be aggravated by the participation in the study. The two equations evaluated proposed by Chumlea et al. 10,11 , are shown below: where: KH = knee height, PBR = arm perimeter, PPER = leg perimeter, SSF = subscapular skinfold.
All anthropometric measurements were performed according to recommendations proposed by Lohman et al. 14 .
Normality of distribution and homogeneity of data variances were respectively evaluated with the aid of Kolmogorov-Smirnov and Levene tests. To characterize the sample, central tendency measure (arithmetic mean) and dispersion measure (standard deviation) were used; amplitude was verified by the difference between maximum (MV) and minimum values (mv) for each variable.
To verify the accuracy of Chumlea's equations based on cross-validation, paired student t, total error (TE), constant error (CE) and standard error of estimation (SEE) statistical tests were used. Additionally, the Bland-Altman test was used to evaluate the agreement between measured values and those estimated by equations proposed by Chumlea et al. 10,11 . For all tests, significance level of p≤0.05 was adopted.
All study participants signed the free and informed consent form in accordance with recommendations of Resolution 466/12 of the National Health Council on research involving human subjects and approved by the ethics committee of the Federal University of Alagoas under protocol No. 23065.020769 / 2009 -30.

RESULTS
Values presented by the group of participants for age, BM, HEI and knee height (KH) measures, as well as mean values obtained by prediction equations can be observed in table 1. To verify the predictive power of Chumlea's equations, cross-validation was performed using the following procedures, suggested by Lohman 15 : 1) comparison test between means (paired t-test) -observed means should not differ statistically; 2) calculation of the standard error of estimation (SEE) -aiming to indicate the expected margin of error in a prediction; 3) constant error (CE), representing differences between estimated and measured values; and 4) total error (TE) -indicating the size of the error associated with the number of subjects evaluated. Results can be seen in table 2.

DISCUSSION
This study aimed to identify the cross-validity of two prediction equations proposed by Chumlea et al. 10,11 to estimate BM and HEI in Brazilian older adults, since such equations are not only pioneer 16 , but also the most accepted and used in Brazil and in most western countries 9 .
The proposed equations use knee height as one of the main alternatives, justified by the fact that it does not change with advancing age. Additionally, it is discussed how possible differences between the two measures could affect BMI results, since this measure is the most used in epidemiological studies investigating NS.
Objectively, the observed results showed significant differences (p <0.001) between actual and predicted measurements for all anthropometric variables, except for BM. These results overestimate measured values by 1.66 kg for BM and 0.02 cm for HEI. As a result of these differences, BMI was also overestimated by 1.47 kg/m².
Standard error values observed were low for HEI (SEE = 0.10 cm) and BMI (SEE = 3.34) although they were high for BM (SEE = 6.33 kg), according to Lohman 16 , who established cutoff point for SEE of ≤3.5. It is important to highlight that in relation to SEE, the proposed cutoff point is appropriate for equations developed with the use of skinfolds among independent variables, which reinforces the inadequacy of formulas to predict BM and HEI proposed by Chumlea, as they present SEE above the proposed cutoff point.
The results found differ from other studies, such as Closs et al. 17 , which showed that knee height may be a reliable alternative measure in the nutritional assessment of older adults. Using sample composed of 186 individuals (74.3 ± 7.1 years), the author found positive correlation between measured height and height estimated by Chumlea's equation, although the predicted result overestimated the actual measurement by 3 cm. Likewise, Muncie et al. 18 evaluated the validity of the Chumlea's equation for predicting HEI in a sample of 19 hospitalized white and black older women (78 ± 6 years) and although it was observed that predicted results underestimated actual results by about 4cm, the results pointed out that the Chumlea's equation presented good predictive value, showing no statistical differences in relation to actual height. In turn, our study showed underestimation much closer to the actual value (0.02cm), but the results showed significant statistical differences. However, it is necessary to consider that, regarding the height variable, prediction errors found in studies by Closs et al. 17 and Muncie et al. 18 and in our study are within cutoff point proposed by Beghetto et al. 19 , which considers 5 cm an acceptable error margin.
On the other hand, Myers et al. 20 investigated the suitability of the same HEI prediction equation used in our study in 16 men (72 ± 7.4 years) and 16 women (72 ± 8.7 years) of Japanese descent and found that the equation overestimated HEI for women by 1.5 (± 0.64cm), which results were not statistically significant. Although values are very close to those found in this study, ethnic and age differences between samples, as well as the quite different physical conditions between samples seem to explain the significant differences found.
Similarly, Berger et al. 8 using 250 subjects aged 16-89 years (61.4 ± 15.2 years), tested the validity of the Chumlea's equation 11 for HEI and found significant differences when compared to direct measurements, overestimating actual values by five and seven centimeters. It is noteworthy that the age groups used in samples were very different and in addition to not reporting the ethnicity of subjects, individuals were physically very fragile, which may explain differences found, since the long time required for measurements, as well as the need for great effort and help in obtaining them can lead to significant measurement errors 21 .
A study by Rabito et al. 7 conducted on hospitalized Brazilians of both sexes (49 ± 17 years) tested some equations proposed by Chumlea for HEI and BM and among them those used in our study, which showed statistically significant differences (p> 0.05). For both HEI and BM, the distinct ethnic characteristics between samples, according to the author, may have been responsible for differences found, although in our study, also with Brazilians (not hospitalized), measured and estimated values were closer, contrary to the justification of that study. It is important to highlight that the ethnicity factor, according to Freire 22 , should not be considered in Brazil, as its intense miscegenation makes it difficult to establish any racial pattern with minimal security.
Oliveira and Filho 4 validated Chumlea et al. 10,11 equations for the prediction of BM and HEI in a sample of 30 physically active women (66.6 ± 6.68 years) from the state of Paraíba, northeastern Brazil. Unlike our results, the authors found no significant difference between measured and estimated BM and HEI, although HEI and BM were both underestimated (2.38 cm and 1.92 kg respectively). However, according to Filho 23 , the small sample (n = 30) and the large data dispersion (evidenced by the high standard deviation) may contribute to estimation errors such as those found in the above study. Despite the clear validation, the authors only verified differences between averages of actual and predicted values using the t-test, which for many authors, is insufficient to validate any prediction method. Similarly, Galisa and Pustiglione 24 validated the Chumlea's equation for HEI in 50 hospitalized Brazilian women, demonstrating strong correlation between actual and estimated measurements. In that study, the sample size may have significantly contributed to results found.
According to Chumlea et al. 25 , the fact that HEI was significantly overestimated seems to be somewhat predicted, and therefore height estimates should be used primarily over direct measurements, since directly measured HEI does not reflect the exact HEI of older adults undergoing physical changes as a result of advancing age. Sampaio et al. 26 reinforces this statement arguing that estimated HEI seems to be more compatible with the height of the individual in adulthood. However, one of the reasons that led us to question the validity of this equation was that some studies, contrary to statements above, found HEI underestimation 27 .
With regard to body mass, Bernal-Orozco et al. 9 were unable to validate the Chumlea et al. 10 equation in a sample of 95 Mexican older women. In that study, values obtained compared to directly measured BM showed differences of -3.7 and -6.6 Kg, underestimating values, similarly to our results. It is important to note that the sample of this study was composed of hospitalized and / or institutionalized older women, which may have influenced BM underestimation, since Chumlea's equations were obtained from physically active older adults. In a study with 209 adult and older adult patients of both sexes from the city of Fortaleza, Sampaio et al. 26 demonstrated that the equations proposed by Chumlea showed good correlation with direct measurements, both in adults and older adults, although with differences in averages obtained, underestimating BM by 1.34 kg, which result are very close to those of this study.
Similarly, a study conducted with a population of hospitalized older adults (> 65 years) of both sexes in Barcelona-Spain 27 , whose ethnicity was not reported, tested the validity of Chumlea's equations for BM, and although finding statistically significant correlations between actual and estimated weight, demonstrated that Chumlea's equations underestimated the actual values of all variables analyzed (p <0.001). The study reinforced the need for the development of specific equations for the estimation of variables analyzed.
In hospitalized or institutionalized older patients, BM tends to be underestimated, especially in women, since in this age group, there is a decline in lean body mass, as well as an inversion in body fat distribution from limbs to the abdominal region, influencing estimated weight validity, since these formulas use arm and calf circumference and subscapular skinfold, and in obese individuals, these errors seem to be greater 28 .
In fact, variations in BM values may reflect relevant nutritional imbalances and may characterize fragility or adverse health effects such as disease aggravation, hospitalization and death 6 . Inadequate BM estimates may lead to the use of drug and diet therapies that do not meet actual individual or collective needs. In physical exercise programs for the elderly population, reliable BM and HEI data are required for adequate and individualized prescription 4 . Therefore, BM is an important tool for the early identification of older individuals at nutritional risk, thus improving the quality of care 9 . In this sense, other studies conducted to verify the applicability of Chumlea's equations in a population of hospitalized / institutionalized older adults in Brazil 6,15,28 could not confirm the validity of these equations.
Consequently, prediction errors in HEI and BM measurements generate inaccuracy in BMI, leading to possible calculation errors for nutritional supply with consequent impairment in the recovery of hospitalized older patients 27 . Therefore, its use is controversial, especially in the elderly, due to the decrease in height, adipose tissue accumulation, reduction in muscle mass and in the amount of body water 3 .
Our results demonstrate BMI underestimation (1.47kg / m²) when predicted and overestimated HEI and predicted and underestimated BM were used. Similarly, Fogal et al. 16 found BMI underestimation in older women (0.9 kg / m²) when overestimated EST was used. The same underestimation was found by Salgado et al. 27 using underestimated HEI and BM to calculate BMI. Similar BMI underestimation results were found in other studies 17,26 . It is important to note that the equations proposed by Chumlea considered in this study were developed from physically active older adults, which can maximize HEI overestimation in less healthy individuals and consequent underestimate BMI; however, considering more homogeneous and specific samples of each population avoids major nutritional assessment errors while promoting health gains.
The divergent results found between above studies and our study allow us observing that the aging process acts individually in people of different ethnicities 5 , also considering possible anatomical differences. Considering that both HEI and BM are important variables for assessing nutritional status and, especially drug dosing, specific prediction equations for these measures should be developed for older adults, especially Brazilians, taking into account gender, age and ethnic miscegenation. It is equally important that predictive models should present partial significance of variables, lower standard error of estimate (SEE), higher multiple correlation coefficient (r²), model practicality and fewer independent variables 16 .
From the statistical point of view, the fact that studies did not analyze the standard error of estimation established by Lohman 15 as one of the main validation techniques of new equations may explain the different results found in the main studies. Moreover, differences in ethnicities, age groups, cultural aspects and physical conditions verified in the different studies may contribute to the discrepancy found between actual and estimated measurements.
Studies using anthropometric measurements should be interpreted with caution. According to Sullivan et al. 28 , to avoid erroneous conclusions, the reliability of the measurement technique should be considered, even when using experienced evaluators, since reproducibility varies considerably, being able to transfer to prediction equations measurement errors that can theoretically be sources of prediction errors. Careful attention should be paid to measurement procedures; otherwise, the results obtained could be totally useless for analysis purposes. This becomes relevant, since many validation studies do not declare the reproducibility of anthropometric measurements used 29,30 .

CONCLUSION
The analyzed equations could not be used in a general way for the Brazilian elderly population, at least with regard subjects with characteristics similar to those of this study. In this sense, further studies should be carried out with the objective of constructing specific equations capable of predicting valid BM, HEI and BMI results for the hospitalized elderly Brazilian population, especially the most fragile ones.