The present study was carried out to verify the cross validity of two of the most widely used anthropometric equations for estimating AMM in the elderly, the equations of Baumgartner et al.
[33] and Tankó et al.
[37]. As it was not possible to validate the equations observed, new and simple regression equation models were developed and validated using anthropometric measurements to estimate AMM in a sample of apparently healthy and functionally independent elderly women using AMM_{DXA} as criterion measure.

Although the equations of Baumgartner et al.
[33] and Tankó et al.
[37] presented high correlation with AMM_{DXA}, respectively: R = 0.84 and R = 0.80, they significantly differed from the criterion method (p <0.001 and p = 0.001, respectively). Therefore, in this study, 10 possible anthropometric equations for estimating AMM_{DXA} were developed. Among them, three stood out for not showing any significant difference with the criterion method (p between 0.056 and 0.158) due to the high correlation (R between 0.83 and 0.86) and concordance (ICC between 0.90 and 0.91 and concordance limits from −2.93 to 2.33 kg) with AMM_{DXA}.

Baumgartner et al.
[33] found sarcopenia prevalence in New Mexico. To this end, the authors developed an anthropometric equation to estimate AMM using AMM_{DXA} as criterion measure in a sub-sample of 199 physically active elderly subjects of both genders. The subjects were divided into two groups: estimation group (GE = 149 subjects) and validation group (GV = 50 subjects).

In that study, AMM predicted by the proposed equation, did not differ statistically from values measured by DXA, showing high correlation (R^{2} = 0.86) and small standard error of estimate (1.72 kg) between techniques. However, in this study, AMM verified by equation of Baumgartner et al.
[33] (AMM_{BAUM}), despite showing high correlation (R^{2} = 0.71) and adequate standard error of estimate (1.32 kg), differed statistically from criterion measure results: AMM_{DXA} (p <0.001). Moreover, the constant error of −7.87 kg indicated a strong tendency toward underestimation of AMM_{DXA} values and a quite high total error (7.98 kg), thus invalidating, in samples with characteristics similar to the present study (Table 03), the use of the proposed equation.

Tankó et al.
[37], using a sample composed of 754 Danish women (17 to 85 years), verified which variables would best explain the variations of AMM and the upper limb muscle mass, estimated by DXA.

Among several independent variables considered in that study, age, BM and ST significantly contributed to variations of muscle parameter, being responsible for explaining 58% of the variance in AMM_{DXA} (R^{2} = 0.58), with moderate correlation coefficient (R = 0.76) and standard error of estimate of 1.70 kg. When the cross-validation of this study was performed (Table 03), AMM verified by the equation of Tankó et al.
[37] (AMM_{TANK}) showed correlation (R = 0.80) and determination coefficients (R^{2} = 0.65) higher than those observed in the original study sample, with low standard error of estimate, constant error and total error: 1.46 kg, -0.52 kg and 1.53 kg respectively. However, when compared, AMM_{DXA} and AMM_{TANK} showed statistically significant differences (p = 0.001). Therefore, the second equation did not meet the validation criteria adopted.

The statistical differences found between methods may be related to morphological differences observed in samples from the three studies: this study, the study of Baumgartner et al.
[33] and that of Tankó et al.
[37]. Baumgartner et al.
[33], for example, did not characterize the samples of both groups: the development and validation of the equation, describing only the mean values of the overall sample composed of 833 individuals. Moreover, Tankó et al.
[37] presented the physical characteristics of the subjects, divided into six age groups, where mean and standard deviation of age ranged from 25.7 ± 2.5 to 75.2 ± 3.4, BM from 62.9 ± 7.7 to 67.6 ± 10.01, ST from 1.59 ± 0.06 to 1.68 ± 0.06 and AMM from 19.4 ± 2.3 to 15.7 ± 2.4; however, such a comparison can be problematic, since the equation used to estimate AMM was developed using the total study sample, where, among the 754 participants, only 152 subjects were older than 60 years.

Due to considerable differences between the populations assessed, it is difficult to make valid comparisons between results found in the three studies. However, it appears that the AMM values measured in the present study (15.16 ± 2.43) were close to those observed by Baumgartner et al.
[33] in their total sample (14.2 ± 1.9) and among the age groups 60–69 and > 70 years of subjects from the study of Tankó et al.
[37] (16.5 ± 2.13 and 15.7 ± 2.4).

In recent research conducted in the city of São Paulo (southeastern Brazil), Gobbo et al.
[52] found and described normative values for total muscle mass AMM and total and appendicular muscle mass indexes stratified by sex and age groups. To achieve their goals, the authors used the equation of Baumgartner et al.
[33] to estimate AMM. However, the use of this equation was not preceded by cross-validation analysis, which very likely may raise doubts about the possible inadequacies of inferences performed in that study. In fact, so far, other Brazilian studies that have verified the validity of anthropometric equations proposed by Baumgartner et al.
[33] and Tankó et al.
[37] were not found.

In the present study, with the aid of multiple linear regression analyses, 10 models of anthropometric equations were developed (Table 03). Among these equations, six did not differ from the criterion method (Table 04).

Equations E2, E3 and E6 explained from 69% to 74% variations in AMM_{DXA} (Figure
1), reaching all validation criteria used. These models showed high correlation coefficients with the criterion method, ranging from 0.83 to 0.86, similar to the study of Baumgartner et al.
[33], and higher than correlation found by Tanko et al.
[37]. Moreover, the prediction errors observed in this study were lower than those observed in New Mexico and Denmark.

As for the analysis of concordance, both the ICC as the Bland and Altman analysis showed satisfactory values, indicating the possibility of using the equations developed and validated in this study. The ICC showed high values (E2 = 0.90, E3 = 0.90 and E6 = 0.91) showing a strong concordance with the DXA criterion method. The limits of the confidence intervals observed in valid models: E2 (2.42, -3.26 kg) E3 (−3.30, 2.40 kg) and E6 (−2.93, 2.33 kg) illustrated in Figure
2, were lower than those observed by Baumgartner et al.
[33] (−5.1, 4.2 kg). Tankó et al.
[37] in turn, did not use any statistical tool to verify the agreement.

The sample power (1-β errprob) calculated by the *post hoc* test in the three equations also appeared to be appropriate by adopting a confidence level of 95% for the sample size used. Thus, the probability of not making a type II error was 0.91, 0.88, and 0.85 for E2, E3 and E6, respectively.

Despite the limitations of this study, for example, the fact that the elderly women that composed the sampled showed homogeneity in relation to anthropometric characteristics, habits and physical skills, the three equations that showed the best conditions for use were therefore selected: E2, E3 and E6, because besides showing high validity, used variables of easy access. Characteristics necessary for the development of strategies to maintain or improve health, independence and quality of life in subjects with sarcopenia.

However, each model has its own advantages. For example, E2 has simple measures such as BM, BMI and the appendicular skeleton perimeter (PANTd) as independent variables, characteristic necessary in some situations of research and / or evaluation of body composition in non-laboratory conditions with the purpose of enabling a lower exposure of body parts and minimizing measurement errors due to the use of inadequate clothing; E3 uses BM, BMI, PANTd and one skinfold thickness measure (TS), E6 has the advantage of considering age as independent variable, This can be useful when evaluating AMM in a sample of elderly individuals with larger age ranges.

Moreover, the explanatory variables of AMM_{DXA} (BM, BMI, age, DCCO, PANTd, PQUAD) are easily mensured. Thus, as Baumgartner et al.
[33], PQUAD was an explanatory variable of AMM_{DXA}, and we can assume that this fact is related to the volume of muscles that make up the hip joint and responsible for the movements of the lower limbs (flexors, extensors, adductors, abductors and medial and lateral rotators of the hip).

The use of valid equations in combination with simple anthropometric models to assess BF% in older women is suggested as a strategy to identify subjects with sarcopenia, obesity and sarcopenic obesity, caused by the accumulation of intramuscular fat.