1. Introduction

The global population has gone through a rapid aging process (^{United Nations [UN], 2020}). Although the advancement of chronological age is not itself a cause of decline in functionality, and robustness is an increasingly frequent concept in gerontology (^{Maia et al., 2020}), older adults may present a series of physiological changes, among which changes in muscle tissues involving different mechanisms (^{Lima et al., 2019}). There is a muscle loss that might occur both in quantity and quality, with decreased strength and risk of impairment of functionality (^{Cruz-Jentoft et al., 2019}).

For this reason, muscle condition of the older adults should be evaluated and one of the ways to identify possible deficits associated with the muscle status of the older adults is by measuring Handgrip Strength (HGS), which can be considered an indicator of overall muscle strength and correlated with strength measurements of other muscle groups, in addition to being considered an aging biomarker (^{Bohannon, 2019}; ^{Lopes et al., 2018}). HGS stands out as a predictor of general health status and it is associated with early mortality from all causes, cardiovascular mortality, as well as related to length of hospital stay, physical function and disabilities (^{Bohannon, 2019}; ^{Soysal et al., 2021}). The HGS measurement can also be a marker of nutritional and functional status, being associated with other indicators for health monitoring throughout the aging process (^{Amaral et al., 2020}).

Monitoring the functional capacity of the older adults has an important and strategical role, especially in Primary Health Care (PHC), which must be potentially prepared for such evaluations. Thus, HGS measurement is relevant for evaluating older adults, given its impact on functionality and quality of life, in addition to being a criterion for screening and diagnosis of sarcopenia and frailty (^{Bohannon, 2019}; ^{Cruz-Jentoft et al., 2019}; ^{Fried et al., 2001}). So, there is a need for PHC instrumentalization to measure and include such analysis in the evaluation protocols of older adults to early identify changes in the functional status of this population. However, the dynamometer, the equipment used to measure force, is not eventually an available tool (^{Soares et al., 2019}).

The process of measuring HGS from equations capable of estimating it by using simple variables costs relatively less, it is a process not dependent on sophisticated equipment in the routine of PHC and, therefore, a viable alternative in health units. So, the objective of this study is to develop equations for predicting HGS in older adults in PHC.

2. Methods

3. Results

Data were collected from 316 individuals (11.2 % of losses related to refusals, non-location, or non attendance of the participant), 61.7 % of whom were female. The sociodemographic characteristics of the sample are shown in Table 1. Regarding the age group, 84.3 % of the older adults were between 60 and 79 years old, and the mean age was 70.4 years (±7.3), 70.2 (±6.9) among women and 70.6 (±7.8) among men, without significant difference between sexes. Most older adults have a marital partner (51.6 %), have fewer than four years of study (72.8 %) and self-reported to be black or brown (51.9 %). As for the BMI classification, low weight was present in 34.2 % of the older adults.

The R-HGS mean was 22.2kg (±7.7), where 28.7kg (±7.0) among men and 18.2 kg (±4.9) women, with a significant difference between the sexes (p<0.001), while the L-HGS mean was 21.3kg (±7.3), 27.3kg (±6.8) among men and 17.6kg (±4.5) among women (p<0.001). Similarly, men had significantly higher values in the anthropometric variables weight, knee height, height and TSF (Table 2).

The correlations between HGS and the predictive variables of the model are presented in Table 3 for the right and left hands and organized by sex. When evaluated without division per sex (data not shown), the correlations were stronger and significantly correlated with the outcome (p < 0.05), however, sex is an important variable in the determination of HGS and relevant to adjust the model.

The equations proposed for predicting HGS of the community-dwelling older adults are described in Table 4. The adjusted model with the best result for R-HGS [F(3.312) = 124.0; p < 0.001; R² = 0.544] was consisted of the variables age (Beta = -0.271; t = -6.648; p < 0.001), knee height (Beta = 0.494; t = 4.405; p < 0.001) and sex (Beta = 8.339; t = 10.526; p < 0.001) and for L-HGS [F(3.312) = 106.3; p < 0.001; R² = 0.505] by the variables age (Beta = -0.223; t = -5.570; p < 0.001), knee height (Beta = 0.432; t = 3.932; p < 0.001), and sex (Beta = 7.800; t = 10.040; p < 0.001).

As for the evaluation of the MLR assumptions, in both sides, normality was observed in the distribution of residues by the Shapiro-Wilk test. The value of the Durbin-Watson independence test was 2.071 (R HGS) and 1.898 (L-HGS), the Goldfeld-Quandt homoscedasticity test was 0.781 (R-HGS) and 0.629 (L-HGS). During the evaluation of multicollinearity between the variables, no Variance Inflation Factor (> 10) was observed.

The reliability of the model was internally evaluated by analyzing the agreement between the HGS measured with the dynamometer and the HGS predicted by the model, as can be observed in the Bland Altman diagram (Figure 1). There was agreement between the measurements for both the right (bias: 0.000084) and the left side (bias: -0.000137), and the bias was analyzed by the Student's t-test. The lower (LLoA) and upper (ULoA) limits of agreement were, respectively, -10.21 and 10.21 for the right side. For the left side, the LLoA was -10.01 and the ULoA was 10.01.

Figure 1 Bland-Altman diagram showing the agreement between HGS measured with the dynamometer and predicted HGS on the right hand (a) and left hand (b) in community-dwelling older adults (n = 316) 

4. Discussion

The results of this study on the development of a model of a predictive equation for HGS showed that age, sex, and KH explained 54% of the variation in R-HGS and 50% of L-HGS for community-dwelling older adults. The need to develop a predictive equation for HGS arises from the insufficient instrumentalization of the PHC units (^{Binagwaho & Adhanom Ghebreyesus, 2019}), with the eventual absence of a dynamometer, which is the gold standard equipment used for gerontological evaluation and body measuring (^{Soares et al., 2019}).

The use of HGS predictive equations, consisted of simple and frequent variables, has practical advantages that are beyond the issues related to the relative cost of equipment. Even in the absence of the measurement instrument, using HGS as an evaluation criterion is justified because it is considered a predictor of mobility limitation (^{Delinocente et al., 2021}), mortality (^{Spexoto et al., 2022}), complications, and increased length of stay, as well as being a significant indicator for these conditions even when adjusted for potentially confounding variables (^{Bohannon, 2019}). Another aspect that makes the use of equations reasonable concerns the execution of the measurement itself. Although it is more simple when compared to other measures, it has strict protocols (^{Fess, 1992}), which can be a limitation in health units, as it requires time and training for the results to be valid and reliable.

In view of this, an alternative easily performed by the professionals who make up the health unit's staff and that requires minimal time and resources is the use of demographic information, such as sex and age, obtained from the individuals' records and basic anthropometric measures to estimate other evaluation parameters less common in PHC, such as HGS.

Thus, considering the feasibility of multivariable models, other equations for predicting HGS by using multiple variables as predictors of the measure were previously proposed for different groups, in different countries and configurations (^{Andres et al., 2013}; ^{Angst et al., 2010}; ^{De Blasio et al., 2017}; ^{Imrhan & Mandahawi, 2010}; ^{Li et al., 2010}; ^{Lopes et al., 2018}; ^{Niempoog et al., 2007}; ^{Novaes et al., 2009}; ^{Tveter et al., 2014}). However, this study considers the peculiarities of a single age group, in addition to the specific care setting, which may enable its application under similar conditions.

The development of prediction equations should favor the use of simple predictors which are quickly and inexpensively obtained, and relevant to the quality of the model. So it is observed that the variable sex is often used as an independent variable, consisting in most cases the final model as one of the most important predictors (^{Andres et al., 2013}; ^{Angst et al., 2010}; ^{Imrhan & Mandahawi, 2010}; ^{Lopes et al., 2018}; ^{Novaes et al., 2009}; ^{Tveter et al., 2014}). This fact can be justified by the significant differences between the HGS values obtained in men and women, being higher in males (^{Dodds et al., 2016}). These discrepancies between sexes may be associated with the difference in body composition between men and women, since men tend to have a higher volume of muscle mass compared to women (^{Bredella, 2017}). Other variables that are related to HGS tend to behave differently with the outcome when sex is considered. For this reason (^{Amaral et al., 2020}), the variable was selected in the present study prior to the modeling, as it significantly contributes to the improvement of the quality of the adjustment.

Confirming the idea of accessible variables, anthropometry is a useful and frequently available tool in the practical evaluation of the older adults, especially in the context of the public health system (^{Closs et al., 2016}; ^{Lopes et al., 2018}). In this research, the anthropometric variable incorporated in the final model of HGS prediction was KH, a consolidated measure in the anthropometric evaluation of older adults because it is widely used in height estimation and undergoes little change with aging (^{Closs et al., 2015}).

The muscle strength loss is an indicator capable of predicting negative outcomes more expressively than the loss of muscle mass alone and this fact is evident with the advancement of age, leading to limitations (^{Bohannon, 2019}; ^{Soysal et al., 2021}). Thus, due to the relationship between age and changes in HGS (^{Albrecht et al., 2021}; ^{Sena Pereira et al., 2022}), the variable was also previously selected to compose the prediction model, as well as observed in other studies, regardless the age group studied (^{Andres et al., 2013}; ^{Angst et al., 2010}; ^{De Blasio et al., 2017}; ^{Imrhan & Mandahawi, 2010}; ^{Niempoog et al., 2007}; ^{Novaes et al., 2009}; ^{Tveter et al., 2014}). Thus, in line with the specialized literature, age was significantly correlated with HGS in both sexes and contributed to improve the ability to explain the variation of the outcome in the final model.

In general, this study presents a random and representative sample of the group researched, which is characterized by being from the Northeast region of Brazil, consisted of individuals dependent on the public health system in urban areas. They are mostly represented by black or brown people, female, with a marital partner, and low education. A Brazilian study presented a review of the older adult's population in the country (^{Travassos et al., 2020}), addressing sociodemographic conditions, and it concluded that the profile of the Brazilian older adult is mostly consisted of white women from urban areas, with a marital partner, and average schooling of more than four years. However, the same authors made important considerations that do not ignore the continental dimensions of Brazil and the consequent regional differences reflected in the older adult's population. Thus, the sample of this study had sociodemographic characteristics similar to those described for the Brazilian population, but peculiarly specific to the Northeastern Brazil, such as lower education in relation to the national average, and lower proportion of people who self-declare as white (^{Travassos et al., 2020}).

Such attributes of the sample related to similarities with the population of interest, as well as the operationalization of the sampling process described, are some of the aspects that represent potentialities of the study. From a practical point of view, this work proposes to present a model capable of estimating a low HGS, a measure considered to be a predictor of adverse outcomes, especially in older adults, contributing both to the construction of a theoretical and methodological framework for the subject, and to the practical use of the model in similar scenarios. In this sense, important aspects were considered for developing a prediction model, such as the adequate number of events per predictor variable, use of TRIPOD as a guiding reference for the development of the model (^{Moons et al., 2015}), low percentage of data loss, as well as the imputation of missing or inconsistent data. The use of appropriate tests to meet the assumptions of MLR was also considered, and the internal evaluation of the model reliability was performed by using the Bland-Altman diagram. In this regard, an agreement was observed between the estimated and measured HGS on both sides and although the limits of agreement (ULoA and SLoA) are relatively high, a value defined as an acceptable parameter was not found in the literature. A study that tested the agreement by the Bland-Altman method between different prediction equations found limits of agreement with higher values (^{Soares et al., 2019}), which may indicate that the values found in this study are more acceptable.

Although the characteristics of the sample might be described as a potentiality of this study, the reproducibility of the findings in other scenarios is not known. Since the internal reliability has been tested, the external validity of the model has not been evaluated. In the same way, although the sampling process guarantees the representativeness and randomness of the group studied, the number of participants can be considered small, limiting the results, as can the age variability of the sample and the inclusion of men and women in the same regression model.

Another issue concerns the selection of predictors that prioritized the practical obtaining of information, in opposition to purely theoretical or mathematical aspects. To elaborate a plausible model for the PHC reality or other situations where the dynamometer is not an available equipment, therefore, other predictors could improve the quality of the model, but not provide the equation with the same viability. Finally, although the results presented are satisfactory, the trend observed in the Bland-Altman concordance diagram might be considered a limitation, even if the assumptions have been met. For this reason, as the next logical step and in line with development studies for prediction models (^{Moons et al., 2015}), it is advisable to update the model with adjustments, and include new viable variables as those used in this study and validation, since prediction equations may be subject to biases.

5. Conclusions

In this study, the variables age, sex, and KH were the ones that had the best feature to explain the HGS variation in the sample, confirming the simplicity of the final equation. The model obtained had its reliability internally evaluated, presenting a good agreement between the values measured directly with the dynamometer and the values predicted by the equation. The use of parameter predictive equations, such as HGS, is a potential option to identify problems and enable early interventions in these individuals, in addition to allowing simple attributes to generate an estimate of the expected HGS in situations where this measure is necessary to improve clinical care efficiency.