To elucidate the predictive performance in estimating the body composition for the elderly by using the linear model and the optimal BP-ANN model, identical dataset were used to develop these two models for comparison. Using the anthropometric data, the BP-ANN model with the simple input layer with five neurons was adopted to predict the FFM and body composition of the elderly. For predicting the FFMDXA, the coefficient of determination for the FFMANN (r2 = 0.960) estimated by the BP-ANN model with a single neuron in the input layer was greater than that of the FFMLR estimated by the linear model (r2 = 0.940). The presence of more neurons in the input layer of the weighted BP-ANN model resulted in a higher coefficient of determination; the r2 value reached up to 0.987 when the five neurons were included in the input layer of the BP-ANN model. As more variables were included in the ANN model the correlation coefficient between predictive value and FFMDXA increased, nearly approached to one. When compare the results with other studies using impedances in linear model, the FFM values for the elderly estimated by Genton et al. , Deurenberg et al.  and Roubenoff et al.  were underestimated approximately 2.9 to 7.1 kg in males and approximately 2.3 to 6.7 kg in females. Nevertheless, in comparison to the values determined by Baumgartner et al. , their results overestimated FFM roughly by 4.3 kg in males and approximately 1.4 kg in females. The data from Kyle et al.  show that the differences between the measured FFM and the DXA were 0.2 ± 2.0 kg in males and 0.0 ± 1.6 kg in females. Despite the acceptable coefficients of determination (r2 = 0.756-0.883) in the above-mentioned studies, improved r2 values were obtained in our five neurons input layer BP-ANN model. In particular, the smallest standard deviation of differences existed in the FFMANN vs. FFMDXA comparison (0.0 ± 1.192 kg).
Because a larger computing capacity and longer processing time were required to exert the arbitrary function mapping or non-linear function mapping, we optimized the training process in BP-ANN model by using the Levenberg-Marquardt Algorithm to improve the convergence. Despite the limits of memory resources , the space required for our analysis is a relatively tiny amount in modern computer hardware. That trend makes our technique more applicable. To prevent the occurrence of a local error minimum in our BP-ANN model, we repeatedly applied various random initial values to the training process for the BP-ANN model. Meanwhile, the trial calculations for the errors and the correlation coefficient fit the optimal BP-ANN model.
With the same training data, the accuracy and precision of the BP-ANN model are directly related to the number of neurons and hidden layers. To prevent over-fitting in our BP-ANN model, the model was optimized by Bayesian Regularization. If the relationship between dependant variable and independent variables were linear, using BP-ANN model to develop linear prediction equation, with proper training similar or nearly identical results to linear regression may be achieved. However, if the relationship were non-linear, using linear regression model to construct prediction equation, the predictive accuracy will be limited . When constructing a BP-ANN model, there was no guideline or rules for how many hidden layers should be constructed, how many neurons should be included, and how to choose proper transfer function for achieving the optimal predictive equation. For practical application, the different combination of layers and neurons may be used to construct model via training conjoin with validation analysis to achieve desired results. In most case, when the included hidden layers and neurons approach certain numbers, the estimated error will be minimized to certain value which cannot be reduced as more hidden layers and neurons are included into model. This phenomenon was observed as we constructed our model. For the minimum sample size, ANN model can generate better results than that of linear model when sample size is lower than 2000 . But ANN model still has its downside, the estimated weight matrix, bias vector cannot have the same interence and interpretation as linear regression coefficient . Another downside of ANN model is the complex calculation of the model which demand higher computation capability of measuring system or device, but recent development of computer hardware had made this obstacle easily be overcome which results in widely application of ANN model .
After ruling out other sources of dependent variability, the linear regression can easily describe the relationship between the single independent variable and the single major dependent variable. However, the linear regression does not work well in the systems with the dependent variables correlated with each others, especially in the complex human physiological system. Many variables, such as sex, age, physical activity, diet, genetics, weight and height, can affect body composition or have non-linear relationship among variables . These variables may interact with each other to influence the estimation of body composition. In other words, the multiple dependent anthropometric variables may exhibit a coupled relationship rather than an independent linear relationship as assumed in a multiple linear regression model .
Consequently, the application of non-linear functions and other more flexible mathematic functions to describe the relationships between body composition parameter (fat free mass) and multiple variables requires much more attention to improve the predictive accuracy. In fact, the RMSE for FFM in our BP-ANN model was much lower than in LR model. Further evidence provided by Liu et al. shows that the application of the BIA system and the ANN model to estimating the FFM of the lower limbs exhibits greater performance than a linear model .
Many studies had successfully apply ANN model in clinical trials [22, 24, 27–31]. However, some indicated that ANN model can't perform better than linear regression model in clinical application. Therefore, the novel ANN model should be validated and use with care .