Information about the energy expenditure assessment of patients with AKI is scarce in the literature. Our study found that the REE estimated by the Harris and Benedict formula  was significantly lower than that measured by IC. This finding corroborates the indication not to use this formula in critically ill patients and in patients with AKI [11, 14, 20, 21] and the need to propose a new equation for those AKI on dialysis [21-25].
It has long been held that critical illness is a hypermetabolic state, i.e. that the basal metabolic rate is higher than that predicted by simple population characteristics [25-27]. Physiological factors such as fever, increased substrate cycling, and synthetic functions associated with the host response to stress and inflammation provide a theoretical basis for this generalization. Energy expenditure is also influenced by common ICU therapies [14,25].
This study aimed to develop and validate predictive equations for REE in severe AKI patients using a machine learning approach. It was found that the models were developed validly and significantly predicted REE in these patients and according to several linear and non-linear algorithms. In the present study, REE was positively correlated with C-reactive protein, minute volume (MV), expiratory positive airway pressure, serum urea, BMI and inversely with age (attachment 02). The principal variables included in the best model were age, BMI, use of vasopressors, expiratory positive airway pressure, minute volume, C-reactive protein, temperature and serum urea. The final r-value in the validation set was 0.69. In the literature, there is no consensus regarding the procedures to be used for the validation of predictive models. Some authors do not suggest the use of determination and correlation coefficients for the validation of techniques or estimated variables . Others consider that the Bland Altman plot is likely to show a systematic proportion bias . We used ten-fold cross-validation and selected the model with the lower RMSE. The performance of the best model was confirmed in a test set of 20% randomly selected unseen data (internal validation). The linear models had the advantage of simplicity of the model built and better interpretability but did not capture the non-linearity of the data. We confirmed this with a very low accuracy of the Harris–Benedict equation in the test set. The use of natural splines to age and BMI predictors improved the linear models but did not reach the same performance as the non-linear models like boost trees or support vector machines [22, 23]. The best model had a higher performance but a trade-off in lower interpretability. In addition, the traditional model like the Harris–Benedict  uses linear models that were easy to implement. Otherwise, the implementation of a model, like the random forest, that requires a calculator. However, currently, we have the facility of computers or apps that may overcome this difficulty.
Another advantage of the machine learning approach is to demonstrate other predictor variables that influence the outcome by finding complex interactions. The principal factors that contributed to the variability of REE were the BMI and age that were previously described with traditional models [24, 25]. The machine analysis in this study reveals other new contributary variables that predict the REE, for example, ventilator parameters and biochemical values. Otherwise, a simple linear model with this data set without pre-processing and feature engineering results in a model with lower accuracy and does not shown new interactions (R2 = 0.21, data not shown).
Thus, this study demonstrates the importance of estimating the REE in severe AKI patients, which is a determining factor in the assessment of nutrition status in critically ill patients. Previous studies reported correlations between morbidity or mortality and REE and indicated that sicker patients and non-survivors had a lower REE [22, 25] but this is not a universal observation [26,27]. Interpretations of these findings are limited by potential survivorship bias and confounders such as age and physical activity.
From a practical and application point of view, it is worth mentioning the capacity for technical evaluations to reduce the difference in REE between IC and that estimated by other conventional formulas, such as HB, the use of these predictive equations for the assessment of passive and active trawling, contributing with relevant information for nutritionists and physicians.
The present study has as main limitations the fact that the predictive models are not valid for non- severe AKI patients and the Bland Altman model was not performed. Although we trained models with a robust estimator with ten-fold cross-validation using RMSE as a metric, an approach regularly used in machine learning analysis, we tested the model in unseen data that may be considered an internal validation.