## 2 Methodology
### Performance Indicators and Model Assessment  
In this section, we assessed the framework to predict each MetS type first by using Random Subsampling validation. Second, we used performance indicators to compare the previously chosen techniques to select the best model to predict the MetS types using the HMS criterion.  
This article uses a dataset summarized by means, standard deviations, and percentages and found the prevalence of MetS. We analyzed each variable of the dataset in two groups (MetS and Non-MetS) assessed with t-tests and Chi2 tests using the SPSS statistical software, version 23 for Windows.  
For the validation of the model, we used random subsampling or Monte Carlo cross-validation on multiple data that are randomly chosen from the dataset and combined to form a new dataset, i.e., multiple hold outs. The remaining data forms the training 70% and testing 30% of the dataset. The test data predictions give a realistic estimate of the external validation data predictions because it is asymptotically consistent. This approach results in more pessimistic predictions of the test data compared to cross-validation [53; 54; 55; 56]. For this article, we made a random subsampling of 100 times using Matlab software.  
Now, in each holdout, a training set equivalent to 70% of the dataset was used to train the ANN, and the training stops when any of these conditions occur: the maximum number of 1000 epochs is reached, the performance gradient falls below \(10^{-6}\), and maximum validation failures to check was 6. For preventing the ANN from performing poorly while learning well on training data, training stops if the validation performance degrades for 6 (default) consecutive epochs. The ANN was tested with the equivalent test set of 30% of the dataset to obtain the performance indicators. After doing this 100 times, the model was validated, obtaining the average of the performance indicators.  
We compared the classification models to diagnose each MetS type (WPG, WPH, WPT, WGH, WGT, WTH, PGT, PGH, PTH, and GHT) without using a blood sample. For this purpose, we used indicators to evaluate their capacity for discrimination, such as Sensitivity (SS), Specificity (SP), False Negative Rate (FNR), False Positive Rate (FPR), AROC [40; 46]. The TP, TN, FP, and FN values represent True Positives, True Negatives, False Positives, and False Negatives, respectively.  
\[Sensitivity(SS)=\frac{TP}{TP+FN} \tag{10}\]  
\[Specificity(SP)=\frac{TN}{TN+FP} \tag{11}\]  
Figure 3: Basic structure of the artificial neural network.  
\[FPR=1-SP \tag{12}\]  
\[FNR=1-SS \tag{13}\]  
\[AROC=\int(SS)(1-SP) \tag{14}\]  
The classifiers used to diagnose diseases prioritize the rate of type 1 and 2 errors known as False Negative Rate (\(FNR\)) and False Positive Rate (\(FPR\)), which are the complement of \(SS\) and \(SP\), respectively. The type 2 error (false negative) is harmful because a patient with Metabolic Syndrome can be diagnosed as a patient without the syndrome, affecting their health since they did not start adequate treatment.  
On the other hand, it should be noted that we evaluated all these models using the AROC and the Hosmer and Lemeshow criterion [57], which is shown in Table 6.