## 2 Material and Methods
### Statistical Analysis  
Categorical data were given as absolute frequencies and percentages. Shapiro-Wilk test was used to examine the normality of continuous variables, and because they were presented with deviations from normality and asymmetric distributions, they were expressed by their medians and interquartile ranges (IQRs). For the univariate analysis, to make comparisons between two independent groups, non-parametric chi-square (\(\chi^{2}\)) or [PERSON]'s exact test (if the applicability conditions of the first test were not verified) were used for categorical variables. Given that normality was not verified for continuous variables, the Mann-Whitney U test was applied for comparisons between the two groups. Concerning the multivariate data analysis, for data exploration and visualization, t-Distributed Stochastic Neighbor Embedding (t-SNE), a non-linear and unsupervised method, was applied. This method preserves the essential structure of the data, enabling assumptions on how data are arranged and facilitating the identification of clusters, e.g., patient groups based on their blood analyses results or cytokine profiles [20]. Naive Bayes, a probability classification algorithm, was used to build the prediction models independently for each set of groups that were compared (A vs. B, B vs. C, and A + B vs. C). Described as one of the most effective and efficient classification algorithms, Naive Bayes is based on the concept of conditional probability as defined by the Bayes' theorem [21]. Despite its strong independence assumptions, the algorithm has shown superior performance in applications such as medical diagnosis [21], even when these assumptions are not fully met [22]. Additionally, its applicability in small-sized datasets has been evidenced [23], making it suitable for the present study. Other methods for binary classification offer their own advantages and limitations. For instance, logistic regression usually requires larger datasets for training, assumes linear relationships between independent variables, and is particularly sensitive to outliers. Support Vector Machines (SVMs), while often delivering high performance in models based on clinical data, can be more challenging to implement due to the need to tune multiple hyperparameters. Additionally, SVMs are more susceptible to the influence of outliers, especially when working with small datasets [24]. Figure 2: Schematic depiction of the proteomic workflow from protein precipitation through data analysis. Serum proteins were precipitated and processed with a filter-assisted sample preparation (FASP) protocol, including denaturation, reduction, alkylation, and trypsin digestion. Peptides were then eluted and analyzed via UHPLC–HRMS in data-dependent acquisition mode. Raw data underwent peptide-spectrum matching, false discovery rate (FDR) control, label-free quantification (LFQ), match-between-runs alignment, protein grouping, and imputation of missing values using MaxQuant and Perseus. Prediction models were initially built using all available features from each dataset, namely all 25 cytokines, nine routine blood analyses results, and a combination of these 34 features (hybrid models). Then, the 10 most relevant features from each dataset were selected using an information gain algorithm, a rank based method that measures the reduction in uncertainty or entropy regarding a certain target variable when the added value of a certain feature is known [25]. This makes the algorithm useful for feature selection, as it identifies the most important features for predicting the target (in this case, the need for IMV and mortality in the ICU). These should enhance the model's performance, providing meaningful information gain and reducing the uncertainty of predictions [26]. In this study, we chose to select the top 10 features, reducing datasets from either 34 or 25 to 10 features (for routine blood analyses all 9 features were used).