# Average Slope vs. Cmax: Which Truly Reflects the Drug-Absorption Rate?
## 2 Materials and Methods
### Machine-Learning Algorithms
#### 2.3.4 Artificial Neural Networks  
The term \"neural network\" originally drew inspiration from the notion of the hidden units resembling neurons in the brain. An ANN typically consists of three layers: input, hidden, and output. An ANN operates by taking an input vector consisting of \(p\) variables, \(X\) = (\(X1\), \(X2\), \(\ldots\), \(Xp\)), and constructs a nonlinear function _f(X)_ to forecast the response Y. In ANN terminology, the features \(X1\), \(\ldots\), \(Xp\) constitute the units within the input layer. The directional arrows signify that each input from the input layer is directed into each of the \(K\) hidden layers. The \(K\) activations originating from the hidden layer subsequently contribute to the output layer, establishing a linear regression model within the \(K\) activations. Activation functions are applied to neurons in the hidden and output layers to facilitate the model in learning complex patterns from the data. The selection of these activation functions can significantly impact the outcomes. The activation function connects the weighted sums of units within a layer to the values of units in the next layer. The sigmoid function converts a linear function into probabilities ranging from zero to one. The ReLU activation function offers computational efficiency compared to the sigmoid activation function. The hyperbolic tangent activation function, commonly known as Tanh, shares similarities with the sigmoid activation function, featuring the same S-shape. The bias in ANNs refers to a constant value added to the product of features and weights. Its role is to adjust or offset the output generated by the network. Bias allows models to shift the activation function towards either the positive or negative side, thereby enhancing their ability to capture complex patterns in the data [23; 53; 54]. In ANNs, these bias units are implemented to correct systematic errors in predictions. Hyperparameter tuning is crucial for optimizing an ANN. The optimal configuration, including parameters like the number of neurons, hidden layers, and activation functions for both hidden and output layers, varies based on the complexity and characteristics of the problem. Typically, determining the best hyperparameter settings involves a mix of experimentation and reviewing the existing literature. In this study, we extensively fine-tuned the hyperparameters, which included exploring various activation functions (such as softmax, linear, ReLU, and sigmoid) and determining the optimal number of hidden layers. Then, batch training of the ANN was performed. In batch training, the synaptic weights are updated only after processing all training data records, meaning it uses information from the entire training dataset at once. This approach is often favored because it directly minimizes the total error. This method is particularly beneficial for smaller datasets where processing the entire dataset in one go is feasible. In this study, hyperparameter tuning was based on a trial-and-error rationale after exploring all possible combinations of the pre-referred factors. Based on the ANN outcomes, the independent variable importance analysis conducts a sensitivity analysis to evaluate the significance of each predictor in influencing the ANN outcome. This analysis is conducted using either the combined training and testing samples or solely the training sample if there is no separate testing sample available. The results are presented in a table and a chart, indicating the importance and normalized importance of each predictor. In this analysis, three distinct ANN models were developed for each drug; thus, a total of 15 models were created for the five drugs of the study. The three distinct ANN models per drug refer to: (a) Tmax set as a continuous response variable, (b) Tmax considered as an ordinal response variable, and (c) AS studied as a continuous response variable. The Tmax values, which were converted from original continuous scales into ordinal scales for the RF analysis, were also used in the ANN analysis.