### I. Introduction

### II. Methods

### 1. Data

^{2}), left or right kidney, type of immunosuppressive drugs used (imuran, prednisolone, and cyclosporine vs. CellCept, prednisolone, and cyclosporine), duration of hospitalization (number of days), volume of urine excretion during the first 24 hours after transplantation (mL/24 hr), and occurrence of acute or hyperacute rejection. Acute rejection is related to the formation of cellular immunity. This occurs to some extent in almost all grafts, except between identical twins, and hyperacute rejection is started by preexisting humoral immunity and usually manifests within minutes after transplantation. The response variable was having chronic nonreversible graft rejection [3].

### 2. Statistical Analysis

*x*'s are the covariates to classify the response, α is the logarithm of odds when no covariates or factors are utilized to model the response variable, and the β

_{i}_{i}'s are the regression coefficients. Predicting the probability of an event is the main advantage of logistic regression due to its modeling approach. The term ${\scriptscriptstyle \left(\frac{\pi}{\mathrm{1}-\pi}\right)}$ indicates the odds of classifying the response variable in category one than zero using several covariates and factors [10]. In the present study, we used the age and sex of donors and recipients, type of donor (living or deceased), etc. as covariates (χ) and having chronic nonreversible graft rejection as the binary response. Thus, π, is the probability of graft rejection.

*f*(χ) = 2 / (1 + exp(−2χ)) − 1) for the hidden layer as well as softmax (${\scriptscriptstyle {\mathit{f}}_{\mathit{i}}\left(\mathit{x}\right)=\frac{{\mathit{e}}^{{\mathit{x}}_{\mathit{j}}}}{{\sum}_{\mathit{i}=\mathrm{1}}^{\mathit{P}}{\mathit{e}}^{{\mathit{x}}_{\mathit{i}}}},\mathit{\hspace{0.33em}j}=\mathrm{1},\hspace{0.33em}\dots ,\mathit{\hspace{0.33em}p},}$ where

*x*'s are predictor variables) in the output layer. The functional form of MLP is written as

_{i}*x*is the

_{i}*i*th nodal value in the preceding layer, and

*y*is the

_{k}*k*th nodal value in the current layer. In addition,

*b*and

_{j}*w*are the bias and a weight connecting

_{ji}*x*and

_{i}*y*of the

_{j}*j*th node, respectively, and

*N*is the number of nodes (in the previous layer). The activation function in the present layer is

*f*. We also provided the variable importance to identify the most important variables for graft rejection. Variable importance can be calculated in different ways. Here, the definition of variable importance is the relative reduction in the predictive power (calculated with some criteria) of the model. In the present study, the mean decrease Gini was used to calculate variable importance, which is a measure calculated based on the Gini impurity index. The Gini impurity index is utilized to calculate splits during training. For making a split in a node on a variable, say m, the Gini impurity criterion (for the two descendent nodes) will be less than that of the parent node. The Gini impurity index is calculated using ${\scriptscriptstyle \mathit{G}=\sum _{\mathit{i}=\mathrm{1}}^{{\mathit{n}}_{\mathit{c}}}{\mathit{p}}_{\mathit{i}}\left(\mathrm{1}-{\mathit{p}}_{\mathit{i}}\right),}$ where

*n*

_{c}shows the number of classes in the output variable, and

*p*

_{i}stands for the ratio of this class.

### 3. Evaluation Criteria

### III. Results

*p*< 0.001). A higher accuracy was achieved by the ANN method in comparison to LR. To evaluate the association of the method predictions and observed value of failure, Φ coefficient, Kendall tau-b, and kappa statistic were performed. The results shown in Table 4 confirm that there is a significant association and agreement of the performed methods with the observed values. Figure 2 demonstrates that ANN outperforms LR due to its higher AUC.