Kidney transplantation is the best renal replacement therapy for patients with end-stage renal disease. Several studies have attempted to identify predisposing factors of graft rejection; however, the results have been inconsistent. We aimed to identify prognostic factors associated with kidney transplant rejection using the artificial neural network (ANN) approach and to compare the results with those obtained by logistic regression (LR).

The study used information regarding 378 patients who had undergone kidney transplantation from a retrospective study conducted in Hamadan, Western Iran, from 1994 to 2011. ANN was used to identify potential important risk factors for chronic nonreversible graft rejection.

Recipients' age, creatinine level, cold ischemic time, and hemoglobin level at discharge were identified as the most important prognostic factors by ANN. The ANN model showed higher total accuracy (0.75 vs. 0.55 for LR), and the area under the ROC curve (0.88 vs. 0.75 for LR) was better than that obtained with LR.

The results of this study indicate that the ANN model outperformed LR in the prediction of kidney transplantation failure. Therefore, this approach is a promising classifier for predicting graft failure to improve patients' survival and quality of life, and it should be further investigated for the prediction of other clinical outcomes.

Chronic kidney disease (CKD), a major risk factor for endstage renal (or kidney) disease, cardiovascular disease, and premature death, is a global public health problem, affecting more than 10% of the global population [

Since failure of transplantation is associated with adverse consequences for patients, exploring, identifying, and controlling for risk factors are of utmost importance. Several potential prognostic factors affecting the success of renal grafts, such as the age and sex of donors and recipients, body mass index, type of donor (living or deceased), anemia, type of immunosuppressive regimen, and so forth, have been investigated in various studies [

Several classification methods are used to predict a categorical response variable based on predictors and covariates. In this regard data mining (machine learning) techniques have been introduced, and they have achieved promising performance in classifying binary responses [

Several studies have applied ANNs and produced promising results in a variety of fields, including economics, medicine, psychology, meteorology, and neurology. These studies suggest that ANNs can be used as an alternative to multivariate analysis. However, their role has remained advisory because there has not been convincing evidence of any real progress in clinical prognosis [

The present study used a dataset obtained through a retrospective cohort study that was conducted in Hamadan, western Iran, from 1994 to 2011. A total of 378 patients underwent kidney transplantation in Ekbatan or Besaat hospitals. The potential risk factors include the age and sex of donors and recipients, type of donor (living or deceased), familial relationship, hemoglobin level, blood groups of donors and recipients, duration of dialysis before transplantation (year), cold ischemic time (minute), creatinine level at discharge, body mass index (BMI) of donor (kg/m^{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 [

LR and ANN were used to analyze the dataset. To validate the results, the dataset (cases) was divided into training and testing sets. The ANN and LR models were first fitted to the training dataset (70% of cases), and the resulting models were evaluated using the test sample (30% of cases).

Logistic regression (LR): LR as a parametric method is the most common and easily interpretable tool to model binary or multinomial response variables. The model can be written as

In this model, the _{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

Artificial neural network (ANN): This method is based on human brain function. Multilayer perceptron (MLP) is the most commonly used method among several artificial neural network methods. This method contains input, output, and hidden layers, where each layer includes several nodes. An activation function transforms the data in each layer to the next layer one by introducing a degree of nonlinearity. The input layer consist of all risk factors affecting the result of graft rejection. The binary response variable of graft rejection shows up in the output layer with two nodes as the possible outcomes for graft rejection. To find the best performance of the network, complex nonlinear mapping between input and output layers is conducted using the number of nodes, which is determined empirically in the hidden layer [_{i}

In the above equation, _{i}_{k}_{j}_{ji}_{i}_{j}_{c} shows the number of classes in the output variable, and _{i} stands for the ratio of this class.

The performance of the models was compared in terms of several measures, including sensitivity, specificity, positive predicted value, negative predicted value, accuracy and area under ROC curve (AUC). Any statistical differences in the resulting proportions obtained by the models was assessed by McNemar's test. To assess the association between the observed and predicted values, several statistics were measures, such as Φ coefficient, Kendall tau-b, and kappa statistic.

The information of 378 patients was used in the present study. The characteristics of the study subjects are shown in

To identify the risk factors affecting failure of transplantation, LR and ANN were performed. The testing and training samples were composed of 114 (30%) and 264 (70%) cases, respectively.

The results obtained by logistic regression are shown in

The importance of the variables is revealed by scores resulting from the sensitivity analysis. Similar to the outputs of LR and based on the shown importance of variables resulting from ANN in

A comparison of sensitivity, specificity, positive probability value, negative probability value, accuracy, and AUC for the training and testing sets of classification methods are shown in

The life expectancy of patients with end-stage renal disease has been extended by the wide availability of alternative treatments [

This study focused on the performance of the ANN method in identifying potential risk factors for kidney graft failure in comparison to the performance of LR. The results showed that ANN achieved better performance. The evaluation criteria, such as AUC and accuracy, showed that the predictions made by ANN were more precise than those made by LR. Several studies have exposed and compared the power of predictions made by various classification methods. In 2014, Lin et al. [

ANN has some advantages and disadvantages in comparison to LR. For example, less formal statistical training is required for the development of neural network models. In addition, they can implicitly detect complex nonlinear relationships between independent and dependent variables and have the ability to detect all possible interactions between predictor variables. On the other hand, neural networks are a ‘black box’ and have limited ability to explicitly identify possible causal relationships, and they require greater computational resources [

There were some limitations in the present study. We utilized a dataset of a retrospective cohort study and medical records. Reliable sources of data, obtained from prospective design, were required to identify prognostic factors of rejection. The quality and accuracy of estimates depend mainly on the quality of recorded data, but it was not possible to verify the accuracy of the data used in the present study. This might have introduced some bias in the results. There are also several data mining techniques that have been used to predict graft kidney rejection [

In conclusion, our study showed that cold ischemic time, creatinine, recipients' age and hemoglobin at discharge are the most important variables affecting failure of transplantation. ANN was compared to LR and was found to be an accurate and promising method for the classification, prediction, and identification of important risk factors in various diseases.

We would like to thank the Vice-Chancellor of Health of Hamadan University of Medical Sciences for the approval and support of this study.

Values are presented as number (%) or mean ± standard deviation.

OR: odds ratio, CI: confidence interval.

ANN: artificial neural network, LR: logistic regression, PPV: positive predicted value, NPV: negative predicted value.

LR: logistic regression, ANN: artificial neural network.