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Neural Network for Predicting the Chance of 2-year Resolution in Children with Vesicoureteral Reflux

Portions of this document were adapted in part from our paper:

Portions of this document were adapted in part from our paper. Computational Model for Predicting the Chance of Early Resolution in Children with Vesicoureteral Reflux. Knudson MN, Austin JC, Wald M, Makhlouf AA, Niederberger CS, Cooper CS. Computational Model for Predicting the Chance of Early Resolution in Children With Vesicoureteral Reflux. J Urol. 2007 Aug 16.

The reader is strongly encouraged to review this paper prior to using the network, as it contains a more specific description of the model. The reader should also note that while our paper describes both a 1- and 2-year model, javascript is currently only available for a 2-year model, presented here.


About Vesicoureteral Reflux

Management of vesicoureteral reflux remains a challenge because while most children spontaneously resolve reflux without serious complications, some children will develop significant problems. Minimally invasive surgery, open surgery, prophylactic antibiotics and watchful waiting constitute the most common treatment options. However, the best treatment of vesicoureteral reflux remains unknown and is largely determined by parent preference and physician assessment of a child’s chance for reflux resolution. While minimally invasive surgery has been proposed to reduce the morbidity and risk of complications, there is a distinct possibility that many children undergo unnecessary treatment. There are also concerns regarding long-term antibiotic prophylaxis.

While the grade of reflux remains the major clinical variable utilized to predict resolution of reflux other variables also impact resolution. A more individualized prediction of which children will resolve reflux early may help with management decisions. The computational model we developed utilizes multiple individualized variables to improve the accuracy of predicting if a child will out grow reflux in 2 years. The ROC noted below is an indicator of this model’s accuracy.

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Neural Network Programming and Training

Clinical data was collected from 205 children (42 males, 163 females) with primary vesico-ureteral reflux.

Input features other than age and bladder volume at onset of reflux were converted into a numeric code and two models were created for output (defined as reflux resolution and coded 0 for non-resolution and 1 for resolution) at 1 and 2 years post-diagnosis. Input features were identical in both datasets and included gender, presenting symptom, age, laterality, bladder volume at onset normalized by percent of predicted bladder capacity (PBC), right/left side grade of reflux, when reflux occurred on right/left, presence of duplicated ureters, and finally, presence of voiding dysfunction. Both datasets were randomized into a modeling (“training”) set of 155 and a separate, completely independent cross-validation (“test”) set of 50 patients, with similar outcome frequencies preserved in each set. We used neUROn++, a set of C++ programs we developed, to model the dataset using linear and quadratic discriminant function analysis, logistic regression, and neural computation with several investigated architectures. We also modeled the dataset with support vector machines using LibSVM, a public domain software library. Receiver operator characteristic curve (ROC) area served to assess the model’s accuracy, and was computed using the statistical method described by Wickens and by the traditional trapezoidal method. Model accuracies, in terms of receiver operator characteristic curve (ROC) area, were higher with radial SVM than those achieved by the nonlinear computational method of neural computation and the traditional linear statistical modeling tools.

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Accuracy of the Neural Network Compared to Linear Methods

ROC area (test set)2
Logistic Regression
Neural Network (3 hidden nodes)
Linear Discriminant Function Analysis
Quadratic Discriminant Function Analysis

  1. A description of this method of training, including weight decay and feature extraction using Wilk’s GLRT, may be found in Golden RM, Mathematical methods for neural network analysis and design, Cambridge, MA: MIT Press, 1996.

  2. Receiver Operating Characteristic Curve area. As numbers approach 1.0, the accuracy of the statistical method improves: a ROC value of 1.0 would indicate a sensitivity of 1.0 and specificity 1.0. ROC areas were computed using the statistical method described by Wickens: Wickens TD, Elementary signal detection theory, New York: Oxford University Press, 2002.

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