This paper presents a neural network-based classifier to predict whether a person is at risk of developing chronic kidney disease (CKD). The model is trained with the demographic data and medical care information of two population groups: on the one hand, people diagnosed with CKD in Colombia during 2018, and on the other, a sample of people without a diagnosis of this disease. Once the model is trained and evaluation metrics for classification algorithms are applied, the model achieves 95% accuracy in the test data set, making its application for disease prognosis feasible. However, despite the demonstrated efficiency of the neural networks to predict CKD, this machine-learning paradigm is opaque to the expert regarding the explanation of the outcome. Current research on eXplainable AI proposes the use of twin systems, where a black-box machine-learning method is complemented by another white-box method that provides explanations about the predicted values. Case-Based Reasoning (CBR) has proved to be an ideal complement as this paradigm is able to find explanatory cases for an explanation-by-example justification of a neural network's prediction. In this paper, we apply and validate a NN-CBR twin system for the explanation of CKD predictions. As a result of this research, 3,494,516 people were identified as being at risk of developing CKD in Colombia, or 7% of the total population. INDEX TERMS Chronic kidney disease prediction, neural networks, case-based reasoning, twin systems, explainable AI, support vector machines, random forest.