Machine learning-based prediction has been effectively applied for many healthcare applications. Predicting breast screening attendance using machine learning (prior to the actual mammogram) is a new field. This paper presents new predictor attributes for such an algorithm. It describes a new hybrid algorithm that relies on back-propagation and radial basis function-based neural networks for prediction. The algorithm has been developed in an open source-based environment. The algorithm was tested on a 13-year dataset (1995-2008). This paper compares the algorithm and validates its accuracy and efficiency with different platforms. Nearly 80% accuracy and 88% positive predictive value and sensitivity were recorded for the algorithm. The results were encouraging; 40-50% of negative predictive value and specificity warrant further work. Preliminary results were promising and provided ample amount of reasons for testing the algorithm on a larger scale.