Hip fracture prediction from a new classification algorithm based on recursive partitioning methods

Classification and regression tree has been useful in medical research to construct algorithms for disease diagnosis or prognostic prediction. Jin et al. 7 Jin, H., Lu, Y., Harris, R. T., Black, D., Stone, K., Hochberg, M. and Genant, H. 2004. Classification algorithms for hip fracture prediction base on recursive partitioning methods. Med. Decis. Mak., 24: 386–398. (doi:10.1177/0272989X04267009)[Crossref], [PubMed], [Web of Science ®] , [Google Scholar] developed a robust and cost-saving tree (RACT) algorithm with application in classification of hip fracture risk after 5-year follow-up based on the data from the Study of Osteoporotic Fractures (SOF). Although conventional recursive partitioning algorithms have been well developed, they still have some limitations. Binary splits may generate a big tree with many layers, but trinary splits may produce too many nodes. In this paper, we propose a classification approach combining trinary splits and binary splits to generate a trinary–binary tree. A new non-inferiority test of entropy is used to select the binary or trinary splits. We apply the modified method in SOF to construct a trinary–binary classification rule for predicting risk of osteoporotic hip fracture. Our new classification tree has good statistical utility: it is statistically non-inferior to the optimum binary tree and the RACT based on the testing sample and is also cost-saving. It may be useful in clinical applications: femoral neck bone mineral density, age, height loss and weight gain since age 25 can identify subjects with elevated 5-year hip fracture risk without loss of statistical efficiency.