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Abstract
In this work, the application of ‘multivariate adaptive regression splines’ (MARS) for modelling osteoporosis is described. This article focuses on the explanation of a new technique that combines the use of the principal components analysis (PCA) method with MARS. The use of this new technique allows for an easier management of large databases with a lower computational cost as the PCA allows the elimination of those variables that are redundant from the point of view of the phenomena under study. Osteoporosis is characterized by low ‘bone mineral density’ (BMD). This illness has a high-cost impact in all developed countries. The aim of this article is the development of a mathematical method capable of predicting the BMD of post-menopausal women, taking into account only certain nutritional variables. A nutritional habits and lifestyle questionnaire is drawn up. The variables obtained from this, together with the BMD of the patients calculated by densitometry, are processed using the ‘principal component analysis’ (PCA) algorithm in order to reduce the size of the database. Finally, the ‘MARS method’ is applied. It has been proved to be possible to build a MARS model in order to forecast the BMD of the post-menopausal women in function of their responses to the questionnaire. This model can be used to determine which women should take a densitometry.
Acknowledgements
The authors express deep gratitude to Departments of Mining Exploitation and Prospecting and Mathematics at Oviedo University as well as to Tecniproject Ltd Company for its computational support. We would like to thank Anthony Ashworth for his revision of the manuscript style.