Evaluating Aortic Stenosis using the Archimedean copula methodology

Abstract

Abstract: In modeling and analyzing multivariate data, the conventionally used measure of dependence structure is the Pearson's correlation coefficient. However use of the correlation as a dependence measure has several pitfalls. Copulas recently have emerged as an alternative measure of the dependence, overcoming most of the drawbacks of the correlation. We discuss Archimedean copulas and their relationships with tail dependence. An algorithm to construct empirical and Archimedean copulas is described. Monte Carlo simulations are carried out to replicate and analyze data sets by identifying the appropriate copula. We apply the Archimedean copula based methodology to assess the accuracy of Doppler echocardiography in determining aortic valve area from the Aortic Stenosis: Simultaneous DopplerCatheter Correlative study carried out at the King Faisal Specialist Hospital and Research Centre, Riyadh, KSA