Evaluating Aortic Stenosis Using the Archimedean Copula Methodology

Abstract

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