On Measuring Dependence of Objects Related by a Tree

• Activity Number: 639
• Type: Topic Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Alexander V. Alekseyenko*+ and Marc A. Suchard and Nick Goldman
• Companies: New York University School of Medicine, Center for Health Informatics and Bioinformatics and UCLA and EMBL-European Bioinformatics Institute
• Keywords: dentity by descent ; weighting ; independence ; phylogenetic dependence

Abstract

Sets of evolutionarily related objects are common subjects of statistical analyses in biomedicine. Examples of such sets include infectious agents, constituents of microbial flora, protein sequences, etc. The evolutionary relatedness through a phylogeny introduces dependence between the respective measurements of quantities of interest between these objects. This dependence often needs to be accounted for explicitly in calculations. For instance, a naïve counting algorithm to establish the number of times a particular variant arose in a set of sequences, will result in overcounting if the dependences are not accounted for. In such settings, we propose to use calculations based on the concept of identity by descent to derive a measure of the amount of unique information that a set of phylogenetically related objects possesses and the contribution of each individual object to this total information. These derivations may effectively be used to abstract the phylogenetic structure through weighting by the amount of independent information. We present the mathematical setting of the problem, computational solution to the weighting problem and describe several applications.