title: On the association between variables with lower detection limits.
abstract: In this paper, we define a modified version τ(b) of Kendall's tau to measure the association in a pair (X,Y) of random variables subject to fixed left censoring due to known lower detection limits. We provide a nonparametric estimator of τ(b) and investigate its asymptotic properties. We then assume an Archimedean copula for (X,Y) and express τ(b) in terms of the copula parameter α and the censoring fractions. We deduce estimators for α and for the global Kendall's tau. We develop a goodness-of-fit test for the assumed copula. We evaluate the finite-sample performance of the proposed methods by simulations and illustrate their use with a real data set on plasma and saliva viral loads.
authors: Département de mathématiques et statistique, Université Laval, 1045 Av. dela médecine, Local 1056, Québec, QC G1V 0A6, Canada.
authors: Héla
authors: H
authors: Romdhani
authors: Lajmi
authors: L
authors: Lakhal-Chaieb
mesh_terms: D000465:Algorithms; D001769:Blood / Q000821:virology; D003198:Computer Simulation / Q000706:statistics & numerical data; D005260:Female; D006801:Humans; D057230:Limit of Detection; D015233:Models, Statistical; D012463:Saliva / Q000821:virology; D018709:Statistics, Nonparametric; D016019:Survival Analysis