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On the association between variables with lower detection limits.

Héla Romdhani¹, Lajmi Lakhal-Chaieb

¹Département de mathématiques et statistique, Université Laval, 1045 Av. dela médecine, Local 1056, Québec, QC G1V 0A6, Canada.

Statistics in Medicine

|September 8, 2011

Summary

This study introduces a modified Kendall's tau for censored data, offering a new way to measure variable association. The research provides estimators and tests for statistical modeling with left-censored data.

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Area of Science:

Statistics
Biostatistics
Statistical Modeling

Background:

Traditional Kendall's tau is sensitive to censored data.
Accurate association measures are crucial for analyzing biological and medical data with detection limits.

Purpose of the Study:

To develop a modified Kendall's tau (τ(b)) for assessing association in left-censored paired random variables.
To provide nonparametric estimators and analyze asymptotic properties of τ(b).
To estimate copula parameters and global Kendall's tau under Archimedean copula assumptions.

Main Methods:

Definition of a modified Kendall's tau (τ(b)) for left-censored data.
Development of a nonparametric estimator for τ(b) and analysis of its asymptotic properties.
Assumption of an Archimedean copula to relate τ(b) to copula parameters and censoring fractions.
Estimation of copula parameter (α) and global Kendall's tau.
Construction of a goodness-of-fit test for the assumed copula.

Main Results:

A novel modified Kendall's tau (τ(b)) is defined for left-censored data.
Nonparametric estimators for τ(b), copula parameter α, and global Kendall's tau are derived.
A goodness-of-fit test for Archimedean copulas is developed.
Simulations demonstrate the finite-sample performance of the proposed methods.

Conclusions:

The proposed methods provide a robust framework for analyzing association in left-censored data.
The methods are applicable to real-world datasets, such as viral load measurements.
This work advances statistical techniques for handling censored data in various scientific fields.