Nonparametric estimation of Spearman's rank correlation with bivariate survival data

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Methods

Background:

• Estimating correlation between right-censored variables is challenging.
• Complete bivariate survival distribution is often not identifiable with end-of-study censoring.
• Nonparametric computation of Spearman's rank correlation is impossible in such cases.

Purpose of the Study:

• Propose novel, nonparametrically estimable correlation measures for right-censored data.
• Define and compare two new measures: Spearman's correlation in a restricted region and for an altered joint distribution.
• Illustrate the utility of these measures in a real-world HIV cohort study.

Main Methods:

• Developed two new rank-based correlation measures suitable for right-censored data.
• Defined population parameters for the proposed measures.
• Proposed consistent estimators for these measures.
• Evaluated estimator performance using simulation studies.

Main Results:

• The proposed measures are nonparametrically estimable.
• Population parameters are described and compared to overall Spearman's correlation.
• Simulation studies demonstrate the performance of the proposed estimators.
• Methods were applied to HIV data, assessing correlation between time to viral failure and regimen change.

Conclusions:

• The novel rank-based correlation measures provide viable alternatives for analyzing right-censored bivariate data.
• These methods address limitations in traditional correlation estimation under censoring.
• The approach is applicable to important public health questions, such as HIV treatment outcomes.