Spearman-like correlation measure adjusting for covariates in bivariate survival data

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Correlation

Background:

• Existing Spearman's correlation estimators for censored data have limitations.
• Nonparametric methods require complex bivariate survival surface estimation.
• Semiparametric methods rely on potentially unmet parametric assumptions about dependence structure.

Purpose of the Study:

• To propose a novel extension of Spearman's correlation for censored continuous and discrete data.
• To enable covariate adjustment in correlation estimation.
• To provide a method that avoids complex survival surface estimation and restrictive parametric assumptions.

Main Methods:

• The proposed method estimates the correlation of probability-scale residuals.
• It relies solely on marginal survival distributions, not bivariate surfaces or parametric models.
• The method is extended to calculate partial, conditional, and partial-conditional correlations.

Main Results:

• The new method is less variable than existing nonparametric estimators.
• Confidence intervals are easily constructed.
• While biased under censoring, it shows good performance with smaller mean squared error than nonparametric approaches under moderate censoring.

Conclusions:

• The proposed method offers a practical and robust extension of Spearman's correlation for censored data with covariate adjustment.
• It is particularly relevant for applications where marginal distributions are known or can be reliably estimated.
• The method was successfully applied to estimate correlations in a cohort of individuals living with HIV.