Covariate-adjusted Spearman's rank correlation with probability-scale residuals

Area of Science:

• Statistics
• Biostatistics
• Correlation Analysis

Background:

• Existing methods for adjusting Spearman's rank correlation for covariates have limitations, lacking sensible population parameters or generalizability to discrete variables.
• There is a need for robust statistical methods to account for confounding variables in rank correlation analysis.

Purpose of the Study:

• To define population parameters for partial and conditional Spearman's rank correlation.
• To develop novel, easily interpretable estimators for adjusted Spearman's rank correlation.
• To provide a framework for rank-based correlation analysis in the presence of covariates.

Main Methods:

• Defined partial and conditional Spearman's correlation using concordance-discordance probabilities.
• Utilized probability-scale residuals (PSRs) to derive estimators for adjusted Spearman's correlation.
• Employed semiparametric cumulative probability models for estimation and inference.

Main Results:

• Developed a partial Spearman's correlation estimator analogous to partial Pearson's correlation using PSRs.
• Introduced a conditional Spearman's correlation estimator based on conditional PSRs.
• Simulations demonstrated the robustness and efficiency of the proposed estimators compared to existing measures.

Conclusions:

• The proposed methods provide natural and generalizable extensions of Spearman's rank correlation for covariate adjustment.
• The use of PSRs offers a unified approach to estimating adjusted rank correlations.
• The methods are applicable to various fields, including biomarker studies and survey research.