“Covariate-adjusted Spearman’s rank correlation for biomarker data”
Abstract: It is desirable to adjust Spearman’s rank correlation for covariates, yet existing approaches have limitations. For example, the traditionally defined partial Spearman’s correlation does not have a sensible population parameter, and conditional Spearman’s correlation defined with copulas cannot be easily generalized to discrete variables. I will define population parameters for both partial and conditional Spearman’s correlation. I will show that they can be neatly expressed and estimated using probability-scale residuals (PSRs). Our partial estimator for Spearman’s correlation between X and Y adjusted for Z is the correlation of PSRs from models of X on Z and of Y on Z, which is analogous to the partial Pearson’s correlation derived as the correlation of observed-minus-expected residuals. As part of this talk, I will discuss a robust approach for fitting semiparametric models of X on Z by using ordinal cumulative probability models. Finally, I will demonstrate the use of the method using HIV biomarker data.
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