Abstract:
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We propose a new approach to examine the rank correlation between two variables X and Y while adjusting for continuous and/or categorical covariates Z. Our approach first fits two separate regression models of X on Z and Y on Z, obtains probability-scale residuals from these two models, and then tests for correlation between the residuals. In the absence of covariates, this residual can be written as a linear transformation of the ranks, and our test statistics is therefore equivalent to Spearman's rank correlation. With covariates, our test statistic estimates the average rank correlation across different levels of Z. Therefore, our approach can be considered a generalization of Spearman's rank correlation. Through simulations, we demonstrate that our approach shares some of the good properties of Spearman's rank correlation: 1) it can handle ordinal variables; 2) it can efficiently capture non-linear monotonic correlation; 3) it is less sensitive to outliers; and 4) it is invariant under monotonic transformation of X and Y when residuals are computed from ordinal regression models. We illustrate the approach using data from HIV-infected patients in Latin America.
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