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The Stata Journal
Volume 6 Number 3: pp. 309-334



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Confidence intervals for rank statistics: Somers' D and extensions

Roger Newson
Imperial College London
London, UK
r.newson@imperial.ac.uk
Abstract.   Somers’ D is an asymmetric measure of association between two variables, which plays a central role as a parameter behind rank or nonparametric statistical methods. Given predictor variable X and outcome variable Y , we may estimate DYX as a measure of the effect of X on Y , or we may estimate DXY as a performance indicator of X as a predictor of Y. The somersd package allows the estimation of Somers’ D and Kendall’s τα with confidence limits as well as p-values. The Stata 9 version of somersd can estimate extended versions of Somers’ D not previously available, including the Gini index, the parameter tested by the sign test, and extensions to left- or right-censored data. It can also estimate stratified versions of Somers’ D, restricted to pairs in the same stratum. Therefore, it is possible to define strata by grouping values of a confounder, or of a propensity score based on multiple confounders, and to estimate versions of Somers’ D that measure the association between the outcome and the predictor, adjusted for the confounders. The Stata 9 version of somersd uses the Mata language for improved computational efficiency with large datasets.
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View all articles with these keywords: somersd, Somers' D, Kendall's τ_a, Harrell's c, ROC area, Gini index, population-attributable risk, rank correlation, rank-sum test, Wilcoxon test, sign test, confidence intervals, nonparametric methods, propensity score

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