Confidence Intervals for Rank Statistics: Somers’ D and Extensions

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 D YX 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 τ A 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.