Confidence intervals for rank statistics: Somers’ D and extensions

Somers’ D is an asymmetric measure of association between two variables, which plays a central role as a parameter behind rank or “non–parametric” statistical methods. Given a predictor variable X and an outcome variable Y , we may estimate DY X 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 τa 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 which 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.