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Confidence intervals for rank statistics: Somers' D and extensions

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  • Roger Newson

    (Imperial College London)

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 D(XY) as a performance indicator of X as a predictor of Y. The somersd package allows the estimation of Somers’ D and Kendall’s tau-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. Copyright 2006 by StataCorp LP.

Suggested Citation

  • Roger Newson, 2006. "Confidence intervals for rank statistics: Somers' D and extensions," Stata Journal, StataCorp LP, vol. 6(3), pages 309-334, September.
    • Handle: RePEc:tsj:stataj:v:6:y:2006:i:3:p:309-334
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    References listed on IDEAS

    as
    1. Roger Newson, 2001. "somersd-Confidence intervals for nonparametric statistics and their differences," Stata Technical Bulletin, StataCorp LP, vol. 10(55).
    2. D. Kerridge, 1975. "The Interpretation of Rank Correlations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(2), pages 257-258, June.
    3. Kosuke Imai & David A. van Dyk, 2004. "Causal Inference With General Treatment Regimes: Generalizing the Propensity Score," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 854-866, January.
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