Somers' Dxy Rank Correlation

DESCRIPTION:

Computes Somers' Dxy rank correlation between a variable x and a binary (0-1) variable y, and the corresponding receiver operating characteristic curve area c. Note that Dxy = 2(c-0.5). somers allows for a weights variable, which specifies frequencies to associate with each observation.

USAGE:

somers2(x, y, weights=NULL, normwt=FALSE, na.rm=TRUE)

ARGUMENTS:

x
typically a predictor variable. NAs are allowed.
y
a numeric outcome variable coded 0-1. NAs are allowed.
weights
a numeric vector of observation weights (usually frequencies). Omit or specify a zero-length vector to do an unweighted analysis.
normwt
set to TRUE to make weights sum to the actual number of non-missing observations.
na.rm
set to FALSE to suppress checking for NAs.

DETAILS:

The rcorr.cens function, which although slower than somers2 for large sample sizes, can also be used to obtain Dxy for non-censored binary y , and it has the advantage of computing the standard deviation of the correlation index.

VALUE:

a vector with the named elements C, Dxy, n (number of non-missing pairs), and Missing. Uses the formula C = (mean(rank(x)[y == 1]) - (n1 + 1)/2)/(n - n1) , where n1 is the frequency of y=1.

AUTHOR(S):

Frank Harrell
Department of Biostatistics
Vanderbilt University School of Medicine
f.harrell@vanderbilt.edu

SEE ALSO:

, , ,

EXAMPLES:

set.seed(1)
predicted <- runif(200)
dead      <- sample(0:1, 200, TRUE)
roc.area <- somers2(predicted, dead)["C"]