Somers' Dxy Rank Correlation

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.

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.

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.

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.

Author

Frank Harrell
Department of Biostatistics
Vanderbilt University School of Medicine
fh@fharrell.com

See also

concordance, rcorr.cens, rank, wtd.rank,

Examples

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

# Check weights
x <- 1:6
y <- c(0,0,1,0,1,1)
f <- c(3,2,2,3,2,1)
somers2(x, y)
#>       C     Dxy       n Missing 
#>   0.889   0.778   6.000   0.000 
somers2(rep(x, f), rep(y, f))
#>       C     Dxy       n Missing 
#>    0.85    0.70   13.00    0.00 
somers2(x, y, f)
#>       C     Dxy       n Missing 
#>    0.85    0.70   13.00    0.00