somers2 {Hmisc}

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
[e-mail]

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)
somers2(rep(x, f), rep(y, f))
somers2(x, y, f)