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)
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.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.
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.
Frank Harrell
Department of Biostatistics
Vanderbilt University School of Medicine
concordance, rcorr.cens, rank, wtd.rank,
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)