Rank Correlation for Censored Data
Computes the c index and the corresponding generalization of Somers' Dxy rank correlation for a censored response variable. Also works for uncensored and binary responses, although its use of all possible pairings makes it slow for this purpose. Dxy and c are related by \var{Dxy} = 2*(\var{c} - 0.5).
rcorr.cens handles one predictor variable. rcorrcens
computes rank correlation measures separately by a series of
predictors. In addition, rcorrcens has a rough way of handling
categorical predictors. If a categorical (factor) predictor has two
levels, it is coverted to a numeric having values 1 and 2. If it has
more than 2 levels, an indicator variable is formed for the most
frequently level vs. all others, and another indicator for the second
most frequent level and all others. The correlation is taken as the
maximum of the two (in absolute value).
rcorr.cens(x, S, outx=FALSE)
## S3 method for class 'formula'
rcorrcens(formula, data=NULL, subset=NULL,
na.action=na.retain, exclude.imputed=TRUE, outx=FALSE,
...)x |
a numeric predictor variable |
S |
an |
outx |
set to |
formula |
a formula with a |
data, subset, na.action |
the usual options for models. Default for |
exclude.imputed |
set to |
... |
extra arguments passed to |
rcorr.cens returns a vector with the following named elements:
C Index, Dxy, S.D., n, missing,
uncensored, Relevant Pairs, Concordant, and
Uncertain
n |
number of observations not missing on any input variables |
missing |
number of observations missing on |
relevant |
number of pairs of non-missing observations for which
|
concordant |
number of relevant pairs for which |
uncertain |
number of pairs of non-missing observations for which
censoring prevents classification of concordance of |
rcorrcens.formula returns an object of class biVar
which is documented with the biVar function.
Frank Harrell
Department of Biostatistics
Vanderbilt University
fh@fharrell.com
Newson R: Confidence intervals for rank statistics: Somers' D and extensions. Stata Journal 6:309-334; 2006.
set.seed(1)
x <- round(rnorm(200))
y <- rnorm(200)
rcorr.cens(x, y, outx=TRUE) # can correlate non-censored variables
library(survival)
age <- rnorm(400, 50, 10)
bp <- rnorm(400,120, 15)
bp[1] <- NA
d.time <- rexp(400)
cens <- runif(400,.5,2)
death <- d.time <= cens
d.time <- pmin(d.time, cens)
rcorr.cens(age, Surv(d.time, death))
r <- rcorrcens(Surv(d.time, death) ~ age + bp)
r
plot(r)
# Show typical 0.95 confidence limits for ROC areas for a sample size
# with 24 events and 62 non-events, for varying population ROC areas
# Repeat for 138 events and 102 non-events
set.seed(8)
par(mfrow=c(2,1))
for(i in 1:2) {
n1 <- c(24,138)[i]
n0 <- c(62,102)[i]
y <- c(rep(0,n0), rep(1,n1))
deltas <- seq(-3, 3, by=.25)
C <- se <- deltas
j <- 0
for(d in deltas) {
j <- j + 1
x <- c(rnorm(n0, 0), rnorm(n1, d))
w <- rcorr.cens(x, y)
C[j] <- w['C Index']
se[j] <- w['S.D.']/2
}
low <- C-1.96*se; hi <- C+1.96*se
print(cbind(C, low, hi))
errbar(deltas, C, C+1.96*se, C-1.96*se,
xlab='True Difference in Mean X',
ylab='ROC Area and Approx. 0.95 CI')
title(paste('n1=',n1,' n0=',n0,sep=''))
abline(h=.5, v=0, col='gray')
true <- 1 - pnorm(0, deltas, sqrt(2))
lines(deltas, true, col='blue')
}
par(mfrow=c(1,1))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.