rcorr.cens {Hmisc}  R Documentation 
Rank Correlation for Censored Data
Description
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
Dxy=2(c0.5)
.
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).
Usage
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,
...)
Arguments
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 
Value
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 nonmissing observations for which

concordant 
number of relevant pairs for which 
uncertain 
number of pairs of nonmissing observations for which
censoring prevents classification of concordance of 
rcorrcens.formula
returns an object of class biVar
which is documented with the biVar
function.
Author(s)
Frank Harrell
Department of Biostatistics
Vanderbilt University
fh@fharrell.com
References
Newson R: Confidence intervals for rank statistics: Somers' D and extensions. Stata Journal 6:309334; 2006.
See Also
concordance
, somers2
, biVar
, rcorrp.cens
Examples
set.seed(1)
x < round(rnorm(200))
y < rnorm(200)
rcorr.cens(x, y, outx=TRUE) # can correlate noncensored 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 nonevents, for varying population ROC areas
# Repeat for 138 events and 102 nonevents
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 < C1.96*se; hi < C+1.96*se
print(cbind(C, low, hi))
errbar(deltas, C, C+1.96*se, C1.96*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))