# rcorr.cens

##### 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).

- Keywords
- nonparametric, survival

##### Usage

`rcorr.cens(x, S, outx=FALSE)`# S3 method for formula
rcorrcens(formula, data=NULL, subset=NULL,
na.action=na.retain, exclude.imputed=TRUE, outx=FALSE,
…)

##### Arguments

- x
a numeric predictor variable

- S
an

`Surv`

object or a vector. If a vector, assumes that every observation is uncensored.- outx
set to

`TRUE`

to not count pairs of observations tied on`x`

as a relevant pair. This results in a Goodman--Kruskal gamma type rank correlation.- formula
a formula with a

`Surv`

object or a numeric vector on the left-hand side- data, subset, na.action
the usual options for models. Default for

`na.action`

is to retain all values, NA or not, so that NAs can be deleted in only a pairwise fashion.- exclude.imputed
set to

`FALSE`

to include imputed values (created by`impute`

) in the calculations.- …
extra arguments passed to

`biVar`

.

##### Value

`rcorr.cens`

returns a vector with the following named elements:
`C Index`

, `Dxy`

, `S.D.`

, `n`

, `missing`

,
`uncensored`

, `Relevant Pairs`

, `Concordant`

, and
`Uncertain`

number of observations not missing on any input variables

number of observations missing on `x`

or `S`

number of pairs of non-missing observations for which
`S`

could be ordered

number of relevant pairs for which `x`

and `S`

are concordant.

number of pairs of non-missing observations for which
censoring prevents classification of concordance of `x`

and
`S`

.

rcorrcens.formula returns an object of class biVar which is documented with the biVar function.

##### References

Newson R: Confidence intervals for rank statistics: Somers' D and extensions. Stata Journal 6:309-334; 2006.

##### See Also

##### Examples

```
# NOT RUN {
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))
# }
```

*Documentation reproduced from package Hmisc, version 4.1-1, License: GPL (>= 2)*