rcorr.cens {Hmisc}

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(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).

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 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

n

number of observations not missing on any input variables

missing

number of observations missing on x or S

relevant

number of pairs of non-missing observations for which S could be ordered

concordant

number of relevant pairs for which x and S are concordant.

uncertain

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.

Author(s)

Frank Harrell
Department of Biostatistics
Vanderbilt University
[e-mail]

References

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