rcorr.cens: 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 formula
rcorrcens(formula, data=NULL, subset=NULL,
          na.action=na.retain, exclude.imputed=TRUE, outx=FALSE,
          ...)

Arguments

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.

References

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

Examples

Run this code

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))