concordance.index: Function to compute the concordance index for survival or...
In survcomp: Performance Assessment and Comparison for Survival Analysis

Description Usage Arguments Value Note Author(s) References See Also Examples

Function to compute the concordance index for a risk prediction, i.e. the probability that, for a pair of randomly chosen comparable samples, the sample with the higher risk prediction will experience an event before the other sample or belongs to a higher binary class.

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concordance.index(x, surv.time, surv.event, cl, weights, comppairs=10,
strat, alpha = 0.05, outx = TRUE, method = c("conservative", "noether",
"nam"), alternative = c("two.sided", "less", "greater"), na.rm = FALSE)

`x`	a vector of risk predictions.
`surv.time`	a vector of event times.
`surv.event`	a vector of event occurence indicators.
`cl`	a vector of binary class indicators.
`weights`	weight of each sample.
`comppairs`	threshold for compairable patients.
`strat`	stratification indicator.
`alpha`	apha level to compute confidence interval.
`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.
`method`	can take the value `conservative`, `noether` or `name` (see paper Pencina et al. for details).
`alternative`	a character string specifying the alternative hypothesis, must be one of `"two.sided"` (default), `"greater"` (concordance index is greater than 0.5) or `"less"` (concordance index is less than 0.5). You can specify just the initial letter.
`na.rm`	`TRUE` if missing values should be removed.

`c.index`	concordance index estimate.
`se`	standard error of the estimate.
`lower`	lower bound for the confidence interval.
`upper`	upper bound for the confidence interval.
`p.value`	p-value for the statistical test if the estimate if different from 0.5.
`n`	number of samples used for the estimation.
`data`	list of data used to compute the index (`x`, `surv.time` and `surv.event`, or `cl`).
`comppairs`	number of compairable pairs.

The "direction" of the concordance index (< 0.5 or > 0.5) is the opposite than the rcorr.cens function in the Hmisc package. So you can easily get the same results than rcorr.cens by changing the sign of x.

Benjamin Haibe-Kains, Markus Schroeder

Harrel Jr, F. E. and Lee, K. L. and Mark, D. B. (1996) "Tutorial in biostatistics: multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing error", Statistics in Medicine, 15, pages 361–387.

Pencina, M. J. and D'Agostino, R. B. (2004) "Overall C as a measure of discrimination in survival analysis: model specific population value and confidence interval estimation", Statistics in Medicine, 23, pages 2109–2123, 2004.

rcorr.cens, phcpe, coxphCPE

set.seed(12345)
age <- rnorm(100, 50, 10)
sex <- sample(0:1, 100, replace=TRUE)
stime <- rexp(100)
cens   <- runif(100,.5,2)
sevent  <- as.numeric(stime <= cens)
stime <- pmin(stime, cens)
strat <- sample(1:3, 100, replace=TRUE)
weight <- runif(100, min=0, max=1)
comppairs <- 10
cat("survival prediction:\n")
concordance.index(x=age, surv.time=stime, surv.event=sevent, strat=strat,
  weights=weight, method="noether", comppairs=comppairs)
cat("binary class prediction:\n")
## is age predictive of sex?
concordance.index(x=age, cl=sex, strat=strat, method="noether")

Loading required package: survival
Loading required package: prodlim
survival prediction:
$c.index
[1] 0.5230613

$se
[1] 0.03343403

$lower
[1] 0.4575318

$upper
[1] 0.5885908

$p.value
[1] 0.4903484

$n
[1] 100

$data
$data$x
  [1] 55.85529 57.09466 48.90697 45.46503 56.05887 31.82044 56.30099 47.23816
  [9] 47.15840 40.80678 48.83752 68.17312 53.70628 55.20216 42.49468 58.16900
 [17] 41.13642 46.68422 61.20713 52.98724 57.79622 64.55785 43.55672 34.46863
 [25] 34.02290 68.05098 45.18353 56.20380 56.12123 48.37689 58.11873 71.96834
 [33] 70.49190 66.32446 52.54271 54.91188 46.75913 33.37950 67.67734 50.25801
 [41] 61.28511 26.19642 39.39734 59.37141 58.54452 64.60729 35.86901 55.67403
 [49] 55.83188 36.93201 44.59614 69.47693 50.53590 53.51663 43.29023 52.77954
 [57] 56.91171 58.23795 71.45065 26.53056 51.49592 36.57469 55.53303 65.89963
 [65] 44.13120 31.67623 58.88139 65.93488 55.16855 37.04328 50.54616 42.15351
 [73] 39.50647 73.30512 64.02705 59.42601 58.26258 41.88460 54.76248 60.21258
 [81] 56.45383 60.43144 46.95631 74.77111 59.71221 68.67099 56.72042 46.92047
 [89] 55.36524 58.24870 40.36099 41.44917 68.86947 46.08181 40.19367 56.87332
 [97] 44.94956 71.57720 44.00202 43.05453

$data$surv.time
  [1] 0.637853355 0.197314564 0.416581293 0.306881320 0.154827937 0.356571066
  [7] 1.096221586 1.406930427 1.064566905 0.847219292 0.938433472 0.365299973
 [13] 0.723795729 0.216887802 0.238225399 0.890783290 0.969024341 0.011000799
 [19] 1.663490611 1.397090765 0.473277677 0.349694525 0.896520485 0.459397995
 [25] 1.094637862 0.356546675 0.253164558 0.590390556 0.030716643 0.369448074
 [31] 0.244754504 0.440600901 0.170370805 0.150545259 1.384699555 0.574045110
 [37] 0.996481281 1.559945725 0.861266141 0.434629776 0.176064291 0.142967952
 [43] 0.060913060 0.569092280 0.430919448 0.992690456 0.924182842 0.613625630
 [49] 0.920003573 0.356111097 0.568598574 0.130677740 0.022247792 0.116445919
 [55] 1.007857130 0.984365617 1.003222533 0.821054509 0.010615575 0.684983060
 [61] 1.678080778 0.853088171 0.192398773 1.657698993 0.164590429 1.164628168
 [67] 0.083792265 0.433889239 1.360584810 1.896422504 0.481232862 0.540298133
 [73] 0.077356379 1.245692946 0.778048342 0.762629318 1.734777190 0.678462227
 [79] 1.249678811 0.687199211 0.187438627 0.247703603 0.980026351 0.862026664
 [85] 0.134605087 1.576969599 0.075869365 0.525945421 0.618154488 1.404378374
 [91] 0.366814601 0.966280999 1.165185511 0.519370650 1.293312739 1.066429030
 [97] 0.645233040 0.009719983 0.392513916 0.177425891

$data$surv.event
  [1] 0 1 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0
 [38] 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1 1 1 1
 [75] 1 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1


$comppairs
[1] 808.7589

binary class prediction:
$c.index
[1] 0.4337789

$se
[1] 0.0548467

$lower
[1] 0.3262813

$upper
[1] 0.5412764

$p.value
[1] 0.2272835

$n
[1] 100

$data
$data$x
  [1] 55.85529 57.09466 48.90697 45.46503 56.05887 31.82044 56.30099 47.23816
  [9] 47.15840 40.80678 48.83752 68.17312 53.70628 55.20216 42.49468 58.16900
 [17] 41.13642 46.68422 61.20713 52.98724 57.79622 64.55785 43.55672 34.46863
 [25] 34.02290 68.05098 45.18353 56.20380 56.12123 48.37689 58.11873 71.96834
 [33] 70.49190 66.32446 52.54271 54.91188 46.75913 33.37950 67.67734 50.25801
 [41] 61.28511 26.19642 39.39734 59.37141 58.54452 64.60729 35.86901 55.67403
 [49] 55.83188 36.93201 44.59614 69.47693 50.53590 53.51663 43.29023 52.77954
 [57] 56.91171 58.23795 71.45065 26.53056 51.49592 36.57469 55.53303 65.89963
 [65] 44.13120 31.67623 58.88139 65.93488 55.16855 37.04328 50.54616 42.15351
 [73] 39.50647 73.30512 64.02705 59.42601 58.26258 41.88460 54.76248 60.21258
 [81] 56.45383 60.43144 46.95631 74.77111 59.71221 68.67099 56.72042 46.92047
 [89] 55.36524 58.24870 40.36099 41.44917 68.86947 46.08181 40.19367 56.87332
 [97] 44.94956 71.57720 44.00202 43.05453

$data$cl
  [1] 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 1
 [38] 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 1
 [75] 1 0 1 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 0


$comppairs
[1] 1646