compute C index for a Cox model

Computes Harrel's C index for predictions from a "coxnet" object.

Usage

Cindex(pred, y, weights = rep(1, nrow(y)))

Arguments

pred: Predictions from a "coxnet" object
y: a survival response object - a matrix with two columns "time" and "status"; see documentation for "glmnet"
weights: optional observation weights

Details

Computes the concordance index, taking into account censoring.

References

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.

Author

Trevor Hastie hastie@stanford.edu

Examples


set.seed(10101)
N = 1000
p = 30
nzc = p/3
x = matrix(rnorm(N * p), N, p)
beta = rnorm(nzc)
fx = x[, seq(nzc)] %*% beta/3
hx = exp(fx)
ty = rexp(N, hx)
tcens = rbinom(n = N, prob = 0.3, size = 1)  # censoring indicator
y = cbind(time = ty, status = 1 - tcens)  # y=Surv(ty,1-tcens) with library(survival)
fit = glmnet(x, y, family = "cox")
#> Warning: Starting in glmnet 5.1, the default Cox tie-handling method will change from 'breslow' to 'efron' (matching survival::coxph). To silence this message and lock in the v5.0 default, pass cox.ties = 'breslow' explicitly. To preview the v5.1 behavior, pass cox.ties = 'efron'.
pred = predict(fit, newx = x)
apply(pred, 2, Cindex, y=y)
#>        s0        s1        s2        s3        s4        s5        s6        s7 
#> 0.5000000 0.6203213 0.6724097 0.6850296 0.6891333 0.6981636 0.7017994 0.7038931 
#>        s8        s9       s10       s11       s12       s13       s14       s15 
#> 0.7059060 0.7104746 0.7145898 0.7189649 0.7215120 0.7235392 0.7256127 0.7277411 
#>       s16       s17       s18       s19       s20       s21       s22       s23 
#> 0.7286190 0.7296009 0.7300918 0.7305654 0.7308167 0.7311054 0.7313451 0.7317437 
#>       s24       s25       s26       s27       s28       s29       s30       s31 
#> 0.7320584 0.7325061 0.7327342 0.7329132 0.7330490 0.7331067 0.7332482 0.7333464 
#>       s32       s33       s34       s35       s36       s37       s38       s39 
#> 0.7335053 0.7337681 0.7337969 0.7339298 0.7338836 0.7339933 0.7340164 0.7340568 
#>       s40       s41       s42       s43       s44       s45       s46       s47 
#> 0.7341319 0.7341955 0.7342099 0.7342763 0.7343283 0.7342561 0.7342648 0.7342445 
#>       s48 
#> 0.7342157 
cv.glmnet(x, y, family = "cox", type.measure = "C")
#> Warning: Starting in glmnet 5.1, the default Cox tie-handling method will change from 'breslow' to 'efron' (matching survival::coxph). To silence this message and lock in the v5.0 default, pass cox.ties = 'breslow' explicitly. To preview the v5.1 behavior, pass cox.ties = 'efron'.
#> Warning: Starting in glmnet 5.1, the default Cox tie-handling method will change from 'breslow' to 'efron' (matching survival::coxph). To silence this message and lock in the v5.0 default, pass cox.ties = 'breslow' explicitly. To preview the v5.1 behavior, pass cox.ties = 'efron'.
#> Warning: Starting in glmnet 5.1, the default Cox tie-handling method will change from 'breslow' to 'efron' (matching survival::coxph). To silence this message and lock in the v5.0 default, pass cox.ties = 'breslow' explicitly. To preview the v5.1 behavior, pass cox.ties = 'efron'.
#> Warning: Starting in glmnet 5.1, the default Cox tie-handling method will change from 'breslow' to 'efron' (matching survival::coxph). To silence this message and lock in the v5.0 default, pass cox.ties = 'breslow' explicitly. To preview the v5.1 behavior, pass cox.ties = 'efron'.
#> Warning: Starting in glmnet 5.1, the default Cox tie-handling method will change from 'breslow' to 'efron' (matching survival::coxph). To silence this message and lock in the v5.0 default, pass cox.ties = 'breslow' explicitly. To preview the v5.1 behavior, pass cox.ties = 'efron'.
#> Warning: Starting in glmnet 5.1, the default Cox tie-handling method will change from 'breslow' to 'efron' (matching survival::coxph). To silence this message and lock in the v5.0 default, pass cox.ties = 'breslow' explicitly. To preview the v5.1 behavior, pass cox.ties = 'efron'.
#> Warning: Starting in glmnet 5.1, the default Cox tie-handling method will change from 'breslow' to 'efron' (matching survival::coxph). To silence this message and lock in the v5.0 default, pass cox.ties = 'breslow' explicitly. To preview the v5.1 behavior, pass cox.ties = 'efron'.
#> Warning: Starting in glmnet 5.1, the default Cox tie-handling method will change from 'breslow' to 'efron' (matching survival::coxph). To silence this message and lock in the v5.0 default, pass cox.ties = 'breslow' explicitly. To preview the v5.1 behavior, pass cox.ties = 'efron'.
#> Warning: Starting in glmnet 5.1, the default Cox tie-handling method will change from 'breslow' to 'efron' (matching survival::coxph). To silence this message and lock in the v5.0 default, pass cox.ties = 'breslow' explicitly. To preview the v5.1 behavior, pass cox.ties = 'efron'.
#> Warning: Starting in glmnet 5.1, the default Cox tie-handling method will change from 'breslow' to 'efron' (matching survival::coxph). To silence this message and lock in the v5.0 default, pass cox.ties = 'breslow' explicitly. To preview the v5.1 behavior, pass cox.ties = 'efron'.
#> Warning: Starting in glmnet 5.1, the default Cox tie-handling method will change from 'breslow' to 'efron' (matching survival::coxph). To silence this message and lock in the v5.0 default, pass cox.ties = 'breslow' explicitly. To preview the v5.1 behavior, pass cox.ties = 'efron'.
#> 
#> Call:  cv.glmnet(x = x, y = y, type.measure = "C", family = "cox") 
#> 
#> Measure: C-index 
#> 
#>      Lambda Index Measure      SE Nonzero
#> min 0.01920    28  0.7269 0.01170      14
#> 1se 0.08509    12  0.7155 0.01094       8