Cindex {SurvMetrics}

The Concordance Index for Right-Censored Survival Time Data

Description

Concordance index is a rank correlation measures between a variable X and a possibly censored variable Y, with event/censoring indicator. In survival analysis, a pair of patients is called concordant if the risk of the event predicted by a model is lower for the patient who experiences the event at a later timepoint. The concordance probability (C-index) is the frequency of concordant pairs among all pairs of subjects. It can be used to measure and compare the discriminative power of a risk prediction models.

Usage

Cindex(object, predicted, t_star = -1)

Arguments

object

object of class Surv created by Surv function or a fitted survival model, including the survival model fitted by coxph, survreg, and rfsrc.

predicted

If the input of the parameter object is a fitted survival model, this parameter should be a survival dataset on which you want to caculate the C-index of the fitted model. Or with an object of class Surv as the parameter object, it should be a vector containing the predicted survival time or probability of each observation.

t_star

the timepoint at which the C-index you want to calculate. If the input of the parameter object is a fitted survival model, the timepoint is necessary to be specified at which the survival probability is predicted, and this function will calculate the C-index between the survival time and the predicted result at that moment. If the input object is a survival object, this parameter can be ignored and the value of this parameter will not have any effect on the result of this fuction.

Details

Pairs with identical observed times, where one is uncensored and one is censored, are always considered usuable (independent of the value of tiedOutcomeIn), as it can be assumed that the event occurs at a later timepoint for the censored observation.

For uncensored response the result equals the one obtained with the functions rcorr.cens and rcorrcens from the Hmisc package (see examples).

Value

Estimates of the C-index between the survival time and the predicted result.

Author(s)

Hanpu Zhou [e-mail]

References

Ishwaran, H. , Kogalur, U. B. , Blackstone, E. H. , & Lauer, M. S. . (2008). Random survival forests. Journal of Thoracic Oncology Official Publication of the International Association for the Study of Lung Cancer, 2(12), 841-860.

Kang, L. , Chen, W. , Petrick, N. A. , & Gallas, B. D. . (2015). Comparing two correlated c indices with right-censored survival outcome: a one-shot nonparametric approach. Statistics in Medicine, 34(4).

TA Gerds, MW Kattan, M Schumacher, and C Yu. Estimating a time-dependent concordance index for survival prediction models with covariate dependent censoring. Statistics in Medicine, Ahead of print:to appear, 2013. DOI = 10.1002/sim.5681

Wolbers, M and Koller, MT and Witteman, JCM and Gerds, TA (2013) Concordance for prognostic models with competing risks Research report 13/3. Department of Biostatistics, University of Copenhagen

Andersen, PK (2012) A note on the decomposition of number of life years lost according to causes of death Research report 12/2. Department of Biostatistics, University of Copenhagen

Paul Blanche, Michael W Kattan, and Thomas A Gerds. The c-index is not proper for the evaluation of-year predicted risks. Biostatistics, 20(2): 347–357, 2018.

Examples

library(survival)
time <- c(1, 1, 2, 2, 2, 2, 2, 2)
status <- c(0, 1, 1, 0, 1, 1, 0, 1)
predicted <- c(2, 3, 3, 3, 4, 2, 4, 3)
Cindex(Surv(time, status), predicted)