concordance {survival}  R Documentation 
The concordance statistic compute the agreement between an observed response and a predictor. It is closely related to Kendall's taua and taub, Goodman's gamma, and Somers' d, all of which can also be calculated from the results of this function.
concordance(object, ...) ## S3 method for class 'formula' concordance(object, data, weights, subset, na.action, cluster, ymin, ymax, timewt= c("n", "S", "S/G", "n/G", "n/G2", "I"), influence=0, ranks = FALSE, reverse=FALSE, timefix=TRUE, ...) ## S3 method for class 'lm' concordance(object, ..., newdata, cluster, ymin, ymax, influence=0, ranks=FALSE, timefix=TRUE) ## S3 method for class 'coxph' concordance(object, ..., newdata, cluster, ymin, ymax, timewt= c("n", "S", "S/G", "n/G", "n/G2", "I"), influence=0, ranks=FALSE, timefix=FALSE) ## S3 method for class 'survreg' concordance(object, ..., newdata, cluster, ymin, ymax, timewt= c("n", "S", "S/G", "n/G", "n/G2", "I"), influence=0, ranks=FALSE, timefix=FALSE)
object 
a fitted model or a formula. The formula should be of
the form 
data 
a data.frame in which to interpret the variables named in
the 
weights 
optional vector of case weights.
Only applicable if 
subset 
expression indicating which subset of the rows of data should be used in
the fit. Only applicable if 
na.action 
a missingdata filter function. This is applied to the model.frame
after any subset argument has been used. Default is

... 
multiple fitted models are allowed. Only applicable if

newdata 
optional, a new data frame in which to evaluate (but not refit) the models 
cluster 
optional grouping vector for calculating the robust variance 
ymin, ymax 
compute the concordance over the restricted range ymin <= y <= ymax. (For survival data this is a time range.) 
timewt 
the weighting to be applied. The overall statistic is a weighted mean over event times. 
influence 
1= return the dfbeta vector, 2= return the full influence matrix, 3 = return both 
ranks 
if TRUE, return a data frame containing the individual ranks that make up the overall score. 
reverse 
if TRUE then assume that larger 
timefix 
if the response is a Surv object, correct for possible rounding error; otherwise this argument has no effect. See the vignette on tied times for more explanation. For the coxph and survreg methods this issue will have already been addressed in the parent routine, so should not be revisited. 
At each event time, compute the rank of the subject who had the
event as compared to all others with a longer survival, where the
rank is value between 0 and 1. The concordance is a weighted mean
of these values, determined by the timewt
option.
For uncensored data each unique response value is compared to all
those which are larger.
Using the default value for timewt
, this gives the area
under the receiver operating curve (AUC) for a binary response,
Harrell's cstatistic when the response is a survival time,
and (d+1)/2 when y is continuous, where d is Somers' d.
An object of class concordance
containing the following
components:
concordance 
the estimated concordance value or values 
count 
a vector containing the number of concordant pairs, discordant, tied on x but not y, tied on y but not x, and tied on both x and y 
n 
the number of observations 
var 
a vector containing the estimated variance of the concordance based on the infinitesimal jackknife (IJ) method. If there are multiple models it contains the estimtated variance/covariance matrix. 
cvar 
a vector containing the estimated variance(s) of the
concordance values, based on the variance formula for the associated
score test from a proportional hazards model. (This was the primary
variance used in the 
dfbeta 
optional, the vector of leverage estimates for the concordance 
influence 
optional, the matrix of leverage values for each of the counts, one row per observation 
ranks 
optional, a data frame containing the Somers' d rank at each event time, along with the time weight, case weight of the observation with an event, and variance (contribution to the proportional hazards model information matrix). A weighted mean of the ranks equals Somer's d. 
Terry Therneau
fit1 < coxph(Surv(ptime, pstat) ~ age + sex + mspike, mgus2) concordance(fit1, timewt="n") # # logistic regression fit2 < glm(pstat ~ age + sex + mspike, binomial, data= mgus2) concordance(fit2) # equal to the AUC