# concordance

##### Compute the concordance statistic for data or a model

The concordance statistic compute the agreement between an observed response and a predictor. It is closely related to Kendall's tau-a and tau-b, Goodman's gamma, and Somers' d, all of which can also be calculated from the results of this function.

- Keywords
- survival

##### Usage

```
concordance(object, …)
# S3 method for 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, keepstrata=10, …)
# S3 method for lm
concordance(object, …, newdata, cluster, ymin, ymax,
influence=0, ranks=FALSE, timefix=TRUE, keepstrata=10)
# S3 method for coxph
concordance(object, …, newdata, cluster, ymin, ymax,
timewt= c("n", "S", "S/G", "n/G", "n/G2", "I"), influence=0,
ranks=FALSE, timefix=FALSE, keepstrata=10)
# S3 method for survreg
concordance(object, …, newdata, cluster, ymin, ymax,
timewt= c("n", "S", "S/G", "n/G", "n/G2", "I"), influence=0,
ranks=FALSE, timefix=FALSE, keepstrata=10)
```

##### Arguments

- object
a fitted model or a formula. The formula should be of the form

`y ~x`

or`y ~ x + strata(z)`

with a single numeric or survival response and a single predictor. Counts of concordant, discordant and tied pairs are computed separately per stratum, and then added.- data
a data.frame in which to interpret the variables named in the

`formula`

, or in the`subset`

and the`weights`

argument. Only applicable if`object`

is a formula.- weights
optional vector of case weights. Only applicable if

`object`

is a formula.- subset
expression indicating which subset of the rows of data should be used in the fit. Only applicable if

`object`

is a formula.- na.action
a missing-data filter function. This is applied to the model.frame after any subset argument has been used. Default is

`options()\$na.action`

. Only applicable if`object`

is a formula.- …
multiple fitted models are allowed. Only applicable if

`object`

is a model object.- 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

`x`

values predict smaller response values`y`

; a proportional hazards model is the common example of this.- 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.

- keepstrata
either TRUE, FALSE, or an integer value. Computations are always done within stratum, then added. If the total number of strata greater than

`keepstrata`

, or`keepstrata=FALSE`

, those subtotals are not kept in the output.

##### Details

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 c-statistic when the response is a survival time,
and (d+1)/2 when y is continuous, where d is Somers' d.

When the number of strata is very large, such as in a conditional
logistic regression for instance (`clogit`

function), a much
faster computation is available when the individual strata results
are not retained. In the more general case the `keepstrata = 10`

default simply keeps the printout managable.

##### Value

An object of class `concordance`

containing the following
components:

the estimated concordance value or values

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

the number of observations

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.

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 `survConcordance`

function.)

optional, the vector of leverage estimates for the concordance

optional, the matrix of leverage values for each of the counts, one row per observation

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.

##### See Also

##### Examples

```
# NOT RUN {
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
# }
```

*Documentation reproduced from package survival, version 3.1-8, License: LGPL (>= 2)*