rcorrp.cens
Rank Correlation for Paired Predictors with a Possibly Censored Response, and Integrated Discrimination Index
Computes Ustatistics to test for whether predictor X1 is more
concordant than predictor X2, extending rcorr.cens
. For
method=1
, estimates the fraction of pairs for which the
x1
difference is more impressive than the x2
difference. For method=2
, estimates the fraction of pairs for
which x1
is concordant with S
but x2
is not.
For binary responses the function improveProb
provides several
assessments of whether one set of predicted probabilities is better
than another, using the methods describe in
Pencina et al (2007). This involves NRI and IDI to test for
whether predictions from model x1
are significantly different
from those obtained from predictions from model x2
. This is a
distinct improvement over comparing ROC areas, sensitivity, or
specificity.
 Keywords
 regression, nonparametric, survival
Usage
rcorrp.cens(x1, x2, S, outx=FALSE, method=1)
improveProb(x1, x2, y)
"print"(x, digits=3, conf.int=.95, ...)
Arguments
 x1

first predictor (a probability, for
improveProb
)  x2

second predictor (a probability, for
improveProb
)  S

a possibly rightcensored
Surv
object. IfS
is a vector instead, it is converted to aSurv
object and it is assumed that no observations are censored.  outx

set to
TRUE
to exclude pairs tied onx1
orx2
from consideration  method
 see above
 y
 a binary 0/1 outcome variable
 x

the result from
improveProb
 digits

number of significant digits for use in printing the result of
improveProb
 conf.int
 level for confidence limits
 ...
 unused
Details
If x1
,x2
represent predictions from models, these
functions assume either that you are using a separate sample from the
one used to build the model, or that the amount of overfitting in
x1
equals the amount of overfitting in x2
. An example
of the latter is giving both models equal opportunity to be complex so
that both models have the same number of effective degrees of freedom,
whether a predictor was included in the model or was screened out by a
variable selection scheme.
Note that in the first part of their paper, Pencina et al.
presented measures that required binning the predicted probabilities.
Those measures were then replaced with better continuous measures that
are implementedhere.
Value

a vector of statistics for
rcorrp.cens
, or a list with class
improveProb
of statistics for improveProb
:References
Pencina MJ, D'Agostino Sr RB, D'Agostino Jr RB, Vasan RS (2008): Evaluating the added predictive ability of a new marker: From area under the ROC curve to reclassification and beyond. Stat in Med 27:157172. DOI: 10.1002/sim.2929 Pencina MJ, D'Agostino Sr RB, D'Agostino Jr RB, Vasan RS: Rejoinder: Comments on Integrated discrimination and net reclassification improvementsPractical advice. Stat in Med 2007; DOI: 10.1002/sim.3106
Pencina MJ, D'Agostino RB, Steyerberg EW (2011): Extensions of net reclassification improvement calculations to measure usefulness of new biomarkers. Stat in Med 30:1121; DOI: 10.1002/sim.4085
See Also
Examples
set.seed(1)
library(survival)
x1 < rnorm(400)
x2 < x1 + rnorm(400)
d.time < rexp(400) + (x1  min(x1))
cens < runif(400,.5,2)
death < d.time <= cens
d.time < pmin(d.time, cens)
rcorrp.cens(x1, x2, Surv(d.time, death))
#rcorrp.cens(x1, x2, y) ## no censoring
set.seed(1)
x1 < runif(1000)
x2 < runif(1000)
y < sample(0:1, 1000, TRUE)
rcorrp.cens(x1, x2, y)
improveProb(x1, x2, y)