rcorrp.cens {Hmisc} | R Documentation

## Rank Correlation for Paired Predictors with a Possibly Censored Response, and Integrated Discrimination Index

### Description

Computes U-statistics 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.

### Usage

    rcorrp.cens(x1, x2, S, outx=FALSE, method=1)

    improveProb(x1, x2, y)

    ## S3 method for class 'improveProb'
    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 right-censored `Surv` object. If `S` is a vector instead, it is converted to a `Surv` object and it is assumed that no observations are censored.
`outx` | set to `TRUE` to exclude pairs tied on `x1` or `x2` 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`:

`n` | number of cases
`na` | number of events
`nb` | number of non-events
`pup.ev` | mean of pairwise differences in probabilities for those with events and a pairwise difference of \mbox{probabilities}>0
`pup.ne` | mean of pairwise differences in probabilities for those without events and a pairwise difference of \mbox{probabilities}>0
`pdown.ev` | mean of pairwise differences in probabilities for those with events and a pairwise difference of \mbox{probabilities}>0
`pdown.ne` | mean of pairwise differences in probabilities for those without events and a pairwise difference of \mbox{probabilities}>0
`nri` | Net Reclassification Index = (pup.ev-pdown.ev)-(pup.ne-pdown.ne)
`se.nri` | standard error of NRI
`z.nri` | Z score for NRI
`nri.ev` | Net Reclassification Index = pup.ev-pdown.ev
`se.nri.ev` | SE of NRI of events
`z.nri.ev` | Z score for NRI of events
`nri.ne` | Net Reclassification Index = pup.ne-pdown.ne
`se.nri.ne` | SE of NRI of non-events
`z.nri.ne` | Z score for NRI of non-events
`improveSens` | improvement in sensitivity
`improveSpec` | improvement in specificity
`idi` | Integrated Discrimination Index
`se.idi` | SE of IDI
`z.idi` | Z score of IDI

### Author(s)

Frank Harrell
Department of Biostatistics, Vanderbilt University
f.harrell@vanderbilt.edu

Scott Williams
Division of Radiation Oncology
Peter MacCallum Cancer Centre, Melbourne, Australia
scott.williams@petermac.org

### 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 27:157-172. 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 improvements-Practical 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 30:11-21; DOI: 10.1002/sim.4085

### See Also

`rcorr.cens`, `somers2`, `Surv`, `val.prob`

### 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)

[Package Hmisc version 4.0-3 Index]