rcorrp.cens: Rank Correlation for Paired Predictors with a Possibly... In harrelfe/Hmisc: Harrell Miscellaneous

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

 1 2 3 4 5 6 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
[email protected]

Scott Williams
Division of Radiation Oncology
Peter MacCallum Cancer Centre, Melbourne, Australia
[email protected]

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