auc.nonpara.kernel {auRoc}

AUC by Kernel Methods

Description

Obtain the point estimate and the confidence interval of the AUC using kernel methods.

Usage

   auc.nonpara.kernel(x, y, conf.level=0.95,
                      integration=c("FALSE","TRUE"),
                      bw=c("nrd0", "sj"), nint=512,
                      method=c("mw", "jackknife", "bootstrapP", "bootstrapBCa"),
                      nboot)

Arguments

x

a vector of observations from class P.

y

a vector of observations from class N.

conf.level

confidence level of the interval. The default is 0.95.

integration

a logical value. If its value is FALSE then the results are based on the kernel estimates of the CDF; otherwise the PDF. The default values is FALSE.

bw

method used for bandwidth selection. nrd0 uses a rule-of-thumb for choosing the bandwidth of a Gaussian kernel density estimation; sj uses the method of Sheather & Jones (1991). The default if nrd0.

nint

the number of equally spaced points at which the density is to be estimated. The default if 512.

method

a method used to construct the CI. mw uses the sd based on the Mann-Whitney statistic; jackknife uses the jackknife method; bootstrapP uses the bootstrap with percentile CI; bootstrapBCa uses bootstrap with bias-corrected and accelerated CI. The default is mw. It can be abbreviated.

nboot

number of bootstrap iterations.

Details

The AUC essentially depends on the CDFs of two classes N and P. We could use kernel smoothing methods to obtain the CDFs. The methods implemented in this function construct the CI based on two different strategies: the first uses kernel smoothing to estimate the PDFs and then the CDFs; and the second starts from the estimate of the CDFs directly. Gaussian kernel is used.

Value

Point estimate and lower and upper bounds of the CI of the AUC.

Note

The observations from class P tend to have larger values then that from class N.

Author(s)

Dai Feng

References

Dai Feng, Giuliana Cortese, and Richard Baumgartner (2015) A comparison of confidence/credible interval methods for the area under the ROC curve for continuous diagnostic tests with small sample size. Statistical Methods in Medical Research DOI: 10.1177/0962280215602040

Simon Sheather and Michael Jones (1991) A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B (Methodological) 53 683-690

Examples

  #Example 1
  data(petBrainGlioma)
  y <- subset(petBrainGlioma, grade==1, select="FDG", drop=TRUE)
  x <- subset(petBrainGlioma, grade==2, select="FDG", drop=TRUE)
  auc.nonpara.kernel(x, y)

   
  ## Not run: 
  #Example 2
  data(petBrainGlioma)
  y <- subset(petBrainGlioma, grade==1, select="ACE", drop=TRUE)
  x <- subset(petBrainGlioma, grade==2, select="ACE", drop=TRUE)
  auc.nonpara.kernel(x, y, integration="TRUE",
                     bw="sj",  method="bootstrapBCa", nboot=999)
  
## End(Not run)