Nonparametric area under the ROC curve

Computes the nonparametric area under the ROC curve and its variance based on U-statistic theory (DDCP).

Usage

roc.area.test(markers, status)
  # S3 method for roc.area.test
print(x, ...)

Arguments

markers

The marker values for each subject. If there are more than one markers then this should be a matrix.

status

binary disease status indicator

x

object of class roc.area.test output from this function.

...

optional arguments to the print function.

Value

a list with the following elements

area

estimated area.

var

estimated variance (matrix).

stat

test statistic for equality of AUCs. Is not returned when only one diagnostic marker is present.

p.value

the p-value for the test of equality (2-sided).

df

the degrees of freedom of the chi-square.

The "print" method formats and returns the output.

Details

It calculates the area and its variance. For more than one marker it calculates the statistic to test for the equality of all AUCs. This statistic has a standard normal reference distribution for two variables and chi-square with number of variables minus 1.

References

DeLong, E. R., D. M. DeLong, and D. L. Clarke-Pearson. 1988. Comparing the areas under two or more correlated receiver operating characteristic curves: A nonparametric approach. Biometrics 44:837-845.

Examples

g <- rep(0:1, 50)
x <- rnorm(100) + g
y <- rnorm(100) + g
z <- rnorm(100) + g
roc.area.test(cbind(x,y), g)
#>   2 markers with AUC 0.7368 0.7368 
#>   test statistic = 0 
#>   p-value = 1 from standard normal reference 
roc.area.test(cbind(x,y,z), g)
#>   3 markers with AUC 0.7368 0.7368 0.7496 
#>   test statistic = 0.03830606 
#>   p-value = 0.9810292 from chi-square (df = 2) reference 
y1 <- y + 0.75*g
roc.area.test(cbind(x,y1), g)
#>   2 markers with AUC 0.7368 0.8628 
#>   test statistic = 2.212703 
#>   p-value = 0.02691816 from standard normal reference