Using R to compute A (aprime) and b diagnostics in Zhang, J., & Mueller, S. T. (2005) for evaluating ROC diagnostics nonparametrically

(Copied from the https://sites.google.com/a/mtu.edu/whynotaprime/ weblink)

A <-function(h,f)
{
  if(f<=.5 & h>=.5)
  {
    a <- .75 + (h-f)/4 - f*(1-h)
  } else if(f<=h & h<=.5)
  {
    a <- .75 + (h-f)/4 - f/(4*h)
  } else {
    a <- .75 + (h-f)/4 - (1-h)/(4 * (1-f))
  } 
  return(a)
  }

b <- function(h,f)
{
  if(f<=.5 & h>=.5)
  {
    b <-(5-4*h)/(1+4*f)
  } else if(f<=h & h<=.5)
  {
    b <-(h^2+h)/(h^2+f) 
  } else { 
    b <- ((1-f)^2 + (1-h))/((1-f)^2 + (1-f))
  } 
  return(b)
}

Reference

Zhang, J., & Mueller, S. T. (2005). A note on ROC analysis and non-parametric estimate of sensitivity. Psychometrika, 70(1), 203–212. doi:10.1007/s11336-003-1119-8