optimal.delta {cgAUC}

optimal.delta

Description

Find the optimal delta.

Usage

optimal.delta(y, z, l, h, ind.d.l)

Arguments

y

The potential variables. It is a matrix with column of values of a variables. It should be standardized in this application.

z

The gold standard variable. It should be standardized.

l

Linear combination. A vector.

h

The value of h falls into (n^(-1/2), n^(-1/5)).

ind.d.l

Void

Value

delta.star

Optimal delta.

Author(s)

Yu-chia Chang

References

Chang, YCI. Maximizing an ROC type measure via linear combination of markers when the gold reference is continuous. Statistics in Medicine 2012.
Obuchowski NA. An ROC-type measure of diagnostic accuracy when the gold standard is continuous-scale. Statistics in Medicine 2006; 25:481–493.
Obuchowski N. Estimating and comparing diagnostic tests accuracy when the gold standard is not binary. Statistics in Medicine 2005; 20:3261–3278.
Friedman JH, Popescu BE. Gradient directed regularization for linear regression and classification. Technical Report, Department of Statistics, Stanford University, 2004.

Examples

##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.

## The function is currently defined as
function (y, z, l, h, ind.d.l) 
{
    l.i = matrix(rep(l, times = 50), nrow = 50, byrow = TRUE)
    delta = seq(0, 5, length = 50)
    m = delta %*% t(ind.d.l)
    l.i = l.i + m
    l.i.max = apply(l.i, 1, max)
    l.i = l.i/l.i.max
    theta = rep(0, 50)
    for (i in 2:50) {
        theta[i] = cntin(y, z, l.i[i, ], h)$theta.sh.h.p
    }
    delta.star = delta[which(theta == max(theta))]
    return(delta.star)
  }