| cgAUC {cgAUC} | R Documentation |
Calculate AUC when gold standard is continuous with large variables.
Description
The cgAUC can calculate the AUC-type measure of Obuchowski(2006) when gold standard is continuous, and find the optimal linear combination of variables with respect to this measure.
Usage
cgAUC(x, z, h, delta = 1, auto = FALSE, tau = 1, scale = 1)
Arguments
x |
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. |
h |
The parameter controls the window width of smoothing function. |
delta |
The parameter be used in TGDM. The default value is one. |
auto |
Find the optimal delta in TGDN using cross-validation. If the auto is TRUE. The default is FALSE. |
tau |
The parameter used in TGDM. The default value is one. |
scale |
Scaling data when scale = 1, no scaling data when scale = 0. The default value is 1. |
Details
In this package, we use the TGDM to find the optimal linear combination of variables in order to maximize the AUC-type measure. Before using this function, all of variables, including gold standard variable, should be standardized first. Below are parameters used in the algorithm:
Value
Rev |
When Rev = 0 means l * 1; otherwise, l * -1. |
l |
The estimate of coefficients for the optimal linear combination of variables. |
theta.sh.h.p |
The estimate of the theta of Chang(2012) for the optimal linear combination of variables. |
theta.sh.h.p.var |
The estimate of variance for the theta of Chang(2012). |
cntin.ri |
The estimate of the theta of Chang(2012) for each single vaiable. |
theta.h.p |
The estimate of the theta of Obuchowski(2006) for the optimal linear combination of variables. |
theta.h.p.var |
The estimate of variance for the theta of Obuchowski(2006). |
dscrt.ri |
The estimate of the theta of Obuchowski(2006) for each single vaiable. |
delta |
The value of 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.
# n = 100; p = 5;
# r.x = matrix(rnorm(n * p), , p) # raw data
# r.z = r.x[ ,1] + rnorm(n) # gold standard
# x = scale(r.x) # standardized of raw data
# z = scale(r.z) # standardized of gold standard
# h = n^(-1 / 2)
# t1 = cgAUC(r.x, r.z, h, delta = 1, auto = FALSE, tau = 1, scale = 1) # the delta be constant
# t1
# t2 = cgAUC(r.x, r.z, h, delta = 1, auto = TRUE, tau = 1, scale = 1) # the delta be variable
# t2
## The function is currently defined as
function (x, z, h, delta = 1, auto = FALSE, tau = 1)
{
x = scale(x)
z = scale(z)
conv = FALSE
n = dim(x)[1]
p = dim(x)[2]
cntin.ri = dscrt.ri = rep(0, p)
id = diag(p)
for (i in 1:p) {
dscrt.ri[i] = dscrt(x, z, id[i, ])$theta.h.p
cntin.ri[i] = cntin(x, z, id[i, ], h)$theta.sh.h.p
}
beta.i = ifelse(cntin.ri > 0.5, 1, -1)
dscrt.ri = ifelse(dscrt.ri > 0.5, dscrt.ri, (1 - dscrt.ri))
cntin.ri = ifelse(cntin.ri > 0.5, cntin.ri, (1 - cntin.ri))
y = x * matrix(beta.i, n, p, byrow = TRUE)
max.x = which(cntin.ri == max(cntin.ri))
theta.sh.h.p = 0
l = id[max.x, ]
while (conv == FALSE) {
d.l = d.theta.sh.h.p(y, z, l, h)
max.d.l = max(d.l)
ind.d.l = ifelse(d.l >= (tau * max.d.l), 1, 0) * d.l
if (auto == TRUE) {
delta = optimal.delta(y, z, l, h, ind.d.l)
}
l = l + delta * ind.d.l
l = l/max(l)
theta.temp = cntin(y, z, l, h)$theta.sh.h.p
ifelse(abs(theta.temp - theta.sh.h.p) < 1e-04, conv <- TRUE, conv <- FALSE)
theta.sh.h.p = theta.temp
}
optimal.dscrt = dscrt(y, z, l)
theta.sh.h.p.var = cntin(y, z, l, h)$var
l = l * beta.i
return(list(l = l, theta.sh.h.p = theta.sh.h.p, theta.sh.h.p.var = theta.sh.h.p.var,
cntin.ri = cntin.ri, theta.h.p = optimal.dscrt$theta.h.p,
theta.h.p.var = optimal.dscrt$var, dscrt.ri = dscrt.ri,
delta = delta))
}
## The function is currently defined as
function (x, z, h, delta = 1, auto = FALSE, tau = 1)
{
x = scale(x)
z = scale(z)
conv = FALSE
n = dim(x)[1]
p = dim(x)[2]
cntin.ri = dscrt.ri = rep(0, p)
id = diag(p)
for (i in 1:p) {
dscrt.ri[i] = dscrt(x, z, id[i, ])$theta.h.p
cntin.ri[i] = cntin(x, z, id[i, ], h)$theta.sh.h.p
}
beta.i = ifelse(cntin.ri > 0.5, 1, -1)
dscrt.ri = ifelse(dscrt.ri > 0.5, dscrt.ri, (1 - dscrt.ri))
cntin.ri = ifelse(cntin.ri > 0.5, cntin.ri, (1 - cntin.ri))
y = x * matrix(beta.i, n, p, byrow = TRUE)
max.x = which(cntin.ri == max(cntin.ri))
theta.sh.h.p = 0
l = id[max.x, ]
while (conv == FALSE) {
d.l = d.theta.sh.h.p(y, z, l, h)
max.d.l = max(d.l)
ind.d.l = ifelse(d.l >= (tau * max.d.l), 1, 0) * d.l
if (auto == TRUE) {
delta = optimal.delta(y, z, l, h, ind.d.l)
}
l = l + delta * ind.d.l
l = l/max(l)
theta.temp = cntin(y, z, l, h)$theta.sh.h.p
ifelse(abs(theta.temp - theta.sh.h.p) < 1e-04, conv <- TRUE,
conv <- FALSE)
theta.sh.h.p = theta.temp
}
optimal.dscrt = dscrt(y, z, l)
theta.sh.h.p.var = cntin(y, z, l, h)$var
l = l * beta.i
return(list(l = l, theta.sh.h.p = theta.sh.h.p, theta.sh.h.p.var = theta.sh.h.p.var,
cntin.ri = cntin.ri, theta.h.p = optimal.dscrt$theta.h.p,
theta.h.p.var = optimal.dscrt$var, dscrt.ri = dscrt.ri,
delta = delta))
}