cgAUC: Calculate AUC when gold standard is continuous with large...
In cgAUC: Calculate AUC-type measure when gold standard is continuous and the corresponding optimal linear combination of variables with respect to it.
Description
Usage
Arguments
Details
Value
Author(s)
References
Examples
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
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
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##---- 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))
}
Example output
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))
}
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))
}
cgAUC documentation built on May 1, 2019, 10:11 p.m.
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Description Usage Arguments Details Value Author(s) References Examples
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
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 | ##---- 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))
}
|
Example output
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))
}
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))
}
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