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```
#' Two-Graphs Receiving Operating Characteristics.
#' @description The function supports the determination and plot of the
#' sensitivity and specificity against the possible thresholds and shows an
#' intermediate range of test results that is considered as less accurate.
#'
#' @param ref The reference standard. A column in a data frame or a vector
#' indicating the classification by the reference test. The reference standard
#' must be coded either as 0 (absence of the condition; controls) or 1
#' (presence of the condition; deviation from controls).
#' @param test The numeric test scores under evaluation. When
#' \code{mean(test[ref == 0]) > mean(test[ref == 1])} it is assumed that
#' higher test scores indicate presence of the condition, otherwise that lower
#' test scores indicate presence of the condition.
#' @param Se.criterion Default = .95. Minimum desired value of Se.
#' @param Sp.criterion Default = .95. Minimum desired value of Sp.
#' @param model Default = 'none'. Model to use, either bi-normal or none
#' (non-parametric)
#' @param plot Defaults= FALSE. Whether a plot is shown for Se and Sp against
#' the thresholds.
#' @param position.legend Default: 'left'. Position of the legend. Most used
#' values: "left", "right".
#' @param cex.legend Default: 1. Relative size of the legend.
#'
#' @details This function implements a non-parametric and a bi-normal model. See
#' Landsheer(2018) for an evaluative description. When model='none' and the
#' data have a limited number of values, the upper and lower threshold show
#' the first values which comply with the criteria.
#'
#' Warning 1: Whn using test scores where higher test scores indicate presence
#' of a disease, the whole range of test scores starting at the lowest test
#' score have perfect Sensitivity (1.00), at the cost of a maximal number of
#' false positives; the sensitivity is 0.00. When moving to higher test
#' scores, the value of sensitivity decreases and the value of specificity
#' increases. Therefore, the lowest test scores are best used for negative
#' classifications, but these are precisely the test scores with the highest
#' sensitivity. In TG-ROC the test scores <= the lower limit are interpreted
#' for negative classifications. However, the whole range of test values >=
#' lower limit provides the minimal desired positive accuracy (Se.criterion)
#' (at the cost of a large number of false positives). Similarly, the test
#' scores >= the upper limit are interpreted for positive classifications,
#' while the whole range of test values <= upper limit provides the minimal
#' desired negative accuracy (Sp.criterion) (at the cost of a large number of
#' false negatives). Of course, this is also true for tests where the lowest
#' scores indicate the presence of the disease, but only reversed.
#'
#' Warning 2: The Intermediate range can cover a relatively small part of the
#' area of overlap between the two distributions. In that case test scores
#' with relative low number of false classifications are considered as
#' intermediate.
#'
#' Please note that the definition of the intermediate interval deviates
#' substantially from the definition of an uncertain interval.
#'
#' The TG-ROC (Two Graphs Receiver Operating Characteristics) plot shows the
#' diminishing values of Se and increasing values of Sp against the possible
#' thresholds.
#' @return Thresholds for the intermediate zone. Lower threshold < Test scores <
#' Upper threshold is the intermediate range. The range of test values >=
#' lower limit provides the desired positive accuracy (Se.criterion), while
#' the range of test values <= upper limit provides the desired negative
#' accuracy (Sp.criterion).
#' @references Greiner, M. (1995). Two-graph receiver operating characteristic
#' (TG-ROC): A Microsoft-EXCEL template for the selection of cut-off values in
#' diagnostic tests. Journal of Immunological Methods, 185(1), 145-146.
#'
#' Greiner, M. (1996). Two-graph receiver operating characteristic (TG-ROC):
#' Update version supports optimisation of cut-off values that minimise
#' overall misclassification costs. Journal of Immunological Methods, 191(1),
#' 93-94.
#'
#' Landsheer, J. A. (2018). The Clinical Relevance of Methods for Handling
#' Inconclusive Medical Test Results: Quantification of Uncertainty in Medical
#' Decision-Making and Screening. Diagnostics, 8(2), 32.
#' https://doi.org/10.3390/diagnostics8020032
#'
#' @examples
#' ref = c(rep(0,100), rep(1,100))
#' test = c(rnorm(100, 0, 1), rnorm(100, 1, 1))
#' TG.ROC(ref, test, model='binormal', plot=TRUE)
#' TG.ROC(ref, test, model='none', plot=TRUE)
#' @export
#' @importFrom stats qnorm
# Se.criterion = .9; Sp.criterion = .9; model = 'binormal'
# plot = T; position.legend = 'left'; cex.legend = 1; test=-test
TG.ROC <- function(ref,
test,
Se.criterion = .9,
Sp.criterion = .9,
model = c('none', 'binormal'),
plot = FALSE,
position.legend = 'left',
cex.legend = 1) {
model = match.arg(model) # model='none'
df = check.data(ref, test, model) # nrow(df)
normhigher = mean(test[ref==0]) > mean(test[ref==1])
if (model == 'none') {
df2 = simple_roc3(df$test[df$ref==0], df$test[df$ref==1]) # head(df2)
if (normhigher){
w = which(df2$fpr <= 1-Sp.criterion) # df2$fpr[w]
wL = w[length(w)]
wU = which(df2$tpr >= Se.criterion)[1]
} else {
w = which(df2$tpr >= Se.criterion) # df2$tpr[w]
wL = w[length(w)]
wU = which(df2$fpr <= (1 - Sp.criterion))[1]
}
thresholds = c(L = df2$testscores[wL], U = df2$testscores[wU])
if (plot) {
plot(
df2$testscores,
df2$tpr,
type = 'l',
col = 'red',
xlab = 'thresholds',
ylab = 'SeSp'
) # Se
# length(df2$test); length(df2$TPR)
lines(df2$testscores, 1 - df2$fpr, type = 'l', col = 'blue') # Sp
abline(v = thresholds)
abline(h = c(Se.criterion, Sp.criterion))
legend(position.legend, legend = c('Se', 'Sp'), lty=c(1,1), col=c('red', 'blue'),
cex=cex.legend)
}
}
if (model == 'binormal') {
mu0 = mean(df$test[df$ref == 0])
sd0 = sd(df$test[df$ref == 0])
mu1 = mean(df$test[df$ref == 1])
sd1 = sd(df$test[df$ref == 1])
thresholds = c(L=qnorm(Se.criterion, mu1, sd1, lower.tail = normhigher),
U=qnorm(Sp.criterion, mu0, sd0, lower.tail = !normhigher))
if (normhigher) {
tmp=thresholds[1]; thresholds[1]=thresholds[2]; thresholds[2]=tmp
}
df$test = sort(df$test)
if (plot) {
plot(
df$test,
pnorm(df$test, mu0, sd0, lower.tail = !normhigher),
type = 'l',
col = 'blue',
xlab = 'thresholds',
ylab = 'SeSp'
) # Sp
lines(df$test,
pnorm(df$test, mu1, sd1, lower.tail = normhigher),
type = 'l',
col = 'red') # Se
abline(v = thresholds)
abline(h = c(Se.criterion, Sp.criterion))
legend(position.legend, legend = c('Se', 'Sp'), lty=c(1,1), col=c('red', 'blue'),
cex=cex.legend)
}
}
return(thresholds)
}
```

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