DiagTest3Grp (version 1.6)

Youden3Grp.Variance.Normal: Variance estimations for the extended Youden index and associated lower and upper optimal cut-point under normality assumption

Description

Calculate the variance estimation for the extended Youden index and the variance estimation for the associated lower and upper optimal cut-point assuming that a diagnostic test follows normal distributions in the three ordinal groups ($D^-$,$D^0$,$D^+$).

Usage

Youden3Grp.Variance.Normal(x, y, z, alpha = 0.05)

Arguments

x

A numeric vector. A diagnostic test's measurements in the $D-$ (usually healthy subjects).

y

A numeric vector. A diagnostic test's measurements in the $D0$ (usually mildly diseased subjects).

z

A numeric vector. A diagnostic test's measurements in the $D+$ (usually severely diseased subjects).

alpha

A numeric value. Significance level so that the function calculates the (1-alpha)*100% confidence interval (CI) on the estimates of the extended Youden index and optimal cut-points under normal assumption. Default, alpha=0.05.

Value

Return a list, including the following components

var.youden

The normal-method based variance on the optimal Youden index.

var.t.minus

A numeric value.The variance on the lower optimal cut-point t.minus.

var.t.plus

A numeric value.The variance on the upper optimal cut-point t.plus.

var.youden.z

A numeric value. The variance on the Fisher's Z transformed optimal Youden index.

youden.CI

A named numeric of length 2. CI for the estimate of youden with the lower and the upper CI limit (under the names alpha/2*100% and (1-alpha/2)*100%).

t.minus.CI

A named numeric of length 2. CI for the estimate of t.minus (the lower optimal cut-point) with the lower and the upper CI limit (under the names alpha/2*100% and (1-alpha/2)*100%) CI

t.plus.CI

A named numeric of length 2. CI for the estimate of t.plus (the upper optimal cut-point) with the lower and the upper CI limit (under the names alpha/2*100% and (1-alpha/2)*100%).

youden.z.CI

A named numeric of length 2. CI for the estimate of Fisher-Z transformed youden with the lower and the upper CI limit (under the names alpha/2*100% and (1-alpha/2)*100%).

partialDeriv

A numeric data frame with one row and multiple columns, containing estimated SD parameters in each diagnosis group and the partial derivatives of Youden estimate w.r.t the relevant mean and SD parameters which are outputted for performance of statistical tests on markers under normal method or NA under nonparametric method.

Details

See details in Youden3Grp.

References

Luo, J and Xiong, C. (2012) Youden Index and Associated Optimal Cut-point for Three Ordinal Groups. Communications In Statistics-Simulation and Computation (in press).

See Also

Youden3Grp Youden3Grp.Variance.Bootstrap

Examples

 data(AL)
 group <- AL$group
 table(group)

 ##take the negated FACTOR1 marker measurements
 factor1 <- -AL$FACTOR1

 x <- factor1[group=="D-"]
 y <- factor1[group=="D0"]
 z <- factor1[group=="D+"]


 temp.res <- Youden3Grp.Variance.Normal(x=x, y=y, z=z, alpha=0.05)

 ###variance of the extended Youden index and optimal cut-points
 temp.res[c("var.youden","var.t.minus","var.t.plus")]