Youden3Grp.PointEst: Provide point estimates for the extended Youden index, the associated optimal cut-points, and sample size for three ordinal groups

Description

Estimate for the extended Youden index, the associated optimal cut-points using normal and non-parametric methods and the associated. The sample size to estimate the extended Youden index of a diagnostic marker within a given margin of error under normal assumptions is also provided.

Usage

Youden3Grp.PointEst(x, y, z, method = "Normal", randomStart.N=1, optim.method = NULL, t.minus.start = NULL, t.plus.start = NULL,  lam.minus = 1/3, lam0 = 1/3, lam.plus = 1/3, typeIerror = 0.05, margin=0.05, FisherZ=FALSE, ...)

Arguments

A numeric vector, a diagnostic test's measurements for subjects in D- (usually a healthy group).

A numeric vector, a diagnostic test's measurements for subjects in D0 (usually a mildly diseased group).

A numeric vector, a diagnostic test's measurements for subjects in D+ (usually a severly diseased group).

method

A character. Specify a method to be used for estimating the extended Youden index Choices include ‘Normal’---Estimate the extended Youden index under the assumption of normal distributions of a diagnostic test in the three groups. ‘TN’---Transformed normal. Implement Box-cox transformation to approximate normality and then estimate the extended Youden index under normality. ‘EMP’---Estimate the extended Youden index by using empirical cumulative density function. ‘KS’---Estimate the extended Youden index by using Kernel density estimation with a normal reference rule for bandwidth selection. ‘KS-SJ’---Estimate the extended Youden index by using Kernel density estimation with the Sheather-Jones Plug-in method for bandwidth selection.

randomStart.N

An argument need to be specified when the method “EMP”, “KS” or “KS-SJ” is used to estimate the optimal cut-point and the extended Youden index J. Default, randomStart.N=1.

optim.method

A character argument. The optimization method specified to derive the optimal cut-points when nonparametric methods are used to estimate the extended Youden index. Default, optim.method=L-BFGS-B.see optim.

t.minus.start

A numeric value. The starting points of the lower optimal cut-point (t-) which separate the $D^-$ and $D^0$ group. Default t.minus.start=NULL will randomly generate starting value.

t.plus.start

A numeric value. The starting points of the upper optimal cut-point (t+) which separate the $D^0$ and $D^+$ group. Default t.plus.start=NULL will randomly generate starting value.

lam.minus

A numeric value. The expected population proportion of the D- group, used for sample size calculation. Default, lam.minus=1/3. The proportions of the three ordinal groups (lam.minus, lam0, lam.plus) should sum to 1.

lam0

A numeric value. The expected population proportion of the D0 group, used for sample size calculation. Default, lam0=1/3. The proportions of the three ordinal groups (lam.minus, lam0, lam.plus) should sum to 1.

lam.plus

A numeric value. The expected population proportion of the D+ group, used for sample size calculation. Default, lam.plus=1/3.The proportions of the three ordinal groups (lam.minus, lam0, lam.plus) should sum to 1.

typeIerror

A numeric value. (1-typeIerror)*100% confidence interval (CI) in sample size calculation. Default typeIerror=0.05, i.e., calculate 95% CI.

margin

A numeric value. The margin of error on the Youden index estimate in sample size calculation. Default, margin=0.05.

FisherZ

Reference to the argument in Normal.VUS.

...

Other options for the R function optim.

Value

mu.minus: The sample mean estimate of the a diagnostic's measurements in the $D^-$ group, which is sample mean of data if method=“Normal”/“EMP”/“KS”/“KS-SJ” while if method=“TN”, mu.minus is the sample mean of the data after Box-cox transformation.
mu0: The sample mean estimate of the a diagnostic's measurements in the D0 group, which is sample mean of data if method=Normal while if method=TN, mu0 is the sample mean of the data after Box-cox transformation.
mu.plus: The sample mean estimate of the a diagnostic's measurements in the D+ group, which is sample mean of data if method=Normal while if method=TN, mu.plus is the sample mean of the data after Box-cox transformation.
s.minus: The sample standard deviation (SD) estimate of the a diagnostic's measurements in the D- group, which is sample SD of data if method=Normal while if method=TN, the s.minus is the sample SD of the data after Box-cox transformation.
s0: The sample standard deviation (SD) estimate of the a diagnostic's measurements in the D0 group, which is sample SD of data if method=Normal while if method=TN, the s0 is the sample SD of the data after Box-cox transformation.
s.plus: The sample standard deviation (SD) estimate of the a diagnostic's measurements in the D+ group, which is sample SD of data if method=Normal while if method=TN, the s.plus is the sample SD of the data after Box-cox transformation.
t.minus: The estimate of the lower optimal cut-point.
t.plus: The estimate of the upper optimal cut-point.
Se: Sensitivity, the probability of a randomly selected subject from D+ group has a test result above t.plus.
Sp: Specificity the probability of a randomly selected subject from D- group has a test result below t.minus.
Sm: The probability of a randomly selected subject from D0 group has a test result between t.minus and t.plus.
youden: The extended Youden index for three ordinal groups attained at the optimal cut-point t.minus and t.plus.
youden.z: The Fisher's Z transformation of the extended Youden index.
lambda.est: The estimated lambda, the parameter used in Box-Cox transformation y=(x^lambda-1)/lambda. The estimate will be a numeric value when the method=TN is used to estimate the extended Youden index and NA when other methods were used.
t.minus.TN: The optimal lower cut-point t.minus estimated for the data after Box-Cox transformation. The estimate will be a numeric value when the method=TN is used to estimate the extended Youden index and NA when other methods are used.
t.plus.TN: The optimal upper cut-point t.plus estimated for the data after Box-Cox transformation. The estimate will be a numeric value when the method=TN is used to estimate the extended Youden index and NA when other methods are used.
sampleSize: The sample size on investigating a diagnostic test based on pilot measurments x, y, z. The sample size calculated such that based on given population proportion of the three diagnosis groups, the margin of error on the (1-typeIerror)*100% confidence interval of the extended Youden index estimate under normality is as specified, by default 0.05.

Details

Let the marker denoted by $T$ and the density function under $Di$ as $fi$, $i=-,0.+$. The Youden index for three ordinal groups is defined as, $J(t-,t+)=1/2*(f_(T<= t-)+f0(t-<="T<=" t+)+f+(t="" <="t+)-1]$." the="" optimal="" index="" achieved="" at="" an="" pair="" will="" be="" adopted="" as="" final="" summary="" measure.="" note="" that="" package="" assumes="" marker="" values="" increase="" monotonically="" and="" stochastically="" with="" disease="" severity="" (the="" means="" in="" three="" group="" $d-$,="" $d0$="" $d+$="" are="" increasing).="" if="" a="" decreasing="" trend,="" should="" negated="" for="" anlaysis.="" p="">

For the extended Youden index and optimal cut-point estimates, see reference paper for details. For sample size calculation, the (1-typeIerror)% CI on the Youden estimate under normality is $(J-Z_a*SE(J),J+Z_a*SE(J))$, then the sample size will be calculated such that margin=$Z_a*SE(J)$ or half of the CI's length, where Z_a is the normal quantile, $Z_a=1.95$ given default typeIerror $a=0.05$.

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).

Examples

Run this code


 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+"]

 ##Normal method
 youden.res.normal <- Youden3Grp.PointEst(x=x, y=y, z=z, method = "Normal")
 youden.res.normal$est$youden

 ##Kernel smoothing method with Sheather-Jones plug-in method
 youden.res.KS <- Youden3Grp.PointEst(x=x, y=y, z=z, method = "KS-SJ",randomStart.N=3)
 youden.res.KS$est$youden

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