thresTH3 {ThresholdROC}

Population-based threshold calculation (three-state setting)

Description

This function estimates the theoretical optimum thresholds for the specific distribution parameters, decision costs and prevalences in a three-state setting.

Usage

thresTH3(dist1, dist2, dist3, par1.1, par1.2,
  par2.1, par2.2, par3.1, par3.2, rho,
  costs = matrix(c(0, 1, 1, rho[1]/rho[2], 0, rho[3]/rho[2], 1, 1, 0),
  3, 3, byrow = TRUE), q1=0.05, q2=0.5, q3=0.95, tol = 10^(-8))

Arguments

dist1

distribution to be assumed for the first population. See Details.

dist2

distribution to be assumed for the second population. See Details.

dist3

distribution to be assumed for the third population. See Details.

par1.1

first parameter of the first distribution.

par1.2

second parameter of the first distribution.

par2.1

first parameter of the second distribution.

par2.2

second parameter of the second distribution.

par3.1

first parameter of the third distribution.

par3.2

second parameter of the third distribution.

rho

3-dimensional vector of prevalences.

costs

cost matrix. Costs should be entered as a 3x3 matrix, where the first row corresponds to the costs associated with the classification of subjects in state 1 (C11, C12 and C13), second row corresponds to the costs associated with the classification of subjects in state 2 (C21, C22 and C23) and the third row corresponds to the costs associated with classification of subjects in state 3 (C31, C32, C33), where Cij is the cost of classifying an individual of class i as class j. Default cost values are a combination of costs that leads to the same thresholds as the Youden index method (see References for details).

q1

probability of the distribution taking lower values in order to determine a low quantile. Default, 0.05. See Details.

q2

probability of the middle distribution in order to determine a medium quantile. Default, 0.5. See Details.

q3

probability of the the distribution taking higher values in order to determine a high quantile. Default, 0.95. See Details.

tol

tolerance to be used in function uniroot. Default, 10^(-8).

Details

Parameters dist1, dist2 and dist3 can be chosen between the following 2-parameter distributions: "beta", "cauchy", "chisq" (chi-squared), "gamma", "lnorm" (lognormal), "logis" (logistic), "norm" (normal) and "weibull".

Parameters q1, q2 and q3 are used to determine two intervals where the uniroot function should look for the two threshold estimates. Thus, the first threshold is expected to be found between quantile-1(q1) and quantile-2(q2) and the second one, between quantile-2(q2) and quantile-3(q3), being quantile-i() the quantile function for the i-th distribution, i=1,2,3.

Value

An object of class thresTH3, which is a list with five components:

thres1

first threshold estimate.

thres2

second threshold estimate.

prev

prevalences provided by the user.

costs

cost matrix provided by the user.

method

method used in the estimation. For an object of class thresTH3 it is always equal to "theoretical" (meaning that the population-based method has been used).

Note

It is assumed that dist1 is the distribution with lower values and dist3 is the one taking higher values. If that is not the case, dist1, dist2 and dist3 (and the corresponding parameters) are re-ordered as needed.

References

Skaltsa K, Jover L, Fuster D, Carrasco JL. (2012). Optimum threshold estimation based on cost function in a multistate diagnostic setting. Statistics in Medicine, 31:1098-1109.

Examples

# example 1
dist <- "norm"
par1.1 <- 0
par1.2 <- 1
par2.1 <- 2
par2.2 <- 1
par3.1 <- 4
par3.2 <- 1
rho <- c(1/3, 1/3, 1/3)

thresTH3(dist, dist, dist,
  par2.1, par2.2, par1.1, par1.2,
  par3.1, par3.2, rho)
  
  
# example 2
dist1 <- "norm"
dist2 <- "lnorm"
dist3 <- "lnorm"
par1.1 <- 0
par1.2 <- 1
par2.1 <- 1
par2.2 <- 0.5
par3.1 <- 2
par3.2 <- 0.5
rho <- rep(1/3, 3)

thresTH3(dist1, dist2, dist3, par1.1, par1.2, par2.1, par2.2, par3.1, par3.2, rho)