README

The objective of this project is to assess the Receiver Operating Characteristic (ROC) surfaces for Gamma, Weibull, and Logistic distributions. Additionally, it supports performance evaluations linked to these ROC surfaces in the context of three-class problems.

Installation

# install.packages("devtools")
devtools::install_github("ErtanSU/ROCsurf")

Example

library(ROCsurf)
dG(c(1,2,3,4,5,200,1000),alpha=6,beta=.8)
#> [1] 9.107742e-03 8.350118e-02 1.816690e-01 2.193342e-01 1.917734e-01
#> [6] 2.715241e-99 0.000000e+00
dW(c(1,2,3,4,5,200,10000),alpha=1,beta=2)
#> [1] 3.032653e-01 1.839397e-01 1.115651e-01 6.766764e-02 4.104250e-02
#> [6] 1.860038e-44 0.000000e+00
dL(c(1,2,3,4,5,200),alpha=1,beta=.1)
#> [1] 2.500000e+00 4.539581e-04 2.061154e-08 9.357623e-13 4.248354e-17
#> [6] 0.000000e+00

library(ROCsurf)
pG(c(.5,1,2,3,4,25),alpha=6,beta=.8)
#> [1] 4.859954e-05 1.838085e-03 4.202104e-02 1.771172e-01 3.840393e-01
#> [6] 1.000000e+00
pW(c(.5,1,2,3,4,100),alpha=1,beta=2)
#> [1] 0.2211992 0.3934693 0.6321206 0.7768698 0.8646647 1.0000000
pL(c(.5,1,2,100),alpha=1,beta=.1)
#> [1] 0.006692851 0.500000000 0.999954602 1.000000000

library(ROCsurf)
qG(c(.9971,0.5,0.3),alpha=6,beta=.8)
#> [1] 11.956348  4.536129  3.613711
qW(c(.9971,0.5,0.3),alpha=1,beta=2)
#> [1] 11.6860891  1.3862944  0.7133499
qL(c(.9971,0.5,0.3),alpha=1,beta=.1)
#> [1] 1.5840140 1.0000000 0.9152702

library(ROCsurf)
rG(10,alpha=6,beta=.8)
#>  [1] 6.342921 5.613297 4.344726 3.548187 4.781843 2.190594 1.504722 8.491058
#>  [9] 1.787702 2.788674
rW(10,alpha=1,beta=2)
#>  [1] 0.3372294 3.5360746 0.9712284 2.0038895 1.2751727 1.6049933 0.2083131
#>  [8] 0.0378331 1.0150278 3.3648067
rL(10,alpha=1,beta=.1)
#>  [1] 0.6838594 1.4337235 0.9796567 1.0586671 1.0282047 1.1179200 1.0458565
#>  [8] 1.1385654 0.9166187 0.8226117

library(ROCsurf)
x<-rW(100,  2,  1)
y <- rG(100,  2, 2)
z <- rW(100,  6,  9)
r.tc_vus(x=x,y=y,z=z,
         init_param=c(alpha1=2,beta1=1,alpha2=2,beta2=2,
                      alpha3=6,beta3=9),
         model=c("WGW"), method=c("MLE"))
#> [1] 0.810257

library(ROCsurf)
x<- rW(100,  2,  1)
y <- rG(100,  2, 2)
z <- rW(100,  6,  9)
r.tc_index(x=x,y=y,z=z,
           init_param=c(alpha1=2,beta1=1,alpha2=2,
                        beta2=2,alpha3=6,beta3=9),
           init_index=c(median(x),median(y)),
           model=c("WGW"),
           method=c("MLE"))
#>          c₁       c₂      TPF₁      TPF₂      TPF₃
#> J  1.765644 6.034736 0.9533556 0.6212299 0.9249205
#> PM 1.486714 6.668990 0.8760312 0.7143641 0.8606857
#> MV 1.658977 6.301341 0.9305363 0.6601923 0.9016357
#> NI 1.671323 6.282483 0.9335618 0.6566622 0.9034494
#> M  1.535361 6.562809 0.8939014 0.6994002 0.8736471

library(ROCsurf)
x<- rW(100,  2,  1)
y <- rG(100,  2, 2)
z <- rW(100,  6,  9)
r.tc_graph(x=x,y=y,z=z,
           init_param=c(alpha1=2,beta1=1,alpha2=2,
                        beta2=2,alpha3=6,beta3=9),
           empirical=FALSE,model=c("WGW"),
           method=c("MLE"))

Corresponding Author

Department of Statistics, Faculty of Science, Selcuk University, 42250, Konya, Turkey

References

Akgenç, E., and Kuş, C., 2023, Statistical Inference for ROC Surface Analysis Under the Three-Class Problems, 7th International Congress of Researchers, Statisticians and Young Statisticians (IRSYSC-2023).

B. R. Mosier and L. E. Bantis., 2021, Estimation and construction of confidence intervals for biomarker cutoff-points under the shortest euclidean distance from the roc surface to the perfection corner, Statistics in medicine, 40(20):4522–4539.

G. Jameson., 2016, The incomplete gamma functions., The Mathematical Gazette, 100(548):298–306.

T. Dong., 2014, Selected Topics on Statistical Methods for Three and Multiple Class Diagnostic Studies, State University of New York at Buffalo.

J. Luo and C. Xiong., 2013, Youden index and associated cut-points for three ordinal diagnostic groups, Communications in Statistics-Simulation and Computation, 42(6):1213–1234.

F. Edition, A. Papoulis, and S. U. Pillai., 2002, Pobability, random variables, and stochastic processes, McGraw-Hill Europe: New York, NY, USA.

A. J. Hallinan Jr., 1993, A review of the weibull distribution, Journal of Quality Technology, 25(2):85–93.