sorocs {sorocs}

A Bayesian Semiparametric Dirichlet Process Mixtures to Estimate Correlated ROC Surfaces with Stochastic Order Constraints

Description

A Bayesian nonparametric Dirichlet process mixtures to estimate the receiver operating characteristic (ROC) surfaces and the associated volume under the surface (VUS), a summary measure similar to the area under the curve measure for ROC curves. To model distributions flexibly, including their skewness and multi-modality characteristics a Bayesian nonparametric Dirichlet process mixtures was used. Between-setting correlations is handled by dependent Dirichlet process mixtures that have bivariate distributions with nonzero correlations as their bases. To accommodate ordering constraints, the stochastic ordering in the context of mixture distributions was adopted.

Usage

sorocs(
  nsim = 4,
  nburn = 2,
  Yvariable1,
  Yvariable2,
  gridY = seq(0, 5, by = 0.05),
  Xvariable1,
  Xvariable2,
  gam0 = -4.6,
  gam1 = 9.2,
  lamb0 = -4.6,
  lamb1 = 9.2,
  H = 30,
  L = 30,
  alpha1 = 1,
  alpha2 = 1,
  alpha3 = 1,
  lambda1 = 1,
  lambda2 = 1,
  mu1 = matrix(c(0.5, 0.5), 2, 1),
  mu2 = matrix(c(1, 1), 2, 1),
  mu3 = matrix(c(3, 3), 2, 1),
  m1 = c(0, 0),
  m2 = c(0, 0),
  m3 = c(0, 0),
  A1 = 10 * diag(2),
  A2 = 10 * diag(2),
  A3 = 10 * diag(2),
  Sig1 = matrix(c(1, 0.5, 0.5, 1), 2, 2),
  Sig2 = matrix(c(1, 0.5, 0.5, 1), 2, 2),
  Sig3 = matrix(c(1, 0.5, 0.5, 1), 2, 2),
  nu = 6,
  C0 = 10 * diag(2),
  a1 = 2,
  a2 = 2,
  b1 = 0.1,
  b2 = 0.1
)

Arguments

nsim

Number of simulations

nburn

Burn in number

Yvariable1

Dependent variable at setting 1

Yvariable2

Dependent variable at setting 2

gridY

a regular sequence spanning the range of Y variable

Xvariable1

independent variable at setting 1

Xvariable2

independent variable at setting 2

gam0

Initial value for the test score distributions (e.g., a priori information between different disease populations for a single test or between multiple correlated tests)

gam1

Initial value for the test score distributions

lamb0

Initial value forthe test score distributions

lamb1

Initial value for the test score distributions

H

trucation level number for Dirichlet process prior trucation approximation

L

trucation level number for Dirichlet process prior trucation approximation

alpha1

fixed values of the precision parameters of the Dirichlet process

alpha2

fixed values of the precision parameters of the Dirichlet process

alpha3

fixed values of the precision parameters of the Dirichlet process

lambda1

fixed values of the precision parameters of the Dirichlet process

lambda2

fixed values of the precision parameters of the Dirichlet process

mu1

fixed values of the bivariate normal parameters of the Dirichlet process

mu2

fixed values of the bivariate normal parameters of the Dirichlet process

mu3

fixed values of the bivariate normal parameters of the Dirichlet process

m1

fixed values of the bivariate normal parameters of the Dirichlet process

m2

fixed values of the bivariate normal parameters of the Dirichlet process

m3

fixed values of the bivariate normal parameters of the Dirichlet process

A1

Initial values of the bivariate normal parameters of the Dirichlet process

A2

Initial values of the bivariate normal parameters of the Dirichlet process

A3

Initial values of the bivariate normal parameters of the Dirichlet process

Sig1

Initial values of the inverse Wishart distribution parameters of the Dirichlet process

Sig2

Initial values of the inverse Wishart distribution parameters of the Dirichlet process

Sig3

Initial values of the inverse Wishart distribution parameters of the Dirichlet process

nu

Initial values of the inverse Wishart distribution parameters of the Dirichlet process

C0

Initial values of the inverse Wishart distribution parameters of the Dirichlet process

a1

Initial shape values of the inverse-gamma base distributions for the Dirichlet process

a2

Initial shape values of the inverse-gamma base distributions for the Dirichlet process

b1

Initial scale values of the inverse-gamma base distributions for the Dirichlet process

b2

Initial scale values of the inverse-gamma base distributions for the Dirichlet process

Value

A list of posterior estimates

References

Zhen Chen, Beom Seuk Hwang. (2018) A Bayesian semiparametric approach to correlated ROC surfaces with stochastic order constraints. Biometrics, 75, 539-550. https://doi.org/10.1111/biom.12997

Examples

library(MASS)
library(MCMCpack)
library(mvtnorm)
data(asrm)
Y1 <- asrm$logREscoremean2[1:10]
Y2 <- asrm$logREscoremean1[1:10]
X1 <-asrm$TN12[1:20]/asrm$JN12[1:10]
X2 <-asrm$TNN12[1:20]/asrm$JNN12[1:10]
try1 <- sorocs:::sorocs( H = 12, L = 12, Yvariable1 =Y1, Yvariable2= Y2,
                         gridY=seq(0,5,by=1), Xvariable1= X1, Xvariable2 =X2)