genSimDataReiser {correctedAUC}

Generate one simulated data set based on Reiser's (2000) model

Description

Generate one simulated data set based on Reiser's (2000) model. The true AUC will also be calculated.

Usage

genSimDataReiser(
  nX = 100, 
  nY = 100, 
  sigma.X2 = 1, 
  mu.X = 0.25, 
  sigma.Y2 = 1, 
  mu.Y = 0, 
  sigma.epsilon2 = 0.5, 
  sigma.eta2 = 0.5) 

Arguments

nX

integer. number of cases.

nY

integer. number of controls.

sigma.X2

variance of the true value for cases.

mu.X

mean of the true value for cases.

sigma.Y2

variance of the true value for controls.

mu.Y

mean of the true value for controls.

sigma.epsilon2

variance of the random error term for cases.

sigma.eta2

variance of the random error term for controls.

Details

Reiser's (2000) measurement error model is:

X_{ik, obs}=X_{i,true}+\epsilon_{ik},\\ X_{i, true} \sim N\left(\mu_X, \sigma_X^2\right),\\ \epsilon_{ik} \sim N\left(0, \sigma_{\epsilon}^2\right),\\ i=1,\ldots, n_X, k=1, 2

Y_{jl, obs}=Y_{j,true}+\xi_{jl},\\ Y_{j, true} \sim N\left(\mu_Y, \sigma_Y^2\right),\\ \xi_{jl} \sim N(0, \sigma_{\eta}^2),\\ j=1,\ldots, n_Y, l=1, 2

Value

A list of 4 elements:

datFrame

A data frame with 4 elements: y: observations; subjID: subject ID; grp: group indicator; myrep: replication indicator.

theta2

(sigma.epsilon2 + sigma.eta2)/(sigma.X2 + sigma.Y2)

mu.true

mu.X-mu.Y

AUC.true

true AUC value

Author(s)

Bernard Rosner <[e-mail]>, Shelley Tworoger <[e-mail]>, Weiliang Qiu <[e-mail]>

References

Rosner B, Tworoger S, Qiu W (2015) Correcting AUC for Measurement Error. J Biom Biostat 6:270. doi:10.4172/2155-6180.1000270

Examples

  set.seed(1234567)
  tt=genSimDataReiser(
       nX = 100, 
       nY = 100, 
       sigma.X2 = 1, 
       mu.X = 0.25, 
       sigma.Y2 = 1, 
       mu.Y = 0, 
       sigma.epsilon2 = 0.5, 
       sigma.eta2 = 0.5) 

  print(dim(tt$datFrame))
  print(tt$datFrame[1:2,1:3])
  print(tt$theta2)
  print(tt$mu.true)
  print(tt$AUC.true)