This procedure simulates an MRMC data set for an MRMC agreement study comparing two modalities. It is a hierarchical model that consists of two interaction terms: reader-case interaction and modality-reader-case-replicate interaction. Both interaction terms are conditionally normally distributed, with the case(-related) factor contributing to the conditional mean and the reader(-related) factor contributing to the conditional variance. The case effect is normally distributed, while the reader effect is an inverse-gamma.
The Hierarchical Inverse-Gamma model is described in this paper:
S. Wen and B. D. Gallas, “Three-Way Mixed Effect ANOVA to Estimate MRMC Limits of Agreement,” Statistics in Biopharmaceutical Research, 14, pp. 532–541, 2022, tools:::Rd_expr_doi("10.1080/19466315.2022.2063169")
sim.NormalIG.Hierarchical(
config,
R = NULL,
AR = NULL,
BR = NULL,
is.within = FALSE
)df [data.frame] with nR x nC x 2 rows including
readerID: [Factor] w/ nR levels "reader1", "reader2", ...
caseID: [Factor] w/ nC levels "case1", "case2", ...
modalityID: [Factor] w/ 2 levels "testA" and "testB"
score: [num] reader score
[list] of simulation parameters:
Experiment labels and size
modalityID: [vector] label modality A and B.
nR: [num] number of readers
nC: [num] number of cases
C_dist: [chr] distribution of the case. Default C_dist="normal"
Mean and fixed effects:
mu: [num] grand mean
tau_A: [num] modality A
tau_B: [num] modality B
Reader-case interaction term
sigma_C: [num] std of case factor (if C_dist="normal")
a_C: [num] alpha for distribution of case (if C_dist="beta")
b_C: [num] beta for distribution of case (if C_dist="beta")
alpha_R: [num] shape parameter for reader
beta_R: [num] scale parameter for reader
Modality-reader-case-replicate interaction term for modality A
sigma_C.A: [num] std of case factor (if C_dist="normal")
a_C.A: [num] alpha for distribution of case (if C_dist="beta")
b_C.A: [num] beta for distribution of case (if C_dist="beta")
alpha_R.A: [num] shape parameter for reader
beta_R.A: [num] scale parameter for reader
Modality-reader-case-replicate interaction term for modality B
sigma_C.B: [num] std of case factor (if C_dist="normal")
a_C.B: [num] alpha for distribution of case (if C_dist="beta")
b_C.B: [num] beta for distribution of case (if C_dist="beta")
alpha_R.B: [num] shape parameter for reader
beta_R.B: [num] scale parameter for reader
Scales for the case related terms and interaction terms
C_scale: [num] weight for the case factor
RC_scale: [num] weight for the reader-case interaction term
tauC_scale: [num] weight for the modality-case term
tauRCE_scale: [num] weight for the modality-reader-case-replicate interaction term
[vector] of size nR of reader factors pre-generated from
a gamma(alpha_R, beta_R) distribution
to allow the reader factor to be fixed across multiple simulations.
Default = NULL
[vector] of size nR of modality-reader interaction terms
pre-generated from a gamma(alpha_R.A, beta_R.A) distribution
to allow the modality-reader interaction terms to be
fixed across multiple simulations the modality-reader interaction.
Default = NULL
[vector] of size nR of modality-reader interaction terms
pre-generated from a gamma(alpha_R.B, beta_R.B) distribution
to allow the modality-reader interaction terms to be
fixed across multiple simulations the modality-reader interaction.
Default = NULL
[bol] whether the data are within-modality (A==B).
In this case the modality-reader and modality-case interaction terms
will be the same.
Default = FALSE
The model has the following structure: X.ijkl = mu + m.i + RC.jk + mRCE.ijkl
mu = grand mean
m.i = modalities (levels: A and B)
RC.jk given R.j,C.k ~ N(C.k, R.j) reader-case interaction term
mRCE.ijkl given mR.ij,mC.ik ~ N(mC.ik, mR.ij) modality-reader-case-replicate term
C.k and mC.ik are Normal/beta distributed
R.j and mR.ij are Inverse-Gamma distributed