sim.NormalIG.Hierarchical: Simulate an MRMC data set comparing two modalities by a...

In iMRMC: Multi-Reader, Multi-Case Analysis Methods (ROC, Agreement, and Other Metrics)

Simulate an MRMC data set comparing two modalities by a hierarchical model

Description

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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/19466315.2022.2063169")}

Usage

sim.NormalIG.Hierarchical(
  config,
  R = NULL,
  AR = NULL,
  BR = NULL,
  is.within = FALSE
)

Arguments

config	[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
R	[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
AR	[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
BR	[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
is.within	[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

Details

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

Value

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

iMRMC documentation built on Sept. 11, 2024, 7:12 p.m.