From 715609b1da4048fe650769a07dff2f200be9ee90 Mon Sep 17 00:00:00 2001 From: Brandon Gallas Date: Thu, 15 Aug 2024 13:42:38 -0400 Subject: [PATCH 1/5] Review and revise documentation --- Rpackage/iMRMC/R/limitsOfAgreement.R | 89 +++++++++------ Rpackage/iMRMC/R/sim.NormalIG.Hierarchical.R | 104 +++++++++-------- .../CompareSimulationModels.Rmd | 52 ++++++++- .../CompareSimulationModels.pdf | Bin 161900 -> 211170 bytes .../extra/limitsOfAgreement/LOA_ANOVA.Rmd | 108 ++++++++++-------- .../extra/limitsOfAgreement/LOA_ANOVA.pdf | Bin 248708 -> 248282 bytes 6 files changed, 218 insertions(+), 135 deletions(-) diff --git a/Rpackage/iMRMC/R/limitsOfAgreement.R b/Rpackage/iMRMC/R/limitsOfAgreement.R index a622b715..4f509e04 100644 --- a/Rpackage/iMRMC/R/limitsOfAgreement.R +++ b/Rpackage/iMRMC/R/limitsOfAgreement.R @@ -1,32 +1,46 @@ +# limitsOfAgreement ########## #' @title MRMC Analysis of Limits of Agreement using ANOVA #' @description -#' These four functions calculate four types of Limits of Agreement using ANOVA: Within-Reader Between-Modality(WRBM), -#' Between-Reader Within-Modality(BRWM), Within-Reader Within-Modality(WRWM) and Between-Reader Between-Modality(BRBM). +#' These four functions calculate four types of Limits of Agreement using ANOVA: +#' Within-Reader Within-Modality(WRWM), Between-Reader Within-Modality(BRWM), +#' Within-Reader Between-Modality(WRBM), and Between-Reader Between-Modality(BRBM). #' The 95\% confidence interval of the mean difference is also provided. If the study is fully crossed, the ANOVA -#' method are realized either by applying stats::aov or by matrix multiplication. Otherwise, the SS in ANOVA is -#' computed as the residual sum of squares of linear models. See more details below about the model structure. +#' methods are realized either by applying \code{stats::aov} or by matrix multiplication. Otherwise, the SS in ANOVA are +#' computed as residual sums of squares of linear models. See details below about the model structure +#' and these references. +#' +#' \itemize{ +#' \item S. Wen and B. D. Gallas, +#' “Three-Way Mixed Effect ANOVA to Estimate MRMC Limits of Agreement,” +#' \emph{Statistics in Biopharmaceutical Research}, \strong{14}, pp. 532–541, 2022, +#' \url{https://www.doi.org/10.1080/19466315.2022.2063169}. +#' \item S. Wen and B. D. Gallas, +#' “Expanding to Arbitrary Study Designs: ANOVA to Estimate Limits of Agreement for MRMC Studies,” +#' \emph{arXiv}, 2023, \url{https://www.doi.org/10.48550/ARXIV.2312.16097}. +#' } #' #' @details -#' Suppose the score from reader j for case k under modality i is\eqn{X_{ijk}}, then the difference score from the -#' same reader for the same cases under two different modalities is \eqn{Y_{jk} = X_{1jk} - X_{2jk}}. +#' Suppose the score from a reader j for case k under modality \eqn{i} is\eqn{X_{ijk}}, then the difference score from the +#' same reader for the same case under two different modalities is \eqn{Y_{jk} = X_{1jk} - X_{2jk}}. #' \itemize{ #' \item\code{laWRBM} use two-way random effect ANOVA to analyze the difference scores \eqn{Y_{jk}}. The model #' is \eqn{Y_{jk}=\mu + R_j + C_k + \epsilon_{jk}}, where \eqn{R_j} and \eqn{C_k} are random effects for readers -#' and cases. The variance of mean and individual observation is expressed as the linear combination of the MS +#' and cases. The variances of mean and individual observations are expressed as linear combinations of the MS #' given by ANOVA. -#' \item\code{laBRWM} use two-way random effect ANOVA to analyze the scores \eqn{X_{ijk}} for a single modality i. +#' \item\code{laBRWM} use two-way random effect ANOVA to analyze the scores \eqn{X_{jk}} for a single modality. #' The model is \eqn{X_{jk}=\mu + R_j + C_k + \epsilon_{jk}}, where \eqn{R_j} and \eqn{C_k} are random effects -#' for readers and cases. The variance of mean and individual observation is expressed as the linear combination +#' for readers and cases. The variances of mean and individual observations are expressed as linear combinations #' of the MS given by ANOVA. #' \item\code{laWRWM} use two-way random effect ANOVA to analyze the difference scores \eqn{Y_{jk}} from the same -#' reader for the same cases under the same modality with different replicates \eqn{Y_{jk} = X_{ijk1} - X_{ijk2}}. +#' reader for the same cases under the same modality with different replicates \eqn{Y_{jk} = X_{jk1} - X_{jk2}}. #' The model is \eqn{Y_{jk}=\mu + R_j + C_k + \epsilon_{jk}}, where \eqn{R_j} and \eqn{C_k} are random effects for -#' readers and cases. The variance of mean and individual observation is expressed as the linear combination of +#' readers and cases. The variances of mean and individual observations are expressed as linear combinations of #' the MS given by ANOVA. #' \item\code{laBRBM} use three-way mixed effect ANOVA to analyze the scores \eqn{X_{ijk}}. The model is given by #' \eqn{X_{ijk}=\mu + R_j + C_k + m_i + RC_{jk} + mR_{ij} + mC_{ik} + \epsilon_{ijk}}, where \eqn{R_j} and -#' \eqn{C_k} are random effects for readers and cases and \eqn{m_i} is a fixed effect for modality. The variance -#' of mean and individual observation is expressed as the linear combination of the MS given by ANOVA. +#' \eqn{C_k} are random effects for readers and cases, \eqn{m_i} is a fixed effect for modality, and the other terms +#' are interaction terms. The variances of mean and individual observations are expressed as linear combinations +#' of the MS given by ANOVA. #' } #' #' @name limitsOfAgreement @@ -41,33 +55,33 @@ #' The caseID is treated as a random effect.} #' \item{modalityID}{The factor corresponding to the different modalities in the study. #' The modalityID is treated as a fixed effect.} -#' \item{score}{The score given by the reader to the case for the modality indicated.} +#' \item{score}{The number (observation) given by the reader to the case for the modality indicated.} #' } #' #' @param modalitiesToCompare -#' The factors identifying the modalities to compare. It should be at length 2. Default -#' \code{modalitiesToCompare = c("testA","testB")} +#' The factors identifying the modalities to compare. It should be length 2. +#' Default = \code{c("testA","testB")} #' #' @param replicatesToCompare -#' The factors identifying the replicates to compare for laWRWM. It should be at length 2. Default -#' \code{modalitiesToCompare = c("testA","testB")} +#' The factors identifying the replicates to compare for \code{laWRWM}. It should be length 2. +#' Default = \code{c("testA","testB")} #' #' @param modality -#' The factor identifying the modality for laBRWM. It should be at length 1. Default -#' \code{modality = c("testA")} +#' The factor identifying the modality for laBRWM. It should be length 1. +#' Default = \code{modality = c("testA")} #' #' @param keyColumns -#' Identify the factors corresponding to the readerID, caseID, modalityID, and score -#' (or alternative random and fixed effects). Default \code{keyColumns = c("readerID", "caseID", -#' "modalityID", "score")} +#' Identify the factors corresponding to the readerID (random effect), caseID (random effect), +#' modalityID (fixed effect), and score (observation). +#' Default = \code{c("readerID", "caseID", "modalityID", "score")} #' #' @param if.aov #' Boolean value to determine whether using aov function to do ANOVA for the fully cross study only. -#' Default \code{if.aov = TRUE} +#' Default = \code{TRUE} #' #' @param is.sparseQR #' Boolean value to determine whether using sparseQR function to do QR decomposition when the study is not fully crossed. -#' Default \code{is.sparseQR = TRUE} +#' Default = \code{TRUE} #' #' @param type #' Identify which type of SS is computed in ANOVA. The possible values are c(1,2,3) @@ -79,21 +93,23 @@ #' #' #' @return -#' A list of two dataframes -#' The first dataframe is \code{limits.of.agreement} with one row. Each column is as following: +#' A list of two dataframes. +#' +#' The first dataframe is \code{limits.of.agreement}. It has one row. Each column is as follows: #' \describe{ -#' \item{meanDiff}{The mean of difference score.} -#' \item{var.MeanDiff}{The variance of mean difference score} -#' \item{var.1obs}{The variance of a single WRBM/BRBM difference score} +#' \item{meanDiff}{The mean difference score.} +#' \item{var.MeanDiff}{The variance of the mean difference score.} +#' \item{var.1obs}{The variance of a single WRBM/BRBM difference score.} #' \item{ci95meanDiff.bot}{Lower bound of 95\% CI for the mean difference score. \code{meanDiff+ #' 1.96*sqrt(var.MeanDiff)}} #' \item{ci95meanDiff.top}{Upper bound of 95\% CI for the mean difference score. \code{meanDiff- #' 1.96*sqrt(var.MeanDiff)}} -#' \item{la.bot}{Lower bound of WRBM/BRBM Limits of Agreement. \code{meanDiff+1.96*sqrt(var.1obs)}} -#' \item{la.top}{Upper bound of WRBM/BRBM Limits of Agreement. \code{meanDiff-1.96*sqrt(var.1obs)}} +#' \item{la.bot}{Lower Limit of Agreement for the difference score. \code{meanDiff+1.96*sqrt(var.1obs)}} +#' \item{la.top}{Upper Limit of Agreement for the difference score. \code{meanDiff-1.96*sqrt(var.1obs)}} #' } -#' The second dataframe is \code{two.way.ANOVA} or \code{three.way.ANOVA} showing the degree of freedom, -#' sum of squares, and variance component estimates for different sources of variation +#' +#' The second dataframe is \code{two.way.ANOVA} or \code{three.way.ANOVA} shows the degrees of freedom, +#' sums of squares, and estimates of variance components for each source of variation #' #' #' @importFrom stats aov var qnorm model.matrix @@ -101,7 +117,12 @@ #' @export #' #' @examples +#' # Initialize the simulation configuration parameters #' config <- sim.NormalIG.Hierarchical.config(modalityID = c("testA", "testB")) +#' +#' # Initizlize the seed and stream of the random number generator +#' init.lecuyerRNG() +#' #' # Simulate an MRMC ROC data set #' dFrame <- sim.NormalIG.Hierarchical(config) #' diff --git a/Rpackage/iMRMC/R/sim.NormalIG.Hierarchical.R b/Rpackage/iMRMC/R/sim.NormalIG.Hierarchical.R index 02e65faf..ef3902d0 100644 --- a/Rpackage/iMRMC/R/sim.NormalIG.Hierarchical.R +++ b/Rpackage/iMRMC/R/sim.NormalIG.Hierarchical.R @@ -1,21 +1,31 @@ #' Simulate an MRMC data set comparing two modalities by a hierarchical model #' #' @description -#' This procedure simulates an MRMC data set for a MRMC agreement study comparing two -#' modalities.It is a hierarchical model consists of two interaction terms: reader-case -#' interaction and modality-reader-case-replicate interaction. Both the interaction -#' terms are conditional normal distributed, with the case(-related) factor contributing +#' 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. +#' 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: +#' +#' \itemize{ +#' \item S. Wen and B. D. Gallas, +#' “Three-Way Mixed Effect ANOVA to Estimate MRMC Limits of Agreement,” +#' \emph{Statistics in Biopharmaceutical Research}, \strong{14}, pp. 532–541, 2022, +#' \url{https://www.doi.org/10.1080/19466315.2022.2063169} +#' } +#' #' @details -#' The model is as the following structure: +#' The model has the following structure: #' X.ijkl = mu + m.i + RC.jk + mRCE.ijkl #' \itemize{ #' \item mu = grand mean #' \item m.i = modalities (levels: A and B) -#' \item RC.jk|R.j,C.k ~ N(C.k, R.j) reader-case interaction term -#' \item mRCE.ijkl|mR.ij,mC.ik ~ N(mC.ik, mR.ij) modality-reader-case-replicate term +#' \item RC.jk given R.j,C.k ~ N(C.k, R.j) reader-case interaction term +#' \item mRCE.ijkl given mR.ij,mC.ik ~ N(mC.ik, mR.ij) modality-reader-case-replicate term #' \item C.k and mC.ik are Normal/beta distributed #' \item R.j and mR.ij are Inverse-Gamma distributed #' } @@ -24,59 +34,59 @@ #' \itemize{ #' \item Experiment labels and size #' \itemize{ -#' \item modalityID: [vector] label modality A and B. -#' \item nR: [num] number of readers -#' \item nC: [num] number of cases -#' \item C_dist: [chr] distribution of the case. Default \code{C_dist="normal"} +#' \item \code{modalityID}: [vector] label modality A and B. +#' \item \code{nR}: [num] number of readers +#' \item \code{nC}: [num] number of cases +#' \item \code{C_dist}: [chr] distribution of the case. Default \code{C_dist="normal"} #' } #' \item Mean and fixed effects: #' \itemize{ -#' \item mu: [num] grand mean -#' \item tau_A: [num] modality A -#' \item tau_B: [num] modality B +#' \item \code{mu}: [num] grand mean +#' \item \code{tau_A}: [num] modality A +#' \item \code{tau_B}: [num] modality B #' } #' \item Reader-case interaction term #' \itemize{ -#' \item sigma_C: [num] std of case factor (if \code{C_dist="normal"}) -#' \item a_C: [num] alpha for distribution of case (if \code{C_dist="beta"}) -#' \item b_C: [num] beta for distribution of case (if \code{C_dist="beta"}) -#' \item alpha_R: [num] shape parameter for reader -#' \item beta_R: [num] scale parameter for reader +#' \item \code{sigma_C}: [num] std of case factor (if \code{C_dist="normal"}) +#' \item \code{a_C}: [num] alpha for distribution of case (if \code{C_dist="beta"}) +#' \item \code{b_C}: [num] beta for distribution of case (if \code{C_dist="beta"}) +#' \item \code{alpha_R}: [num] shape parameter for reader +#' \item \code{beta_R}: [num] scale parameter for reader #' } #' \item Modality-reader-case-replicate interaction term for modality A #' \itemize{ -#' \item sigma_C.A: [num] std of case factor (if \code{C_dist="normal"}) -#' \item a_C.A: [num] alpha for distribution of case (if \code{C_dist="beta"}) -#' \item b_C.A: [num] beta for distribution of case (if \code{C_dist="beta"}) -#' \item alpha_R.A: [num] shape parameter for reader -#' \item beta_R.A: [num] scale parameter for reader +#' \item \code{sigma_C.A}: [num] std of case factor (if \code{C_dist="normal"}) +#' \item \code{a_C.A}: [num] alpha for distribution of case (if \code{C_dist="beta"}) +#' \item \code{b_C.A}: [num] beta for distribution of case (if \code{C_dist="beta"}) +#' \item \code{alpha_R.A}: [num] shape parameter for reader +#' \item \code{beta_R.A}: [num] scale parameter for reader #' } #' \item Modality-reader-case-replicate interaction term for modality B #' \itemize{ -#' \item sigma_C.B: [num] std of case factor (if \code{C_dist="normal"}) -#' \item a_C.B: [num] alpha for distribution of case (if \code{C_dist="beta"}) -#' \item b_C.B: [num] beta for distribution of case (if \code{C_dist="beta"}) -#' \item alpha_R.B: [num] shape parameter for reader -#' \item beta_R.B: [num] scale parameter for reader +#' \item \code{sigma_C.B}: [num] std of case factor (if \code{C_dist="normal"}) +#' \item \code{a_C.B}: [num] alpha for distribution of case (if \code{C_dist="beta"}) +#' \item \code{b_C.B}: [num] beta for distribution of case (if \code{C_dist="beta"}) +#' \item \code{alpha_R.B}: [num] shape parameter for reader +#' \item \code{beta_R.B}: [num] scale parameter for reader #' } #' \item Scales for the case related terms and interaction terms #' \itemize{ -#' \item C_scale: [num] weight for the case factor -#' \item RC_scale: [num] weight for the reader-case interaction term -#' \item tauC_scale: [num] weight for the modality-case term -#' \item tauRCE_scale: [num] weight for the modality-reader-case-replicate interaction term +#' \item \code{C_scale}: [num] weight for the case factor +#' \item \code{RC_scale}: [num] weight for the reader-case interaction term +#' \item \code{tauC_scale}: [num] weight for the modality-case term +#' \item \code{tauRCE_scale}: [num] weight for the modality-reader-case-replicate interaction term #' } #' } -#' @param R [vector] fix the reader factor across different simulation. Default \code{R = NULL} -#' @param AR [vector] fix the modality-reader interaction. Default \code{AR = NULL} -#' @param BR [vector] fix the modality-reader interaction. Default \code{BR = NULL} -#' @param is.within [bol] whether the data are within-modality (AR==BR). Default \code{is.within=FALSE} +#' @param \code{R} [vector] fix the reader factor across different simulation. Default \code{R = NULL} +#' @param \code{AR} [vector] fix the modality-reader interaction. Default \code{AR = NULL} +#' @param \code{BR} [vector] fix the modality-reader interaction. Default \code{BR = NULL} +#' @param \code{is.within} [bol] whether the data are within-modality (AR==BR). Default \code{is.within=FALSE} #' #' @return df [data.frame] with nR x nC x 2 rows including #' \itemize{ #' \item readerID: [Factor] w/ nR levels "reader1", "reader2", ... #' \item caseID: [Factor] w/ nC levels "case1", "case2", ... -#' \item modalityID: [Factor] w/ 1 level config$modalityID +#' \item modalityID: [Factor] w/ 2 levels "testA" and "testB" #' \item score: [num] reader score #' } #' @@ -182,14 +192,15 @@ sim.NormalIG.Hierarchical = function(config,R = NULL,AR = NULL,BR = NULL,is.with return(df) } -#' Create a configuration object for the sim.NormalIG.Hierarchical program -#' -#'#' @description -#' This function creates a configuration object for the Hierarchical -#' simulation model to be used as input for the sim.NormalIG.Hierarchical program. +#' Create a configuration object for the sim.NormalIG.Hierarchical function #' +#' @description +#' This function creates a configuration object that sets the parameters +#' for the Hierarchical Inverse-Gamma simulation model. The configuration +#' object is an to the \code{\link{sim.NormalIG.Hierarchical}} function. +#' #' @details If no arguments, this function returns a default simulation -#' configuration for sim.NormalIG.Hierarchical +#' configuration for the \code{\link{sim.NormalIG.Hierarchical}} function. #' #' @param nR [num] Number of readers. Default \code{nR = 5} #' @param nC [num] Number of cases. Default \code{nC = 100} @@ -211,7 +222,8 @@ sim.NormalIG.Hierarchical = function(config,R = NULL,AR = NULL,BR = NULL,is.with #' @param tauC_scale [num] weight for the modality-case term. Default \code{tauC_scale = 1} #' @param tauRCE_scale [num] weight for the modality-reader-case-replicate interaction term. Default \code{tauRCE_scale = 1} #' -#' @return config [list] Refer to the sim.NormalIG.Hierarchical input variable +#' @return config [list] of input parameters for \code{\link{sim.NormalIG.Hierarchical}}. +#' #' @export #' diff --git a/Rpackage/iMRMC/inst/extra/limitsOfAgreement/CompareSimulationModels.Rmd b/Rpackage/iMRMC/inst/extra/limitsOfAgreement/CompareSimulationModels.Rmd index 5b4d86d9..121f1189 100644 --- a/Rpackage/iMRMC/inst/extra/limitsOfAgreement/CompareSimulationModels.Rmd +++ b/Rpackage/iMRMC/inst/extra/limitsOfAgreement/CompareSimulationModels.Rmd @@ -13,11 +13,25 @@ library(iMRMC) knitr::opts_chunk$set(echo = TRUE) ``` -There are two functions in this package that can simulate Multi-reader Multi-case (MRMC) data. sim.NormalIG.Hierarchical is the function to simulate the MRMC agreement data with no binary truth state. The sim.gRoeMetz is the function to simulate MRMC ROC data. +Here we demonstrate how to simulate Multi-reader Multi-case (MRMC) data using functions in the iMRMC package. + + + +`sim.NormalIG.Hierarchical` is a function that simulates MRMC **agreement** data (no binary truth state). The model for the `sim.NormalIG.Hierarchical` function is described here: + +* 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, https://www.doi.org/10.1080/19466315.2022.2063169. + + + +`sim.gRoeMetz` is a function that simulates MRMC **ROC** data. We note here that the model for `sim.gRoeMetz` does not yield readers with different average/expected levels of agreement with one another. This limitation was the reason for developing the model for the `sim.NormalIG.Hierarchical` simulation. The model for the `sim.gRoeMetz` function is described here: + +* B. D. Gallas and S. L. Hillis, “Generalized Roe and Metz ROC model: analytic link between simulated decision scores and empirical AUC variances and covariances,” *J Med Img*, **1**, no. 3, p. 031006, 2014, https://www.doi.org/10.1117/1.JMI.1.3.031006. + + ## 1. Using the new hierachical model to simulate the MRMC agreement data -The following is how to use the sim.NormalIG.Hierachcial.R to simulate MRMC data with no truth state, the MRMC agreement data +The following is how to use the `sim.NormalIG.Hierachcial` function to simulate MRMC agreement data (with no truth state). First, we initialize a list of simulation parameters using the `sim.NormalIG.Hierarchical.conf` function. There are many simulation parameters. All have default values that can be changed in the function call. There are some parameters that are set equal for convenience and might need to be changed before simulating the data. Below, we demonstrate specifying non-default numbers of readers and cases. ```{r} @@ -27,6 +41,19 @@ nC = 100 #number of cases config <- sim.NormalIG.Hierarchical.config(nR=nR, nC=nC, modalityID = c("testA","testB")) +``` +Here are all the simulation parameters: + +```{r} + +print(names(config)) + +``` + +Next, we set the random seed for reproducible simulations (if needed) and simulate the MRMC agreement data based on the `config` list of parameters. The data frame for 5 readers and 100 cases for 2 modalities has 1000 rows (6x50x2). The 4 columns specify the reader ID, the case ID, the modality ID, and the score, or observation. + +```{r} + # simulate MRMC study set.seed(1, kind = "L'Ecuyer-CMRG") dFrame.newH <- sim.NormalIG.Hierarchical(config) @@ -37,11 +64,10 @@ print(dFrame.newH[(nrow(dFrame.newH) - 5):nrow(dFrame.newH), ]) ``` -We simulated 5 readers and 100 cases for 2 modalities, so the total number of scores is 5x100x2=1000. ## 2. Using sim.gRoeMetz in iMRMC package to simulate MRMC ROC data -The following is how to use the sim.gRoeMetz.R to simulate MRMC data with truth state, the MRMC ROC data +The following demonstrated how to use the `sim.gRoeMetz` function to simulate MRMC ROC data (with truth state). Again, the process starts by creating a `config` list of the simulation parameters that can be changed in the function call. ```{r} @@ -52,6 +78,19 @@ nC.pos = 50 #number of negative cases config <- sim.gRoeMetz.config(nR = nR, nC.neg = nC.neg, nC.pos = nC.neg) +``` + +Here are the simulation parameters for the `sim.gRoeMetz` simulation function. Note that there are some parameters that are set equal for convenience and might need to be changed before simulating the data. + +```{r} + +print(names(config)) + +``` + +We again set the seed for reproducible simulations (if needed) before we simulate the data. As we see below, the simulated data starts with truth state of each case. This is followed by the reading scores from each of the readers. Since we simulate 50 positive cases and 50 negative cases, there are 100 rows for the truth and 100x5x2 = 1000 rows for the scores from 5 readers for 2 modalities. Therefore, the data frame has 1100 rows. + +```{r} # simulate MRMC study set.seed(1, kind = "L'Ecuyer-CMRG") dFrame.gRM <- sim.gRoeMetz(config) @@ -62,9 +101,10 @@ print(dFrame.gRM[(nrow(dFrame.gRM) - 5):nrow(dFrame.gRM), ]) ``` -The simulated data starts with truth state of each case, and followed by the reading scores from each of the readers. Since we simulate 50 positive cases and 50 negative cases, there are 100 lines for the truth and 100x5x2 = 1000 lines for the scores from 5 readers for 2 modalities. -To combine the truth data and the reader scores and change the data to a dataframe with 5 columns: readerID, caseID, modalityID, score, truth, we can use the function undoIMRMCdf in iMRMC pacakge: + +To combine the truth data and the reader scores and change the data to a dataframe with 5 columns (readerID, caseID, modalityID, score, truth) we can use the function undoIMRMCdf in iMRMC pacakge. + ```{r} dFrame.gRM.2 <- undoIMRMCdf(dFrame.gRM) diff --git a/Rpackage/iMRMC/inst/extra/limitsOfAgreement/CompareSimulationModels.pdf b/Rpackage/iMRMC/inst/extra/limitsOfAgreement/CompareSimulationModels.pdf index b89c1d3715ae5b4b409e2b60c03e7e0fe323bb70..b61358c95c718557bbabb238497e0b878832f1ea 100644 GIT binary patch delta 113739 zcmZtNQ*19x_$Tn%w%wlEwr!o-w%z_}+dZ{y+qP}n*1ns6_F}VpGnr(rW-@ucpFESf 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z0E;qnwXX=!#)X@<=Ch!Uub-qao_b*AxHQND96i(|2cB6qJ0wU<-|qy;(a#kaU%x-F z>~w>b;Bep#6vMx2ZDRz7uRk#OZb1hOw9}t47lXTbdv>&E8y4egPC`va;0j@Ya9lwJ%im%s3Q($rH48oy!TwOyh#nsLI7?2AFsck^^}KiF}2x_JSl3IgyBx&!l9(GQj^*om|U0m%Y` z-)3qK4BAL|C9Bg0rl;3N>E;ixVnL;%VF&q#%UFM4@COn!4Hb5vmQp_~lZ1$3gc9&Y zHiG(#W(%3x4D}O>nXmm|$qfDyMO--eLQqk|gLh8I)X~mP4uq2nh)H|Cy}iE^hwaSc s@SL4E6a{Kt;CSb;h_=n=Or|5CR+YkYB~up?Bo~w|rk0k@-Y%y92bL5neE Date: Thu, 15 Aug 2024 17:48:25 -0400 Subject: [PATCH 2/5] Update repo README --- README.md | 22 +++++++--------------- 1 file changed, 7 insertions(+), 15 deletions(-) diff --git a/README.md b/README.md index ba926bad..7c01727f 100644 --- a/README.md +++ b/README.md @@ -1,4 +1,4 @@ -

README for iMRMC and iRoeMetz

+# README for iMRMC and iRoeMetz Here is a high-level overview of the iMRMC software: @@ -7,15 +7,15 @@ Here is a high-level overview of the iMRMC software: Examples of specific MRMC analyses and other FAQs are available in the [iMRMC repository's Wiki](https://github.com/DIDSR/iMRMC/wiki). -Visit the release Page to download the software or access the repository [HERE](https://github.com/DIDSR/iMRMC). +The R package is available from [CRAN](https://cran.r-project.org/web/packages/iMRMC/index.html). You can also visit the release Page to download the R package (source tar.gz file and binary zip file), the zip and tar.gz files of the entire repository, or the iMRMC java app (jar file). -The documentation for both packages can be found here. +Documentation of the java app can be found here: http://didsr.github.io/iMRMC/. -Here is a summary of updates to [iMRMC](https://github.com/DIDSR/iMRMC/blob/master/UPDATES_iMRMC.md) and a summary of updates to [iRoeMetz](https://github.com/DIDSR/iMRMC/blob/master/UPDATES_iRoeMetz.md). +Here are summaries of updates to the now frozen java apps: [iMRMC](https://github.com/DIDSR/iMRMC/blob/master/UPDATES_iMRMC.md) and [iRoeMetz](https://github.com/DIDSR/iMRMC/blob/master/UPDATES_iRoeMetz.md). Please check out a statement of the licenses related to our software [here](LICENSE.md). -
iMRMC
+## iMRMC Desc: The primary objective of the iMRMC application is to assist investigators with analyzing and sizing multi-reader multi-case (MRMC) reader studies that compare the difference in the area under Receiver Operating Characteristic curves (AUCs) from two modalities. The core elements of this application include the ability to perform MRMC variance analysis and the ability to size an MRMC trial. @@ -23,23 +23,15 @@ Desc: The primary objective of the iMRMC application is to assist investigators * There is also an R package that utilizes the core Java application. Examples for using the programs can be found in the R help files. Here are some ways to cite our work: +* FDA/CDRH, “iMRMC: Software for the Statistical Analysis of multi-reader multi-case studies,” *RST Catalog*, 2022, https://doi.org/10.5281/ZENODO.6628838. * Gallas, Brandon D., Andriy Bandos, Frank Samuelson, and Robert F. Wagner. “A Framework for Random-Effects ROC Analysis: Biases with the Bootstrap and Other Variance Estimators.” Commun Stat A-Theory 38, no. 15 (2009): 2586–2603. https://doi.org/10.1080/03610920802610084. * Gallas, Brandon D. “One-Shot Estimate of MRMC Variance: AUC.” Acad Radiol 13, no. 3 (2006): 353–62. https://doi.org/10.1016/j.acra.2005.11.030. -To cite the java code, please use this (with the appropriate version number): -* Gallas, Brandon D., "IMRMC-java vX.XX: Application for Analyzing and Sizing MRMC Reader Studies." Silver Spring, MD, 2017. https://github.com/DIDSR/iMRMC/releases. -To cite the R package, please use this (version number depends on whether you downloaded the code from GitHub or CRAN): -* Gallas, Brandon D., "IMRMC-R vX.XX: Application for Analyzing and Sizing MRMC Reader Studies." Silver Spring, MD, 2017. https://cran.r-project.org/web/packages/iMRMC/index.html. - -
iRoeMetz
+## iRoeMetz Desc: The iRoeMetz application can be used to simulate the reader scores for MRMC experiments via Monte Carlo methods given variance components of the ROC scores. The application also estimates the variance components of AUC and can calculate the variance components directly with numerical integration. The simulated experiments can be saved and used in MRMC variance analysis programs, such as iMRMC. The iRoeMetz application is a stand-alone, precompiled, license-free Java applications and the source code. -
R package iMRMC
- -Desc: The R package iMRMC executes the iMRMC program which writes the results to the local files system, it reads the analysis results from the local file system, packs the analysis results into a list object, deletes the data and analysis results from the local file system, and returns the list object. - Here is one way to cite our work: * Gallas, Brandon D., and Stephen L. Hillis. “Generalized Roe and Metz ROC Model: Analytic Link between Simulated Decision Scores and Empirical AUC Variances and Covariances.” J Med Img 1, no. 3 (2014): 031006. https://doi.org/doi:10.1117/1.JMI.1.3.031006. From 0d1c7bc254b531138f5d6a8b1577941a70fda5d4 Mon Sep 17 00:00:00 2001 From: Brandon Gallas Date: Thu, 15 Aug 2024 17:48:54 -0400 Subject: [PATCH 3/5] Update NEWS and DESCRIPTION files in the R package --- Rpackage/iMRMC/DESCRIPTION | 2 +- Rpackage/iMRMC/NEWS.md | 6 ++++++ 2 files changed, 7 insertions(+), 1 deletion(-) diff --git a/Rpackage/iMRMC/DESCRIPTION b/Rpackage/iMRMC/DESCRIPTION index bc7d8f1b..0eb07535 100644 --- a/Rpackage/iMRMC/DESCRIPTION +++ b/Rpackage/iMRMC/DESCRIPTION @@ -1,7 +1,7 @@ Package: iMRMC Type: Package Title: Multi-Reader, Multi-Case Analysis Methods (ROC, Agreement, and Other Metrics) -Version: 2.0.0 +Version: 2.1.0 Author: Brandon Gallas Maintainer: Brandon Gallas Description: This software does Multi-Reader, Multi-Case (MRMC) analyses of data from imaging studies where clinicians (readers) evaluate patient images (cases). What does this mean? ... Many imaging studies are designed so that every reader reads every case in all modalities, a fully-crossed study. In this case, the data is cross-correlated, and we consider the readers and cases to be cross-correlated random effects. An MRMC analysis accounts for the variability and correlations from the readers and cases when estimating variances, confidence intervals, and p-values. The functions in this package can treat arbitrary study designs and studies with missing data, not just fully-crossed study designs. An overview of this software, including references presenting details on the methods, can be found here: . diff --git a/Rpackage/iMRMC/NEWS.md b/Rpackage/iMRMC/NEWS.md index 53c29b4c..05c94de9 100644 --- a/Rpackage/iMRMC/NEWS.md +++ b/Rpackage/iMRMC/NEWS.md @@ -11,6 +11,12 @@ A big thank you to all that have worked on this software throughout the years. W * Yousun Ko          • Rowhan Pathare * Si Wen             • Adam Wunderlich +# iMRMC 2.1.0 +*08/2024* +- Add functions and tests to do MRMC analysis of limits of agreement `laWRWM`, `laWRBM`, `laBRWM`, `laBRBM` +- Add function and test to simulate MRMC agreement data: `sim.NormalIG.Hierarchical` +- Add scripts to demonstrate new simulation and analysis of MRMC agreement data in the `Rpackage/iMRMC/inst/extra/limitsOfAgreement` folder + # iMRMC 2.0.0 *04/2024* - Add R only functions to analyze MRMC studies, notably `doIMRMC()` From bd8475ab0ede95fa4f98c038b215c14d22af61b5 Mon Sep 17 00:00:00 2001 From: Brandon Gallas Date: Thu, 15 Aug 2024 17:49:34 -0400 Subject: [PATCH 4/5] Revisions to the software documentation --- Rpackage/iMRMC/R/limitsOfAgreement.R | 15 ++++++++---- Rpackage/iMRMC/R/sim.NormalIG.Hierarchical.R | 25 ++++++++++++++++---- 2 files changed, 32 insertions(+), 8 deletions(-) diff --git a/Rpackage/iMRMC/R/limitsOfAgreement.R b/Rpackage/iMRMC/R/limitsOfAgreement.R index 4f509e04..e8751340 100644 --- a/Rpackage/iMRMC/R/limitsOfAgreement.R +++ b/Rpackage/iMRMC/R/limitsOfAgreement.R @@ -76,15 +76,22 @@ #' Default = \code{c("readerID", "caseID", "modalityID", "score")} #' #' @param if.aov -#' Boolean value to determine whether using aov function to do ANOVA for the fully cross study only. +#' Boolean value to determine whether to use the `stats::aov` function or to +#' calculate the ANOVA statistics explicitly. `stats::aov` is only appropriate +#' for fully-crossed study only. This flag permits head-to-head comparisons of +#' the output from `stats::aov` and the explicit calculations. #' Default = \code{TRUE} #' #' @param is.sparseQR -#' Boolean value to determine whether using sparseQR function to do QR decomposition when the study is not fully crossed. +#' Boolean value to determine whether the `base::qr` function assumes the input +#' data is sparse or not. #' Default = \code{TRUE} #' #' @param type -#' Identify which type of SS is computed in ANOVA. The possible values are c(1,2,3) +#' Identify how SS are computed in ANOVA for unbalanced study designs. +#' The possible values are c(1,2,3), corresponding to the approaches +#' introduced in the SAS package(Langsrud2003_Stat-Comput_v13p163). +#' #' Default \code{type= 1} #' #' @param reader.first @@ -99,7 +106,7 @@ #' \describe{ #' \item{meanDiff}{The mean difference score.} #' \item{var.MeanDiff}{The variance of the mean difference score.} -#' \item{var.1obs}{The variance of a single WRBM/BRBM difference score.} +#' \item{var.1obs}{The variance of the difference score.} #' \item{ci95meanDiff.bot}{Lower bound of 95\% CI for the mean difference score. \code{meanDiff+ #' 1.96*sqrt(var.MeanDiff)}} #' \item{ci95meanDiff.top}{Upper bound of 95\% CI for the mean difference score. \code{meanDiff- diff --git a/Rpackage/iMRMC/R/sim.NormalIG.Hierarchical.R b/Rpackage/iMRMC/R/sim.NormalIG.Hierarchical.R index ef3902d0..92c85977 100644 --- a/Rpackage/iMRMC/R/sim.NormalIG.Hierarchical.R +++ b/Rpackage/iMRMC/R/sim.NormalIG.Hierarchical.R @@ -77,10 +77,27 @@ #' \item \code{tauRCE_scale}: [num] weight for the modality-reader-case-replicate interaction term #' } #' } -#' @param \code{R} [vector] fix the reader factor across different simulation. Default \code{R = NULL} -#' @param \code{AR} [vector] fix the modality-reader interaction. Default \code{AR = NULL} -#' @param \code{BR} [vector] fix the modality-reader interaction. Default \code{BR = NULL} -#' @param \code{is.within} [bol] whether the data are within-modality (AR==BR). Default \code{is.within=FALSE} +#' @param R [vector] of size \code{nR} of reader factors pre-generated from +#' a gamma(\code{alpha_R}, \code{beta_R}) distribution +#' to allow the reader factor to be fixed across multiple simulations. +#' Default \code{= NULL} +#' +#' @param AR [vector] of size \code{nR} of modality-reader interaction terms +#' pre-generated from a gamma(\code{alpha_R.A}, \code{beta_R.A}) distribution +#' to allow the modality-reader interaction terms to be +#' fixed across multiple simulations the modality-reader interaction. +#' Default \code{= NULL} +#' +#' @param BR [vector] of size \code{nR} of modality-reader interaction terms +#' pre-generated from a gamma(\code{alpha_R.B}, \code{beta_R.B}) distribution +#' to allow the modality-reader interaction terms to be +#' fixed across multiple simulations the modality-reader interaction. +#' Default \code{= NULL} +#' +#' @param 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 \code{= FALSE} #' #' @return df [data.frame] with nR x nC x 2 rows including #' \itemize{ From 8a30981c1e3d7e5534884552bb3f4820283e21f2 Mon Sep 17 00:00:00 2001 From: Brandon Gallas Date: Thu, 15 Aug 2024 17:49:59 -0400 Subject: [PATCH 5/5] Revisions to the limits of agreement R markdown files --- .../CompareSimulationModels.Rmd | 12 ++++----- .../CompareSimulationModels.pdf | Bin 211170 -> 211242 bytes .../extra/limitsOfAgreement/LOA_ANOVA.Rmd | 25 +++++++++--------- .../extra/limitsOfAgreement/LOA_ANOVA.pdf | Bin 248282 -> 248507 bytes 4 files changed, 19 insertions(+), 18 deletions(-) diff --git a/Rpackage/iMRMC/inst/extra/limitsOfAgreement/CompareSimulationModels.Rmd b/Rpackage/iMRMC/inst/extra/limitsOfAgreement/CompareSimulationModels.Rmd index 121f1189..fe691323 100644 --- a/Rpackage/iMRMC/inst/extra/limitsOfAgreement/CompareSimulationModels.Rmd +++ b/Rpackage/iMRMC/inst/extra/limitsOfAgreement/CompareSimulationModels.Rmd @@ -17,7 +17,7 @@ Here we demonstrate how to simulate Multi-reader Multi-case (MRMC) data using fu -`sim.NormalIG.Hierarchical` is a function that simulates MRMC **agreement** data (no binary truth state). The model for the `sim.NormalIG.Hierarchical` function is described here: +`sim.NormalIG.Hierarchical` is a function that simulates MRMC **agreement** data (no binary truth state returned). The model for the `sim.NormalIG.Hierarchical` function is described here: * 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, https://www.doi.org/10.1080/19466315.2022.2063169. @@ -31,7 +31,7 @@ Here we demonstrate how to simulate Multi-reader Multi-case (MRMC) data using fu ## 1. Using the new hierachical model to simulate the MRMC agreement data -The following is how to use the `sim.NormalIG.Hierachcial` function to simulate MRMC agreement data (with no truth state). First, we initialize a list of simulation parameters using the `sim.NormalIG.Hierarchical.conf` function. There are many simulation parameters. All have default values that can be changed in the function call. There are some parameters that are set equal for convenience and might need to be changed before simulating the data. Below, we demonstrate specifying non-default numbers of readers and cases. +The following is how to use the `sim.NormalIG.Hierachcial` function to simulate MRMC agreement data (with no truth state). First, we initialize a list of simulation parameters using the `sim.NormalIG.Hierarchical.config` function. There are many simulation parameters. All have default values that can be changed in the function call. There are some parameters returned by the function that are equal for convenience and might need to be changed before simulating the data. Below, we demonstrate specifying non-default numbers of readers and cases. ```{r} @@ -50,7 +50,7 @@ print(names(config)) ``` -Next, we set the random seed for reproducible simulations (if needed) and simulate the MRMC agreement data based on the `config` list of parameters. The data frame for 5 readers and 100 cases for 2 modalities has 1000 rows (6x50x2). The 4 columns specify the reader ID, the case ID, the modality ID, and the score, or observation. +Next, we set the random seed for reproducible simulations (if needed) and simulate the MRMC agreement data based on the `config` list of parameters. The data frame for 5 readers and 100 cases for 2 modalities has 1000 rows (5x100x2). The 4 columns specify the reader ID, the case ID, the modality ID, and the score, or observation. ```{r} @@ -67,7 +67,7 @@ print(dFrame.newH[(nrow(dFrame.newH) - 5):nrow(dFrame.newH), ]) ## 2. Using sim.gRoeMetz in iMRMC package to simulate MRMC ROC data -The following demonstrated how to use the `sim.gRoeMetz` function to simulate MRMC ROC data (with truth state). Again, the process starts by creating a `config` list of the simulation parameters that can be changed in the function call. +The following demonstrates how to use the `sim.gRoeMetz` function to simulate MRMC ROC data (with truth state). Again, the process starts by creating a `config` list of default simulation parameters that can be changed in the function call. ```{r} @@ -88,7 +88,7 @@ print(names(config)) ``` -We again set the seed for reproducible simulations (if needed) before we simulate the data. As we see below, the simulated data starts with truth state of each case. This is followed by the reading scores from each of the readers. Since we simulate 50 positive cases and 50 negative cases, there are 100 rows for the truth and 100x5x2 = 1000 rows for the scores from 5 readers for 2 modalities. Therefore, the data frame has 1100 rows. +We again set the seed for reproducible simulations (if needed) before we simulate the data. As we see below, the simulated data starts with truth state of each case. This is followed by the reading scores from each of the readers. Since we simulate 50 positive cases and 50 negative cases, there are 100 rows for the truth and 100x5x2 = 1000 rows for the scores from 5 readers for 2 modalities. Therefore, the data frame has 1100 rows total. ```{r} # simulate MRMC study @@ -103,7 +103,7 @@ print(dFrame.gRM[(nrow(dFrame.gRM) - 5):nrow(dFrame.gRM), ]) -To combine the truth data and the reader scores and change the data to a dataframe with 5 columns (readerID, caseID, modalityID, score, truth) we can use the function undoIMRMCdf in iMRMC pacakge. +To combine the truth data and the reader scores and change the data to a dataframe with 5 columns (readerID, caseID, modalityID, score, truth) we can use the function `undoIMRMCdf` in iMRMC pacakge. ```{r} dFrame.gRM.2 <- undoIMRMCdf(dFrame.gRM) diff --git a/Rpackage/iMRMC/inst/extra/limitsOfAgreement/CompareSimulationModels.pdf b/Rpackage/iMRMC/inst/extra/limitsOfAgreement/CompareSimulationModels.pdf index b61358c95c718557bbabb238497e0b878832f1ea..2d2486e9af6cc8be4c50dc6b6f5464c5753f33ec 100644 GIT binary patch delta 6676 zcmV+v8tdia@eHc+43HxOG&DDp&Ye?Nerz8odl?DabLVv-;U0wC}MD06S+aqsOBf1*9R zJUabG#hx%s3LSWtH=dM+X(hcdjF^alwDdmtAM?#jhW@@tnrt>#T>2M_i*xFKy-u2B z_VeWjU=(>Vi$fVApSjT5GMej%1w151@3IOQ$SC%2XEO3#f0=EzW!+SkI}+AgoV}$% zvxPS1ex1*R4|14R4xGH$7fn8|vSgXTY(*`NFCI{(g9%e~@rnO_3TSI{QV9&V_EY_Md-6bjN@Jq7F7@0?#fq8JX zVX;!Qy3RN3yKS{eiuZ5XyF9CsDqZJkQcPG@r~qz80t>q}2hmiZ{REo;Wwrtnv00<` z4Gn6%#fYruHnq}&bfY75%%ln0Ba&5>Wt*&=Dd{&862VPN-3dh2MDA#R?Q%jEKf&tg>cbmDv(6i_PW%Y`H|+E2aDmIz|NEQ_%QkTVW@# zw{zd*LUCqzr_^&z&ZBncz{GH>wLi4WtWK-^+KQAdiM9rJe~J9Mhy$78VU&Q~SO~1= z5Oz`QqU5s_{9xBu9LbD-60JBN(JsRHKg}ZL!zI~4QZA`;=4M~pHuB#lMUm7eFi;U( zkmQ$ZxZF8x4#0&VxbA5EMgDu{SiJenmCDkFMz6m69=+(tnGnK%MKlaiWd5dZ@{Ns6 z%fey=_P)(Gc~et=d*k?^Q_ZJB2R#i=Xih*pLAMd|f%;0ZFp4{W^}&O3I5$Q9aQPUb zfztk2zTK@8xZiZ9g`e$V#Y{^d?$=H)EERA8nxw+tbUk(RCT3c8w*K=UCsW~Kz&kqk z5Wy55!2<9`x5S#?_`99E9KcD?RqH^w8Ofz|ceJ*)Xm<6>)6?7ATejThY+J2P1!ojD zG7!vw?M5~fJmRN+fZt)L1VksWgCFRJ@e~>X4;FLdyioT6vRZ7ji>&!$LL=WWqr&JUm?RE&S~)5Ohffn+ zzNp`a#p@QOfkk1r=%K_Y4b<+uyMqtF!vMP49Ji#w`^{>?l>(^$Nm~C|b|BwXz$@ZP4Rv z_j>_f#B zg<~J+Gn3)My)X>i9KJ9pPaz%O8c22T3+&qWg?l`}3pez?$*Z~n&oi-faZU^KGH-H! 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Definition @@ -25,13 +25,13 @@ If $j\neq j'$, the difference score $D_{jj'k}^{12}$ denotes the between-reader b \overline{D_{BR}^{12}}\pm2\sqrt{V_{BR}^{12}}. \] -To construct the WRBM and BRBM limits of agreement, we need to estimate $\overline{D_{WR}^{12}}$, $V_{WR}^{12}$, $\overline{D_{BR}^{12}}$, and $V_{BR}^{12}$. The two mean differences are easy to estimate. +To construct the WRBM and BRBM limits of agreement, we need to estimate $\overline{D_{WR}^{12}}$, $V_{WR}^{12}$, $\overline{D_{BR}^{12}}$, and $V_{BR}^{12}$. The two mean differences are easy to estimate: \[ \hat{\overline{D_{WR}^{12}}}=\frac{1}{JK}\sum_j\sum_kD_{jj,k}^{12}=\frac{1}{JK}\sum_j\sum_k(X_{1jk}-X_{2jk})=\overline{X_1..}-\overline{X_2..}, \] where sums are over all samples implied by the index unless otherwise described. Also, $\overline{X_i..}=\frac{1}{JK}\sum_j\sum_kX_{ijk}$ for $i=1,2$ denotes the average score across all the readers and cases for a single modality. Similarly, \[ -\hat{\overline{D_{BR}^{12}}}=\frac{1}{J(J-1)K}\sum_j\sum_{j\neq j'}\sum_kD_{jj'k}^{12}=\frac{1}{J(J-1)K}\sum_j\sum_{j\neq j'}\sum_k(X_{1jk}-X_{2j'k})=\overline{X_1..}-\overline{X_2..} +\hat{\overline{D_{BR}^{12}}}=\frac{1}{J(J-1)K}\sum_j\sum_{j\neq j'}\sum_kD_{jj'k}^{12}=\frac{1}{J(J-1)K}\sum_j\sum_{j\neq j'}\sum_k(X_{1jk}-X_{2j'k})=\overline{X_1..}-\overline{X_2..}. \] Therefore, $\hat{\overline{D_{WR}^{12}}}=\hat{\overline{D_{BR}^{12}}}=\overline{X_1..}-\overline{X_2..}$. The WRBM and BRBM limits of agreement will be different only by the variances $V_{WR}^{12}$ and $V_{BR}^{12}$. In the following two sections, we will discuss how to use two-way random effect ANOVA to estimate $V_{WR}^{12}$ and three-way mixed effect ANOVA to estimate $V_{BR}^{12}$. @@ -70,9 +70,9 @@ Putting it all together, the estimate of the variance of $Y_{jk}$, \hat V_{WR}^{12}=\hat Var[Y_{jk}]=\hat\sigma_R^2+\hat\sigma_C^2+\hat\sigma_\varepsilon^2=\frac{1}{JK}(J*MSR+K*MSC+(JK-J-K)*MSE) \] -The following is an example demonstrating the use of the function `laWRBM.anova` to compute the WRBM limits of agreement for simulated MRMC agreement data. The example starts by simulating MRMC agreement data with the function `sim.NormalIG.Hierarchical` and finishes by printing the output. +The following is an example demonstrating the use of the function `laWRBM` to compute the WRBM limits of agreement for simulated MRMC agreement data. The example starts by simulating MRMC agreement data with the function `sim.NormalIG.Hierarchical` and finishes by printing the output. -```{r simulation & laWRBM.anova} +```{r simulation & laWRBM} # Simulate MRMC data config <- sim.NormalIG.Hierarchical.config(modalityID = c("testA","testB")) set.seed(1) @@ -83,7 +83,7 @@ laWRBM_result <- laWRBM(data.sim) print(laWRBM_result) ``` -The output is a list of two objects. The first object in the list is a data frame with key summary statistics. In order, they are the mean difference, the variance of the mean difference, the variance of WRBM differences $\hat V_{WR}^{12}$ (1 observation), the confidence interval of the mean difference, and the limits of agreement. +The output is a list of two objects. The first object in the list is a data frame with key summary statistics. In order, the key summary statstics are the mean difference, the variance of the mean difference, the variance of WRBM differences $\hat V_{WR}^{12}$ (1 observation), the confidence interval of the mean difference, and the limits of agreement. The second object in the list is a data frame containing the typical ANOVA table. @@ -96,7 +96,8 @@ X_{ijk} = \mu+m_i+R_j+C_k+RC_{jk}+mR_{ij}+mC_{ik}+\varepsilon_{ijk}, \] where $m_i$ denotes the fixed effect for modality, $\sum_im_i=0$, and the other variables are independently normally distributed: $R_j\sim N(0,\sigma_R^2)$, $C_k\sim N(0,\sigma_C^2)$, $RC_{jk}\sim N(0,\sigma_{RC}^2)$, $mR_{ij}\sim N(0,\sigma_{mR}^2)$, $mC_{ik}\sim N(0,\sigma_{mC}^2)$, and $\varepsilon_{ijk}\sim N(0,\sigma_\varepsilon^2)$. -The mixed effect model we applied is the unrestricted mixed model. Compared to the restricted model, the interaction term of the mixed effect and random effect in the unrestricted model will not be correlated at the same random level. This makes the model easier to work with. +The mixed effect model we applied is the unrestricted mixed model. Unlike the restricted model, we do not force the sum over modalities of the modality-reader +terms to equal zero, and we do not force the sum over modalities of the modality-case terms to equal zero. This makes the model easier to work with. Under this model, the BRBM difference $D_{jj'k}^{12}$ can be expressed as \[ @@ -142,9 +143,9 @@ Putting it all together, the estimate of the variance BRBM differences is \end{aligned} \] -The following is an example demonstrating the use of the function `laBRBM.anova` to compute the BRBM limits of agreement for simulated MRMC agreement data. The example uses the previously simulated MRMC agreement data. The output is a list of the same two objects as for `laWRBM`. +The following is an example demonstrating the use of the function `laBRBM` to compute the BRBM limits of agreement for simulated MRMC agreement data. The example uses the previously simulated MRMC agreement data. The output is a list of the same two objects as for `laWRBM`. -```{r laBRBM.anova} +```{r laBRBM} # Using ANOVA to calculate BRBM limits of agreement laBRBM_result <- laBRBM(data.sim) print(laBRBM_result) @@ -161,7 +162,7 @@ Then, the variance of $Y_{jk}$ is \[ V_{WR}^{12}=Var[Y_{jk}]=2\sigma_{mR}^2+2\sigma_{mC}^2+2\sigma_\varepsilon^2. \] -Now, if we insert in the unbiased estimate of the variance components, we get the estimate of $V_{WRBM}$ +Now, if we insert the unbiased estimates of the variance components, we get the estimate of $V_{WRBM}$ \[ \hat V_{WR}^{12}=2\hat\sigma_{mR}^2+2\hat\sigma_{mC}^2+2\hat\sigma_\varepsilon^2 =\frac{2}{JK}(J*MSMR+K*MSMC+(JK-J-K)*MSE) @@ -196,7 +197,7 @@ SST_{3w}&=\sum_i\sum_j\sum_k(X_{ijk}-\overline{X_{...}})^2\\ &=\sum_i\sum_j\sum_k(X_{ijk}-\overline{X_{i..}}-\overline{X_{.jk}}+\overline{X_{...}})^2+SSM_{3w}+I\sum_j\sum_k(\overline{X_{.jk}}-\overline{X_{...}})^2 \end{aligned} \] -The last term on the right-hand-side of the fomula above can be decomposed as +The last term on the right-hand-side of the formula above can be decomposed as \[ \begin{aligned} &\ \ \ \ \ I\sum_j\sum_k(\overline{X_{.jk}}-\overline{X_{...}})^2\\ @@ -208,7 +209,7 @@ Thus, \[ \begin{aligned} SSE_{2w} &= SST_{2w}-SSR_{2w}-SSC_{2w}\\ -&=2(SST_{3w}-SSM_{3w}-SSR_{3w}-SSC_{3w}-SSRC_{3w})-2SSMR_{3w}-2SSMC_{3w}=2SSE_{3w} +&=2(SST_{3w}-SSM_{3w}-SSR_{3w}-SSC_{3w}-SSRC_{3w})-2SSMR_{3w}-2SSMC_{3w}\\&=2SSE_{3w} \end{aligned} \] diff --git a/Rpackage/iMRMC/inst/extra/limitsOfAgreement/LOA_ANOVA.pdf b/Rpackage/iMRMC/inst/extra/limitsOfAgreement/LOA_ANOVA.pdf index aff8f67da36eb2348a87992d7b91172038d3ba71..94e006db06465d3bc4302ec336b2515be2475fcd 100644 GIT binary patch delta 57629 zcmV({K+?b3lMlO<50E1RI50Su!G8lNf7M)DcN@16e)q57>C@`eL>G6ga{6E=X&N`~ z#c`ANBfV~prE+r}_d9Ve7*uh{hGx%mO%Y5=~l21N+mJj@W z`S#hL{vwMBw@h%YCU37NRx@Yq#2CkTfu8x~o9y4)#p>O~ROTXk@%MjR2$Owvf5CH| zy$F4~b@=<~cDJ~l?aJ`!i^c6?w+-#}HT~t;i+7ugDbLCa{JSkzL}?dBT(38w@%qi{ 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