R/NI.Array.R

In binGroup: Evaluation and Experimental Design for Binomial Group Testing

# Start  NI.Array() function
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#' @title Find the optimal testing configuration for non-informative 
#' array testing without master pooling
#'
#' @description Find the optimal testing configuration (OTC) for
#' non-informative array testing without master pooling and
#' calculate the associated operating characteristics.
#'
#' @param p the probability of disease, which can be specified as an overall
#' probability of disease or a homogeneous vector of individual probabilities.
#' @param group.sz a single group size (representing the row/column size)
#' for which to calculate the operating characteristics, or a range of group
#' (row/column) sizes over which to find the OTC.
#' The details of group size specification are given under 'Details'.
#' @inheritParams OTC
#'
#' @details This function finds the OTC and computes the associated 
#' operating characteristics for non-informative array testing without 
#' master pooling. Array testing without master pooling involves 
#' amalgamating specimens in rows and columns for the first stage of testing. 
#' This function uses only square arrays, which is the way array-based group 
#' testing is carried out in most real-world applications. Operating 
#' characteristics calculated are expected number of tests, pooling sensitivity, 
#' pooling specificity, pooling positive predictive value, and pooling negative 
#' predictive value for the algorithm. See Hitt et al. (2018) at
#' \url{http://chrisbilder.com/grouptesting} or Kim et al. (2007) 
#' for additional details on the implementation of non-informative array
#' testing without master pooling.
#' 
#' The value(s) specified by \kbd{group.sz} represent the initial group 
#' (row/column) size. If a single value is provided for \kbd{group.sz}, operating
#' characteristics will be calculated and no optimization will be performed.
#' If a range of group sizes is specified, the OTC will be found over all 
#' group sizes.
#' 
#' The displayed pooling sensitivity, pooling specificity, pooling positive 
#' predictive value, and pooling negative predictive value are weighted 
#' averages of the corresponding individual accuracy measures for all 
#' individuals within the initial group for a hierarchical algorithm.
#' Expressions for these averages are provided in the Supplementary 
#' Material for Hitt et al. (2018). These expressions are based on accuracy 
#' definitions given by Altman and Bland (1994a, 1994b).
#'
#' @return A list containing:
#' \item{prob}{the probability of disease, as specified by the user.}
#' \item{Se}{the sensitivity of the diagnostic test.}
#' \item{Sp}{the specificity of the diagnostic test.}
#' \item{opt.ET, opt.MAR, opt.GR}{a list for each objective function specified 
#' by the user, containing:
#' \describe{
#' \item{OTC}{a list specifying elements of the optimal testing configuration, 
#' which include:
#' \describe{
#' \item{Array.dim}{the row/column size for the first stage of testing.}
#' \item{Array.sz}{the overall array size (the square of the row/column size).}}}
#' \item{p.mat}{the matrix of individual probabilities.}
#' \item{ET}{the expected testing expenditure for the OTC.}
#' \item{value}{the value of the objective function per individual.}
#' \item{PSe}{the overall pooling sensitivity for the algorithm.
#' Further details are given under 'Details'.}
#' \item{PSp}{the overall pooling specificity for the algorithm.
#' Further details are given under 'Details'.}
#' \item{PPPV}{the overall pooling positive predictive value for the algorithm.
#' Further details are given under 'Details'.}
#' \item{PNPV}{the overall pooling negative predictive value for the algorithm.
#' Further details are given under 'Details'.}}}
#' 
#' @author Brianna D. Hitt
#'
#' @references
#' \insertRef{Altman1994a}{binGroup}
#' 
#' \insertRef{Altman1994b}{binGroup}
#' 
#' \insertRef{Graff1972}{binGroup}
#' 
#' \insertRef{Hitt2018}{binGroup}
#' 
#' \insertRef{Kim2007}{binGroup}
#' 
#' \insertRef{Malinovsky2016}{binGroup}
#' 
#' @seealso
#' \code{\link{Inf.Array}} for informative array testing without master pooling,
#' \code{\link{NI.A2M}} for non-informative array testing with master pooling, and
#' \code{\link{OTC}} for finding the optimal testing configuration for a number
#' of standard group testing algorithms.
#'
#' \url{http://chrisbilder.com/grouptesting}
#'
#' @family OTC functions
#'
#' @examples
#' # Find the OTC for non-informative array testing 
#' #   without master pooling over a range of group
#' #   (row/column) sizes.
#' # This example takes less than 1 second to run.
#' # Estimated running time was calculated using a 
#' #   computer with 16 GB of RAM and one core of an 
#' #   Intel i7-6500U processor.
#' NI.Array(p=0.04, Se=0.95, Sp=0.95, group.sz=3:10,
#' obj.fn=c("ET", "MAR"))
#'
#' # Calculate the operating characteristics for a specified 
#' #   group (row/column) size for non-informative array 
#' #   testing without master pooling.
#' # This example takes less than 1 second to run.
#' # Estimated running time was calculated using a 
#' #   computer with 16 GB of RAM and one core of an 
#' #   Intel i7-6500U processor.
#' NI.Array(p=rep(0.01, 64), Se=0.90, Sp=0.90, group.sz=8,
#' obj.fn=c("ET", "MAR", "GR"), 
#' weights=matrix(data=c(1,1,10,10,100,100), 
#' nrow=3, ncol=2, byrow=TRUE))

# Brianna Hitt - 05-01-17
# Updated: Brianna Hitt - 06-20-18
NI.Array <- function(p, Se, Sp, group.sz, obj.fn, weights=NULL){
  
  start.time<-proc.time()
  
  set.of.I <- group.sz
  
  save.it <- matrix(data=NA, nrow=length(set.of.I), ncol=18)
  count <- 1
  
  for(I in set.of.I){
    N <- I^2
    
    # build a matrix of probabilities
    # this is the same for an overall probability p and for a vector p
    p.mat <- matrix(data=p[1], nrow=I, ncol=I)
    
    # call Array.Measures to calculate descriptive measures for the given array size
    save.info <- Array.Measures(p=p.mat, se=Se, sp=Sp)
    
    # extract accuracy measures for each individual
    ET <- save.info$T
    PSe.mat <- save.info$PSe
    PSp.mat <- save.info$PSp
    if("MAR" %in% obj.fn){
      MAR <- MAR.func(ET=ET, p.vec=p.mat, PSe.vec=PSe.mat, PSp.vec=PSp.mat)
    } else{MAR <- NA}
    
    # calculate overall accuracy measures
    PSe <- sum(p.mat*PSe.mat)/sum(p.mat)
    PSp <- sum((1-p.mat)*(PSp.mat))/sum(1-p.mat)
    PPPV <- sum(p.mat*PSe.mat)/sum(p.mat*PSe.mat + (1-p.mat)*(1-PSp.mat))
    PNPV <- sum((1-p.mat)*PSp.mat)/sum((1-p.mat)*PSp.mat + p.mat*(1-PSe.mat))
    
    # for each row in the matrix of weights, calculate the GR function
    if(is.null(dim(weights))){
      GR1 <- NA
      GR2 <- NA
      GR3 <- NA
      GR4 <- NA
      GR5 <- NA
      GR6 <- NA
    } else{
      GR1 <- GR.func(ET=ET, p.vec=p.mat, PSe.vec=PSe.mat, PSp.vec=PSp.mat, D1=weights[1,1], D2=weights[1,2])
      if(dim(weights)[1]>=2){
        GR2 <- GR.func(ET=ET, p.vec=p.mat, PSe.vec=PSe.mat, PSp.vec=PSp.mat, D1=weights[2,1], D2=weights[2,2])
      } else{GR2 <- NA}
      if(dim(weights)[1]>=3){
        GR3 <- GR.func(ET=ET, p.vec=p.mat, PSe.vec=PSe.mat, PSp.vec=PSp.mat, D1=weights[3,1], D2=weights[3,2])
      } else{GR3 <- NA}
      if(dim(weights)[1]>=4){
        GR4 <- GR.func(ET=ET, p.vec=p.mat, PSe.vec=PSe.mat, PSp.vec=PSp.mat, D1=weights[4,1], D2=weights[4,2])
      } else{GR4 <- NA}
      if(dim(weights)[1]>=5){
        GR5 <- GR.func(ET=ET, p.vec=p.mat, PSe.vec=PSe.mat, PSp.vec=PSp.mat, D1=weights[5,1], D2=weights[5,2])
      } else{GR5 <- NA}
      if(dim(weights)[1]>=6){
        GR6 <- GR.func(ET=ET, p.vec=p.mat, PSe.vec=PSe.mat, PSp.vec=PSp.mat, D1=weights[6,1], D2=weights[6,2])
      } else{GR6 <- NA}
    }
    
    save.it[count,] <- c(p[1], Se, Sp, I, N, ET, ET/N, MAR, GR1/N, GR2/N, GR3/N, GR4/N, GR5/N, GR6/N, PSe, PSp, PPPV, PNPV)
    cat("Row/Column Size=", I, ", Array Size=", N, "\n", sep="")
    count <- count + 1
    
  }
  
  # find the optimal testing configuration, over all array sizes considered
  result.ET <- save.it[save.it[,7]==min(save.it[,7]),c(1:6,7,15:ncol(save.it))]
  result.MAR <- save.it[save.it[,8]==min(save.it[,8]),c(1:6,8,15:ncol(save.it))]
  result.GR1 <- save.it[save.it[,9]==min(save.it[,9]),c(1:6,9,15:ncol(save.it))]
  result.GR2 <- save.it[save.it[,10]==min(save.it[,10]),c(1:6,10,15:ncol(save.it))]
  result.GR3 <- save.it[save.it[,11]==min(save.it[,11]),c(1:6,11,15:ncol(save.it))]
  result.GR4 <- save.it[save.it[,12]==min(save.it[,12]),c(1:6,12,15:ncol(save.it))]
  result.GR5 <- save.it[save.it[,13]==min(save.it[,13]),c(1:6,13,15:ncol(save.it))]
  result.GR6 <- save.it[save.it[,14]==min(save.it[,14]),c(1:6,14,15:ncol(save.it))]
  
  p.mat.ET <- matrix(data=result.ET[1], nrow=result.ET[4], ncol=result.ET[4])
  if("MAR" %in% obj.fn){
    p.mat.MAR <- matrix(data=result.MAR[1], nrow=result.MAR[4], ncol=result.MAR[4])
  } else{p.mat.MAR <- NA}
  if(is.null(dim(weights))){
    p.mat.GR1 <- NA
    p.mat.GR2 <- NA
    p.mat.GR3 <- NA
    p.mat.GR4 <- NA
    p.mat.GR5 <- NA
    p.mat.GR6 <- NA
  } else{
    p.mat.GR1 <- matrix(data=result.GR1[1], nrow=result.GR1[4], ncol=result.GR1[4])
    if(dim(weights)[1]>=2){
      p.mat.GR2 <- matrix(data=result.GR2[1], nrow=result.GR2[4], ncol=result.GR2[4])
    } else{p.mat.GR2 <- NA}
    if(dim(weights)[1]>=3){
      p.mat.GR3 <- matrix(data=result.GR3[1], nrow=result.GR3[4], ncol=result.GR3[4])
    } else{p.mat.GR3 <- NA}
    if(dim(weights)[1]>=4){
      p.mat.GR4 <- matrix(data=result.GR4[1], nrow=result.GR4[4], ncol=result.GR4[4])
    } else{p.mat.GR4 <- NA}
    if(dim(weights)[1]>=5){
      p.mat.GR5 <- matrix(data=result.GR5[1], nrow=result.GR5[4], ncol=result.GR5[4])
    } else{p.mat.GR5 <- NA}
    if(dim(weights)[1]>=6){
      p.mat.GR6 <- matrix(data=result.GR6[1], nrow=result.GR6[4], ncol=result.GR6[4])
    } else{p.mat.GR6 <- NA}
  }
  
  # create a list of results for each objective function
  opt.ET <- list("OTC"=list("Array.dim"=result.ET[4], "Array.sz"=result.ET[5]), "p.mat"=p.mat.ET, "ET"=result.ET[6], "value"=result.ET[7], "PSe"=result.ET[8], "PSp"=result.ET[9], "PPPV"=result.ET[10], "PNPV"=result.ET[11])
  opt.MAR <- list("OTC"=list("Array.dim"=result.MAR[4], "Array.sz"=result.MAR[5]), "p.mat"=p.mat.MAR, "ET"=result.MAR[6], "value"=result.MAR[7], "PSe"=result.MAR[8], "PSp"=result.MAR[9], "PPPV"=result.MAR[10], "PNPV"=result.MAR[11])
  opt.GR1 <- list("OTC"=list("Array.dim"=result.GR1[4], "Array.sz"=result.GR1[5]), "p.mat"=p.mat.GR1, "ET"=result.GR1[6], "value"=result.GR1[7], "PSe"=result.GR1[8], "PSp"=result.GR1[9], "PPPV"=result.GR1[10], "PNPV"=result.GR1[11])
  opt.GR2 <- list("OTC"=list("Array.dim"=result.GR2[4], "Array.sz"=result.GR2[5]), "p.mat"=p.mat.GR2, "ET"=result.GR2[6], "value"=result.GR2[7], "PSe"=result.GR2[8], "PSp"=result.GR2[9], "PPPV"=result.GR2[10], "PNPV"=result.GR2[11])
  opt.GR3 <- list("OTC"=list("Array.dim"=result.GR3[4], "Array.sz"=result.GR3[5]), "p.mat"=p.mat.GR3, "ET"=result.GR3[6], "value"=result.GR3[7], "PSe"=result.GR3[8], "PSp"=result.GR3[9], "PPPV"=result.GR3[10], "PNPV"=result.GR3[11])
  opt.GR4 <- list("OTC"=list("Array.dim"=result.GR4[4], "Array.sz"=result.GR4[5]), "p.mat"=p.mat.GR4, "ET"=result.GR4[6], "value"=result.GR4[7], "PSe"=result.GR4[8], "PSp"=result.GR4[9], "PPPV"=result.GR4[10], "PNPV"=result.GR4[11])
  opt.GR5 <- list("OTC"=list("Array.dim"=result.GR5[4], "Array.sz"=result.GR5[5]), "p.mat"=p.mat.GR5, "ET"=result.GR5[6], "value"=result.GR5[7], "PSe"=result.GR5[8], "PSp"=result.GR5[9], "PPPV"=result.GR5[10], "PNPV"=result.GR5[11])
  opt.GR6 <- list("OTC"=list("Array.dim"=result.GR6[4], "Array.sz"=result.GR6[5]), "p.mat"=p.mat.GR6, "ET"=result.GR6[6], "value"=result.GR6[7], "PSe"=result.GR6[8], "PSp"=result.GR6[9], "PPPV"=result.GR6[10], "PNPV"=result.GR6[11])
  
  # create a list of results, including all objective functions
  opt.all <- list("opt.ET"=opt.ET, "opt.MAR"=opt.MAR, "opt.GR1"=opt.GR1, "opt.GR2"=opt.GR2, 
                  "opt.GR3"=opt.GR3, "opt.GR4"=opt.GR4, "opt.GR5"=opt.GR5, "opt.GR6"=opt.GR6)
  # remove any objective functions not requested by the user
  opt.req <- Filter(function(x) !is.na(x$ET), opt.all)
  time.it(start.time)
  c("prob"=list(p), "Se"=Se, "Sp"=Sp, opt.req)
  
}

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