In LW1949: An Automated Approach to Evaluating Dose-Effect Experiments Following Litchfield and Wilcoxon (1949)

Evaluation of Dose-Effect Experiments using Litchfield and Wilcoxon (1949)

This is a simple demonstration of the R package LW1949, which automates the manual approach to evaluating dose-effect experiments described by Litchfield and Wilcoxon (1949). Use of LW1949 saves time and yields the best Litchfield Wilcoxon model fit possible, by minimizing the chi-squared statistic.

You can give it a try here, by providing information on three key inputs (on the left): the chemical concentration or dose, the number tested, and the number affected. Effective doses will be estimated for the specified percentages affected (on the right).

# Shinyapps.io automatically finds this package on GitHub!
require(LW1949)

# read in the data
mydat <- reactive({
  dose <- c(input$dose1, input$dose2, input$dose3, input$dose4, input$dose5, 
    input$dose6, input$dose7, input$dose8, input$dose9, input$dose10)
  ntot <- c(input$ntot1, input$ntot2, input$ntot3, input$ntot4, input$ntot5, 
    input$ntot6, input$ntot7, input$ntot8, input$ntot9, input$ntot10)
  nfx <- c(input$nfx1, input$nfx2, input$nfx3, input$nfx4, input$nfx5, 
    input$nfx6, input$nfx7, input$nfx8, input$nfx9, input$nfx10)
  sel <- !is.na(dose) & !is.na(ntot) & !is.na(nfx)
  if (sum(sel) < 1) stop("No dose effect data entered.")
  if (any(ntot[sel] < 0)) stop("No. tested should be greater than zero.")
  if (any(ntot[sel] < nfx[sel])) 
    stop("No. affected should not be greater than No. tested.")
  dataprep(dose[sel], ntot[sel], nfx[sel])
})

# fitted LW model
fLW <- reactive({
  LWestimate(fitLWauto(mydat()), mydat())
})

# % affected
pctaffected <- reactive({
  pa <- c(input$pa1, input$pa2, input$pa3)
  sel <- !is.na(pa)
  if (sum(sel) < 1) stop("No % Affected values entered.")
  if (any(pa[sel] < 0.001) | any(pa[sel] > 99.999))
    stop("% Affected should be between 0.001 and 99.999.")
  pa[sel]
})

# predicted
predLW <- reactive({
  predlinear(pctaffected(), fLW())
})

# plot of dose vs. % affected, log scale
output$onePlot <- renderPlot(
  {
    par(mar=c(4, 4, 1, 1), cex=1.5)
    plotDELP(mydat())
    predLinesLP(fLW())
    y <- probit(predLW()[, "pct"]/100)
    arrows(log10(predLW()[, "lower"]), y, log10(predLW()[, "ED"]), y, 
      length=0.1, angle=90, code=3, col="red")
    arrows(log10(predLW()[, "ED"]), y, log10(predLW()[, "upper"]), y, 
      length=0.1, angle=90, code=3, col="red")
  }, 
  width=700, 
  height=700,
)

# plot of dose vs. % affected, arithmetic scale
output$twoPlot <- renderPlot(
  {
    par(mar=c(4, 4, 1, 1), cex=1.5)
    plotDE(mydat(), ref=NA)
    predLines(fLW())
    y <- predLW()[, "pct"]
    arrows(predLW()[, "lower"], y, predLW()[, "ED"], y, 
      length=0.1, angle=90, code=3, col="red")
    arrows(predLW()[, "ED"], y, predLW()[, "upper"], y, 
      length=0.1, angle=90, code=3, col="red")
  }, 
  width=700, 
  height=700,
)

# table of predicted 
output$oneTable <- renderTable(
  {
    predLW()
  },
  digits=c(2, 3, 3, 3, 3)
)

fluidPage(
  fluidRow(
    column(2, 
      numericInput("dose1", "Dose", value=0.0625),
      numericInput("dose2", NULL, value=0.125),
      numericInput("dose3", NULL, value=0.25),
      numericInput("dose4", NULL, value=0.5),
      numericInput("dose5", NULL, value=1.0),
      numericInput("dose6", NULL, value=NA),
      numericInput("dose7", NULL, value=NA),
      numericInput("dose8", NULL, value=NA),
      numericInput("dose9", NULL, value=NA),
      numericInput("dose10", NULL, value=NA)
    ),
    column(2, 
      numericInput("ntot1", "No. tested", value=8),
      numericInput("ntot2", NULL, value=8),
      numericInput("ntot3", NULL, value=8),
      numericInput("ntot4", NULL, value=8),
      numericInput("ntot5", NULL, value=8),
      numericInput("ntot6", NULL, value=NA),
      numericInput("ntot7", NULL, value=NA),
      numericInput("ntot8", NULL, value=NA),
      numericInput("ntot9", NULL, value=NA),
      numericInput("ntot10", NULL, value=NA)
    ),
    column(2,
      numericInput("nfx1", "No. affected", value=1),
      numericInput("nfx2", NULL, value=4),
      numericInput("nfx3", NULL, value=4),
      numericInput("nfx4", NULL, value=7),
      numericInput("nfx5", NULL, value=8),
      numericInput("nfx6", NULL, value=NA),
      numericInput("nfx7", NULL, value=NA),
      numericInput("nfx8", NULL, value=NA),
      numericInput("nfx9", NULL, value=NA),
      numericInput("nfx10", NULL, value=NA)
    ),
    column(2),
    column(2,
      numericInput("pa1", label="% Affected", value=25),
      numericInput("pa2", label=NULL, value=50),
      numericInput("pa3", label=NULL, value=99.9)
    )
  ),
  fluidRow(
    plotOutput("onePlot", inline=TRUE),
    h5("FIGURE 1. -  Plot of the observed data with the Litchfield Wilcoxon fitted model on the log10-probit scale. Predicted effective doses with 95% confidence intervals for the specified percentages affected are in red.  Observations with 0% or 100% affected are plotted at 0.1 and 99.9% respectively using white filled circles.")
  ),
  fluidRow(
    plotOutput("twoPlot", inline=TRUE),
    h5("FIGURE 2.  -  Plot of the observed data with the Litchfield Wilcoxon fitted model on the arithmetic scale. Predicted effective doses with 95% confidence intervals for the specified percentages affected are in red.  Observations with 0% or 100% affected are shown as white filled circles.")
  ),
  fluidRow(
    h5("TABLE 1.  -  Predicted effective doses (with 95% confidence intervals) for the specified percentages affected using the Litchfield Wilcoxon approach."),
    tableOutput("oneTable")
  )
)

References

Adams, J. V., K. S. Slaght, and M. A. Boogaard. 2016. An automated approach to Litchfield and Wilcoxon's evaluation of dose-effect experiments using the R package LW1949. Environmental Toxicology and Chemistry 35(12):3058-3061. DOI 10.1002/etc.3490

Litchfield, J. T. Jr. and F. Wilcoxon. 1949. A simplified method of evaluating dose-effect experiments. Journal of Pharmacology and Experimental Therapeutics 96(2):99-113.

LW1949. An automated approach (R package) to Litchfield and Wilcoxon's (1949) evaluation of dose-effect experiments. Available on Cran, with the latest development version on GitHub.

---

Last modified: 19 March 2017
Author: Jean V. Adams, USGS - Great Lakes Science Center and Great Lakes Fishery Commission

Created with: R Shiny by Rstudio

LW1949 documentation built on May 2, 2019, 6:11 a.m.