The R package LW1949 automates the steps taken in Litchfield and Wilcoxon's (1949) manual approach to evaluating dose-effect experiments (Adams et al. 2016). Letting the computer do the work saves time and yields the best fit possible using the Litchfield Wilcoxon approach (by minimizing the chi-squared statistic). You can also try a brief demonstration of LW1949 in this web app.
and load the LW1949 package.
dataprep function to create a data frame with the results of a dose-effect experiment. Provide information on three key input variables,
conc <- c(0.0625, 0.125, 0.25, 0.5, 1, 2, 3) numtested <- rep(8, 7) numaffected <- c(1, 4, 4, 7, 8, 8, 8) mydat <- dataprep(dose=conc, ntot=numtested, nfx=numaffected)
dataprep function puts the input variables into a data frame along with several new variables,
fxcateg) identifying none (0), partial (50), and complete (100) effects, and
LWkeep) to identify observations to keep when applying Litchfield and Wilcoxon's (1949) method (their step A).
LWestimate functions to fit a dose-effect relation following Litchfield and Wilcoxon's (1949) method.
intslope <- fitLWauto(mydat) fLW <- LWestimate(intslope, mydat)
The output from
fitLWauto is a numeric vector of length two, the estimated intercept and slope of the best fitting line on the log10-probit scale..
The output from
LWestimate is a list with three elements,
chi, the chi-squared test comparing observed and expected effects, including the expected effects, the "corrected" expected effects (step B in Litchfield and Wilcoxon 1949), and the contribution to the chi-squared statistic (their step C);
params, the estimated intercept and slope on the log10-probit scale; and
LWest, additional estimates calculated in the process of using Litchfield and Wilcoxon's (1949) method (their steps D and E).
predlinear function and the fitted Litchfield and Wilcoxon model to estimate the effective doses for specified percent effects (with 95% confidence limits).
pctaffected <- c(25, 50, 99.9) predlinear(pctaffected, fLW)
plotDE functions to plot the raw data on the log10-probit and arithmetics scales. Observations with no or 100% affected are plotted using white filled circles (at 0.1 and 99.9% respectively in the log10-probit plot).
predLines functions to add the L-W predicted relations to both plots, with 95% horizontal confidence intervals for the predicted dose to elicit a given percent affected.
plotDELP(mydat) predLinesLP(fLW) plotDE(mydat) predLines(fLW)
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.
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