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.

Install

install.packages("LW1949")

and load the **LW1949** package.

```
library(LW1949)
```

Use the `dataprep`

function to create a data frame with the results of a dose-effect experiment. Provide information on three key input variables,

- chemical concentration (
`dose`

), - total number tested (
`ntot`

), and - number affected (
`nfx`

).

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)

The `dataprep`

function puts the input variables into a data frame along with several new variables,

- record number (
`rec`

), - proportional effects (
`pfx`

), - log10 transformed dose (
`log10dose`

), - probit transformed effects (
`bitpfx`

), - an effects category (
`fxcateg`

) identifying none (0), partial (50), and complete (100) effects, and - a column (
`LWkeep`

) to identify observations to keep when applying Litchfield and Wilcoxon's (1949) method (their step A).

mydat

Use the `fitLWauto`

and `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..

intslope

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).

fLW

Use the `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)

Use the `plotDELP`

and `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).

Use the `predLinesLP`

and `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.

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.

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