Introduction to LW1949

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)

Prepare data

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

##     dose ntot nfx rec   pfx  log10dose    bitpfx fxcateg LWkeep
## 1 0.0625    8   1   1 0.125 -1.2041200 -1.150349      50   TRUE
## 2 0.1250    8   4   2 0.500 -0.9030900  0.000000      50   TRUE
## 3 0.2500    8   4   3 0.500 -0.6020600  0.000000      50   TRUE
## 4 0.5000    8   7   4 0.875 -0.3010300  1.150349      50   TRUE
## 5 1.0000    8   8   5 1.000  0.0000000       Inf     100   TRUE
## 6 2.0000    8   8   6 1.000  0.3010300       Inf     100   TRUE
## 7 3.0000    8   8   7 1.000  0.4771213       Inf     100  FALSE

Fit model

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

## Intercept     Slope 
##  1.749662  2.308293

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

## $chi
## $chi$chi
##   chistat        df      pval 
## 1.0439487 4.0000000 0.9030603 
## 
## $chi$contrib
##            exp   obscorr    contrib
## [1,] 0.1515518 0.1250000 0.03721500
## [2,] 0.3688371 0.5000000 0.37314483
## [3,] 0.6405505 0.5000000 0.43966002
## [4,] 0.8542407 0.8750000 0.02365253
## [5,] 0.9599117 0.9868022 0.14430194
## [6,] 0.9927479 0.9976003 0.02597436
## 
## 
## $params
## Intercept     Slope 
##  1.749662  2.308293 
## 
## $LWest
##        ED50       lower       upper     npartfx        ED16        ED84 
##  0.17458650  0.08783511  0.34701895  4.00000000  0.06474275  0.47079321 
##           S      lowerS      upperS      Nprime       fED50          fS 
##  2.69661856  1.40677894  5.16907910 16.00000000  1.98766192  1.91687441

Predict

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)

##       pct         ED      lower      upper
## [1,] 25.0 0.08908568 0.03942532  0.2012985
## [2,] 50.0 0.17458650 0.08783511  0.3470189
## [3,] 99.9 3.80857563 0.45491114 31.8858942

Plot

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)

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.