Eduard Szöcs

Data in Environmental Science and Eco(toxico-)logy

# Quantitative Ecotoxicology, Page 147, Example 4.3, LC50

This is about example 4.3 on page 147 of Quantitative Ecotoxicology. This example is about Calculations of $LC_{50}$ values. In this post I won’t reproduce the SAS-Code since I do not have any experience with SAS PROC PROBIT and I do not fully understand whats happening there.

Instead I will fit Dose-Response-Models using the drc-package to this data.

Get the data from here and read it into R:

So the data consists of number of dead animals (DEAD) from all animals (TOTAL) exposed to a concentration (CONC). First we create a new column with the proportion of dead animals:

Lets have a look at the raw data (note that I use a logarithmic scale for the x-axis):

I will use the drc-package of Christian Ritz and Jens Strebig to fit dose-response-curves to this data. The main function of this package is drm:

Here I fit a two-parameter log-logistic model to the data (see Ritz (2010) for a review of dose-response-models used in ecotoxicology):

So the usage is similar to lm() or nls() with some addtions: The fct argument defines the model that is fitted to the data here a 2-parameter log-logistic. weights specifies the sample size for each group and type = 'binomial' specifies that we have a binomial response (default is continuous for normally distributed errors).

We can compare this model with other models using the AIC (the smaller the better).

Here I compare the 2-parameter log-logistic model with a two-parameter Weibull and a 2-parameter Gompertz model.

drc has for this purpose the mselect() function that shows some diagnostics for every model:

• likelihood (the higher the better; however use this only when your models are nested)
• AIC (the lower the better)
• residual variance (the lower the better)

The LL.2-model has the lowest AIC so I will keep this. Lets see how the model looks like:

We can get the $LC_{50}$ with confidence interval from the model using the ED() function:

Code and data is available on my github-repo under file name ‘p147’.

#### References

[1] C. Ritz. “Toward a unified approach to dose-response modeling in ecotoxicology”. In: Environmental Toxicology and Chemistry 29.1 (Jan. 2010), pp. 220-229. DOI: 10.1002/etc.7. <URL: http://dx.doi.org/10.1002/etc.7>.

Written on February 25, 2013