Eduard Szöcs

Data in Environmental Science and Eco(toxico-)logy

# Quantitative Ecotoxicology, Page 178, Example 4.9, Time-to-death

This is example 4.9 on page 178 of Quantitative Ecotoxicology - time-to-death data.

Thankfully, Prof. Newman provided me the data for this example. You can get it from the github-repo (TOXICTY.csv).

The data consists of 5 columns:

• TTD : Time to death
• TANK : Tank
• PPT : NaCl Concentration
• WETWT : wet weight
• STDLGTH : Standard length

Columns 4 and 5 have 70 NA’s (no data available due to measurement error), but we won’t use these in this example. The observations with TTD = 97 are ‘survivors’, since the experiment run only 96 hours.

First we need to create a column FLAG for the status of the animal (dead/alive):

So 1 denotes alive and 2 dead.

Then we can plot the data. Each line is a tank and colors denote the NaCl concentrations.

We see a clear relationship between concentration and the survival curves. In this example we are interested in differences between the duplicates. We see that the two curves for the 11.6 g/L concentration are quite similar, while there is more divergence between tanks in the 13.2 g/L treatment.

We can test for differences using the survdiff function. With the rho argument we can specify the type of test: rho = 0 is a log-rank test and rho = 1 is equivalent to the Peto & Peto modification of the Gehan-Wilcoxon test.

First the log-rank test for each concentration:

We could also run this in a for loop (here the Wilcoxon test):

Basically we get the same results as in the book:

None of the log-rank tests is statistically significant (at the 0.05 level). The wilcoxon test for the 13.2 g/L treatment shows a p < 0.05. This is also in agreement with the plot.

The $\chi^2$ values differ slightly but share the same trend - I suspect this is due to different data used.

With this dataset we can do much more. We already saw that there might be a relationship between survival time and concentration, but more on this later (example 4.10).

Code and data are available on my github-repo under file name ‘p176’.

Written on April 6, 2013