brsr / tsk

Trimmed Spearman-Karber Method

Notice

You probably want to use the ecotoxicology package instead of this.

tsk

Trimmed Spearman-Karber Method. A simple nonparametric method to determine median effective doses (LD50, etc.) from dose-response curves. This package is based on the paper by Hamilton et al (1977, 1978).

To install, just type this in your R session:

install.packages("devtools")
install.packages("isotone")
devtools::install_github(repo="brsr/tsk")

The package contains one function, tsk. Type ?tsk in your R terminal for detailed help on the function. An example:

> tsk( c(1, 10, 100, 1000), 20, c(0, 3, 17, 20) )
$use.log.doses
calculations done using the logs of the doses? 
                                          TRUE 
$trim
[1] 0
$was.smoothed
[1] FALSE
$LD50
[1] 31.62278
$gsd
geometric standard deviation of LD50 estimate 
                                     1.296928 
$conf.int
[1] 18.99717 52.63942
attr(,"conf.level")
[1] 0.95

This code was written several years ago. It runs and produces valid results, but may not be written in a contemporary R idiom.

This package was formerly located at https://r-forge.r-project.org/projects/tskarber/ . The R-forge project is being kept around to direct any existing users here. Any future updates will happen on Github.

Citations

Hamilton, M. A.; Russo, R. C.; Thurston, R. V. Trimmed Spearman-Karber Method for Estimating Median Lethal Concentrations in Toxicity Bioassays. Enviro. Sci. Tech. 1977, 11 (7), 714-719. http://dx.doi.org/10.1021/es60130a004

Ibid, 1978, 12 (4), 417. http://dx.doi.org/10.1021/es60140a017

tsk's Issues

Is it possible to perform Abbott's correction before smooth the data using the PAVA algorithm?

Dear Brenton,

I got two questions here:

First of all, in tsk::tsk(), you smooth the data (of course only when the data do not show monotonically increasing trend) before doing the Abbott's correction of the control response (when control response is not 0). Shouldn't the Abbott's correction be done before smoothing?

In tsk::tsk(), smoothing using gpava() will sometimes result in a smoothed control p different from the original control p.

# Correct for the control dose.
  data.smoothed$p <- (data.smoothed$p-control)/(1-control)

Then you correct the smoothed data with the original control p based on Abbott's formula. It will not normalize the smoothed corrected control p to 0, likely leading to biases in the results.

Secondly, in the ecotoxicology::TSK(), after Abbott's correction, sample size (n) for all groups is also corrected to n_i_-r[1], where ni is the sample size of each test group, r[1] is the number of original control response. I am not sure if it is correct to do this sample size correction, but would like to hear your opinion. Thank you very much!

n vs n-1 in variance estimation

Received by e-mail in February from Dr. Jerry Lewis:

Variance of m is calculated by noting that within each dose, the number of responders, X, is distributed binomial(n,P), where P is a monotonic function of dose. But, as noted in all editions of Finney (Statistical Method in Biological Assay), while p = X/n is unbiased for P, E[ p_(1-p)/n ] < P_(1-P)/n. You need p_(1-p)/(n-1) for unbiased estimation of P_(1-P)/n, which Finney used in his worked Karber example (omitted from 3rd ed). Without this modification, the Karber intervals seem too narrow when compared to the 50% horizontal slice through intervals from generalized linear models.

The original goal of this package was to replicate a program that used $n$ in the variance estimate, so that's what the current state is. It would be reasonable to add an option to use $n-1$ instead, but I can't determine what needs to be changed in the variance calculation from Dr Lewis's email alone, since there are multiple different $n$s that appear.

Different CIs compared to those in the [correction](http://pubs.acs.org/doi/abs/10.1021/es60140a017)

According to the correction, the 0,5,10,20% trimmed TSK CI for dataset 1c in Table II is (39.14, 44.49), (39.86, 45.38), (39.51, 46.34) and (40.77, 45.17). However, the tsk package give results as following, (39.19, 44.44), (39.91, 45.32), (39.57, 46.26), and (40.81, 45.12). They are all very close but not identical or with negligible differences. Is there an explanation for this?